A financial system risk stability fusion early warning method and system

Abstract

The application discloses a financial system risk stability fusion early warning method and system, from the perspective of a nonlinear dynamic system, by phase space reconstruction on a financial time series, three types of stability indexes are extracted: a first index (maximum Lyapunov index) representing orbit divergence rate, a second index (Lyapunov function growth rate) representing system energy drift, and a third index (false neighbor ratio drift) representing phase space structure change. Further, dynamic weights are used to fuse the three types of indexes into a unified stability risk index (USRI), and an adaptive threshold is set according to the distribution quantile of a training period, and a confirmation window mechanism is combined to realize four-level graded early warning. The application changes the financial risk analysis from a statistical fluctuation paradigm to a dynamic stability paradigm, can quantitatively represent the distance of the system from the instability boundary, does not need to rely on a risk exposure matrix, verifies the forward-looking early warning effect in multiple types of crisis scenarios, and has good interpretability and industrial applicability.

Description

Technical Field

[0001] This invention relates to the field of financial risk management technology, and in particular to a method and system for early warning of systemic financial risk stability. Background Technology

[0002] Existing financial systemic risk measurement techniques can be broadly categorized into four types. The first type is risk measurement based on statistical distributions, including Value at Risk (VaR), Expected Shortfall (ES / CoVaR), GARCH volatility models, and their coherence risk measures. These methods characterize tail risk based on the statistical moments of historical return distributions. The second type is stress testing and scenario analysis methods, including inverse stress testing, sensitivity analysis, and Monte Carlo simulations. The third type is risk models based on network contagion, including interbank exposure matrix networks and cascading default models. The fourth type is empirical early warning methods based on market indicators, including single-indicator or composite indicator methods such as CDS spreads, TED spreads, and the volatility index (VIX).

[0003] The common inherent drawback of the aforementioned methods is that they can only analyze volatility (second moment), not stability (dynamic divergence). Specifically: First, VaR and GARCH family models are based on the assumptions of stationarity and near-normal distribution of return sequences. Essentially, they model the second moment (volatility) of the return distribution, systematically underestimating tail risk in scenarios of regime shift, structural breakpoints, and heavy-tailed distributions, and failing to answer the fundamental question of "how far is the system from the instability boundary?". Second, network contagion models rely on a complete two-sided risk exposure matrix, which in reality is highly opaque due to off-exchange trading, off-balance-sheet activities, and information asymmetry. Maximum entropy filling introduces uncontrollable errors. Third, stress testing relies on pre-set scenarios, essentially a retrospective and conditional method, making it difficult to provide forward-looking quantification for "unknown unknowns" that have not yet occurred. Fourth, while empirical indicators such as VIX and TED spreads are market-sensitive, they lack a theoretical connection to the stability of dynamical systems and cannot quantitatively characterize the rate of divergence from equilibrium.

[0004] In summary, the fundamental flaw of existing technologies lies in the lack of a "stability boundary" concept derived from dynamical systems theory. This prevents the quantitative characterization of the system's distance from the instability boundary before risks become apparent, and also results in insufficient sensitivity to nonlinear coupling, phase transitions, and institutional shifts. The microstructure of financial markets is essentially a high-dimensional nonlinear dynamical system, with its price series being a projection of this system onto the observation dimension. When the system transitions from a stable to an unstable region, neighboring trajectories in phase space diverge at an exponential rate. Therefore, it is necessary to shift from a volatility analysis paradigm to a dynamical stability analysis paradigm, using stability indicators to quantitatively characterize the system's instability trend. Summary of the Invention

[0005] The technical problem to be solved by the embodiments of the present invention is to provide a financial system risk stability fusion early warning method and system to solve the problem of financial market system stability evaluation. That is, without relying on the complete risk exposure matrix, by performing dynamic stability analysis on financial time series, the distance of the system from the instability boundary can be quantitatively characterized, thereby realizing a forward-looking, quantitative, and multi-level early warning of systemic risk.

[0006] To address the aforementioned technical problems, embodiments of the present invention provide a financial systemic risk stability fusion early warning method, comprising the following steps: Step S1: Obtain the financial time series and preprocess the time series to obtain the observation series; Step S2: Perform stability analysis on the observation sequence to obtain a first stability index, a second stability index, and a third stability index characterizing the dynamic characteristics of the system. Step S3: The first stability index, the second stability index, and the third stability index are uniformly represented as a single risk quantity, and a unified stability risk index is formed. Step S4: Output a graded early warning signal based on the unified stability risk index; Step S3 includes the following sub-steps: Step S31: Calculate the mean and standard deviation of the first stability index, the second stability index and the third stability index on the training period prefix, and perform z-score standardization on each; Step S32: Apply logistic normalization to each standardized index and map it to the (0, 1) interval; Step S33: The three normalized indicators are merged according to their weights into the unified stability risk index.

[0007] Furthermore, the preprocessing in step S1 includes the following sub-steps in sequence: Step S11, missing value imputation, using forward filling or linear interpolation to complete the missing values ​​in the sequence; Step S12, outlier removal: outliers are identified and removed using the three-standard-deviation criterion or the interquartile range criterion. The removed outliers are then filled in using the missing value imputation method. Step S12, frequency domain alignment, resample sequences with different sampling frequencies to the same frequency; Step S12, normalization processing: z-score standardization is performed on each source sequence to make the mean of each sequence 0 and the standard deviation 1, thus eliminating the difference in dimensions. Step S13, Multi-source fusion: When it is necessary to perform cross-asset or cross-market fusion monitoring on multi-source financial time series, the standardized multi-source series are fused into a single scalar observable by principal component analysis to obtain the first principal component, or by equal weight or inverse variance weighted average, and then the scalar observable is used as the observation series for stability analysis.

[0008] Further, step S2 includes the following steps: By reconstructing the phase space of the observation sequence, the one-dimensional scalar projection is restored to a high-dimensional phase space trajectory. The phase space reconstruction is achieved using a time-delay embedding method, including the following steps: Step S211, determine the delay time The delay time The average mutual information function of the observed sequence is determined by the first local minimum value of the average mutual information function, which is:

[0009] in, To estimate the number of boxes using mutual information, for Falling into Column and number The joint probability of a row-joint histogram. and These are the marginal probabilities, Measured and The strength of the nonlinear dependency between them, and the delay time Pick about The value corresponding to the first local minimum; Step S212: Determine the embedding dimension m, which is determined by the false nearest neighbor method, taking the minimum dimension when the proportion of false nearest neighbors first drops below a preset threshold; Step S213, construct the embedding vector to determine the... With m, construct an m-dimensional delay embedding vector for the observed sequence: ,in, Let be the observation value on the t-th trading day. To reconstruct the t-th point in the phase space, all embedded vectors form the reconstructed phase space trajectory matrix. ,in M represents the number of reconstructed phase space points, and N represents the length of the observation sequence (i.e., the total number of trading days).

[0010] Further, in step S2, the first stability index is the maximum Lyapunov exponent. By tracking the distance change of the nearest neighbor pairs in the reconstructed phase space with the number of evolution steps, the average logarithmic divergence curve is obtained. Linear fitting is performed in the linear scaling region of the curve, and the resulting slope is the first stability index. The second stability index is the drift growth rate of the Lyapunov function, which measures the trend of stress energy change in the system by constructing a quadratic Lyapunov function. The third stability index is the dynamic drift of the false nearest neighbor ratio over time under a fixed embedding dimension. The false nearest neighbor ratio under a fixed embedding dimension is calculated in each window by sliding a window along the time axis to obtain the rolling false nearest neighbor ratio value, which is used to characterize the change in the stability of the phase space structure.

[0011] Further, in step S2, the calculation step of the first stability index includes: Step S221, for each reference point in the reconstructed phase space ( Search for its nearest neighbor in the kd-tree. Record the initial distance ; Step S222: For each reference point, track its time with its nearest neighbor. Separation distance after step: , in, For the number of evolutionary steps, For the maximum number of evolutionary steps, For reference point Its nearest neighbor is The Euclidean distance of the step; Step S223: Take the sample average of the logarithmic distances for all valid reference points:

[0012] in, For at any time There is still a set of reference points that can be effectively tracked. Let its number of elements be , For the first The mean logarithmic divergence of the steps; Step S224, in about Identify linear scaling regions on the curve and traverse all possible intervals. Perform least squares linear regression on each interval and select the coefficient of determination for the fit. The highest interval is used as the scaling region. Linear fitting is performed within the scaling region, and the slope is calculated:

[0013] in, The sampling period is For automatically detected linear scaling regions, This represents the slope of the linear regression.

[0014] Furthermore, in step S4, the graded early warning adopts an adaptive threshold and confirmation window mechanism. The adaptive threshold is determined based on the distribution quantile of the unified stability risk index during the training period, including the following steps: Step S41: Collect all uniform stability risk index values ​​during the training period and calculate their multiple quantiles as warning thresholds at each level; Step S42: Map the unified stability risk index value of each step to a discrete early warning level; Step S43: Using a confirmation window mechanism, the warning level will be upgraded to the level corresponding to the threshold only if the original warning level continuously meets the corresponding threshold condition for h consecutive cycles.

[0015] Accordingly, embodiments of the present invention also provide a financial systemic risk stability fusion early warning system, including: The data acquisition module is used to acquire financial time series data, perform preprocessing, and output the observation series. The stability analysis module, connected to the data acquisition module, is used to analyze the observation sequence and output a first stability index, a second stability index, and a third stability index. The risk fusion module, connected to the stability analysis module, is used to normalize the three types of stability indicators and then fuse them into a unified stability risk index according to their weights. The graded early warning module is connected to the risk fusion module and is used to output graded early warning signals based on the unified stability risk index.

[0016] Furthermore, it also includes a backtesting calibration module, which is connected to the graded early warning module, and is used to backtest the early warning signal based on historical risk events, and accordingly adaptively calibrate the weight and graded threshold.

[0017] Furthermore, the weights are dynamic weights, adaptively determined based on the statistical discriminancy of the three stability indices during the training period. The discriminancy is measured by the variance of the normalized sequence of each index during the training period. The dynamic weight calculation formula is as follows:

[0018] in, Let be the variance of the i-th type of normalized index during the training period. is the lower bound of the weights. Here, j is the index of the summation of the indicator categories, and j = 1, 2, 3 correspond to the first stability indicator (MLE), the second stability indicator (gV), and the third stability indicator (FNN), respectively.

[0019] Accordingly, embodiments of the present invention also provide a computer-readable storage medium storing a computer program thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of the above-described financial systemic risk stability fusion early warning method.

[0020] Implementing the embodiments of the present invention has the following beneficial effects: (1) Shifting from volatility analysis to stability analysis fills the gap in the stability evaluation paradigm. Existing methods can only analyze volatility (second moment). This invention introduces dynamic stability indicators into financial risk early warning for the first time, quantitatively characterizing the distance of the system from the instability boundary, fundamentally making up for the lack of stability evaluation in the existing paradigm.

[0021] (2) Unified integration of three types of stability information enhances the comprehensiveness of instability identification. This invention, for the first time, integrates the first stability index characterizing the divergence rate of the trajectory, the second stability index characterizing the drift of stable energy, and the third stability index characterizing the stability of the phase space structure into a unified stability risk index. The three types of indicators characterize system instability from three complementary dimensions: trajectory, energy, and structure. After integration, it can capture the instability trend more comprehensively than any single indicator. Verified by real A-share data, the three types of indicators are complementary (each leading in different crisis types). After integration, if any single indicator misses a report, the other indicators can make up for it. The three types of crises maintain a 3 / 3 hit rate with no catastrophic missed reports, achieving the synergistic robustness of "1+1+1>3"—the overall early warning robustness is better than any single indicator.

[0022] (3) Dynamic weights and adaptive thresholds adapt to different market environments, improving the robustness of early warning. The weights are adaptively determined based on the discriminative power of each indicator during the training period, and the thresholds are determined based on the distribution quantiles of the unified stability risk index during the training period. Both are automatically calibrated with the market environment rather than being fixed, so that the present invention can maintain stable early warning performance in different markets and different sample periods.

[0023] (4) Early identification of system instability trends improves the timeliness of risk warnings and reduces misjudgments. This invention can identify system instability trends in advance and issue warnings before risks become apparent, thus improving the timeliness of risk warnings; it also suppresses false alarms of single spike jitters through the confirmation window mechanism, thereby reducing misjudgments.

[0024] (5) Low model dependency, no need for complete risk exposure matrix. This method only uses publicly available price and interest rate time series as input, does not rely on opaque information such as interbank bilateral exposure matrix, avoids the uncontrollable error introduced by maximum entropy filling in network contagion model, and the data availability and reproducibility are significantly better than network-based methods.

[0025] (6) Provide an interpretable measure of stable energy. The stable energy function constructed by the second stability index has a clear physical meaning of the dynamic system. Its drift, together with the first stability index, constitutes a dual characterization of the distance of the system from the instability boundary. Compared with the black box machine learning risk model, it has a significant advantage in interpretability, which facilitates regulatory attribution and liability determination.

[0026] (7) Supports multi-asset and multi-market integrated monitoring. By integrating multi-source sequences into a single scalar observable through principal component analysis or weighted average, and then analyzing the data, it is possible to simultaneously monitor the systemic risk contagion and resonance across markets and asset classes, thus avoiding the one-sidedness of single-market indicators.

[0027] (8) The algorithm is highly parallelizable and suitable for real-time and near-real-time deployment. The index calculations at each reference point are independent of each other and can be executed in high parallel on GPUs or distributed clusters, meeting the latency requirements of high-frequency monitoring scenarios. Attached Figure Description

[0028] Figure 1 This is an overall flowchart of the method of the present invention; Figure 2 This is a schematic diagram of phase space reconstruction of the present invention; Figure 3 This is a schematic diagram of the maximum Lyapunov exponent scaling region curve of the present invention; Figure 4 This is a schematic diagram of the time series of the Unified Stability Risk Index (USRI) and multi-level early warning signals described in this invention; Figure 5 This is a schematic diagram of the backtesting confusion matrix of the present invention; Figure 6 This is a schematic diagram of the overall architecture of the system of the present invention; Figure 7 This is a schematic diagram of the system state transition of the stability fusion analysis framework described in this invention; Figure 8 This is a schematic diagram of the module interface of the stability fusion analysis framework described in this invention; Figure 9 This is a table of default parameters for each embodiment of the present invention; Figure 10 This is the output mapping table for the four-level warning level; Figure 11 This is a summary table of verification metrics for the three embodiments; Figure 12 This is a data table regarding individual early warnings for each indicator in a single-indicator experiment; Figure 13 This is a data table about removing one type of index from the fusion USRI in ablation experiments. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0030] The first aspect of this invention provides a method for integrated early warning of systemic financial risk stability, implemented through the following steps, such as... Figure 1 As shown.

[0031] Step S1, Data Acquisition and Preprocessing. Acquire the financial time series and preprocess it to obtain the observation series.

[0032] The financial time series can be derived from multiple sources, including securities market indices, interbank market interest rates, foreign exchange rates, commodity prices, CDS spreads, and market liquidity indicators.

[0033] The above preprocessing includes the following sub-steps in sequence: Step S11, missing value imputation. Missing values ​​in each source sequence are filled using forward imputation (filling with the most recent valid value) or linear interpolation to ensure the sequence is continuous and uninterrupted on the time axis. For multi-source data with asynchronous market opening days (such as the foreign exchange market and the A-share market), the data is aligned with the trading calendar, and non-common trading days are filled with the value of the previous common trading day.

[0034] Step S12, outlier removal. The three-standard-deviation criterion is used. Outliers are identified and removed using either the interquartile range (IQR) criterion or the interquartile range criterion, and the removed outliers are then imputed using missing value imputation methods. Specifically, for sequences... Calculate the mean with standard deviation ,like If it is an outlier, it will be replaced with an interpolated value.

[0035] Step S13, frequency domain alignment. Resample sequences with different sampling frequencies (e.g., daily frequency vs. weekly frequency) to the same frequency (default daily frequency), using either the last value sampling method (taking the last observation of each period) or the mean sampling method (taking the mean of each period) to give all sequences a unified timestamp.

[0036] Step S14, normalization. Perform z-score normalization on each source sequence:

[0037] Among them, s t For the original observation value on the t-th trading day, Let σ be the sequence mean. s The standard deviation of the sequence. t These are the standardized observations.

[0038] To eliminate dimensional differences, the mean and standard deviation of each series are set to 0. When the input is a price series, it is first converted to logarithmic returns.

[0039] Re-standardize.

[0040] Where, r k Let p be the logarithmic return on the k-th trading day. k Let p be the closing price on the k-th trading day. (k-1) The closing price of the previous trading day.

[0041] Step S15, Multi-source fusion (optional). When it is necessary to perform cross-asset and cross-market fusion monitoring of multi-source financial time series, the standardized multi-source series are fused into a single scalar observable by principal component analysis (PCA) to obtain the first principal component, or by equal weight / inverse variance weighted average, and then the scalar observable is used as the observed series for stability analysis. Specifically, let the multi-source standardized series form a matrix. ( (for the source number), for Perform singular value decomposition Take the first principal component As a scalar observation sequence after fusion.

[0042] Where N is the length of the observed sequence (i.e., the total number of trading days), and d is the number of sources in the multi-source sequence.

[0043] After the above preprocessing, a standard observation sequence with a unified timestamp is obtained. ,in For the first scalar observations for a single trading day. The length of the observation sequence.

[0044] Step S2, stability analysis.

[0045] Stability analysis was performed on the observed sequence to obtain the first stability index, the second stability index, and the third stability index characterizing the dynamic characteristics of the system.

[0046] Step S2 is implemented through the following sub-steps: Step S21, phase space reconstruction.

[0047] Since the financial system is a high-dimensional nonlinear dynamical system, and only its one-dimensional scalar projection can be observed in practice, it is necessary to reconstruct the one-dimensional observation sequence into a high-dimensional phase space trajectory through phase space reconstruction in order to calculate the dynamic invariants in the reconstructed phase space. Phase space reconstruction is achieved using the time-delay embedding method, combined with... Figure 2 As shown, the specific steps include: Step S211, determine the delay time .

[0048] Delay time It is determined by the first local minimum of the average mutual information (AMI) function of the observed sequence.

[0049] The average mutual information is defined as:

[0050] in, Estimate the number of bins for mutual information (default 64). for Falling into Column and number The joint probability of a row-joint histogram. and These are the marginal probabilities. Measured and The nonlinear dependence strength between them (unit: bits).

[0051] Delay time Pick about The value corresponding to the first local minimum – this choice strikes a balance between “coordinate independence” and “preservation of dynamic information”, minimizing redundancy between reconstructed coordinates. The scanning range is (default (One trading day).

[0052] Step S212, determine the embedding dimension .

[0053] Embedded Dimension It is determined by the False Nearest Neighbors (FNN) method. The principle is: when the embedding dimension is insufficient, the phase space is "projected," and points that are originally far apart are squeezed into "false neighbors"; when... When the size is large enough, false nearest neighbors disappear. Specifically, for 3D embedding vector Let its nearest neighbor be Both The Euclidean distance is When ascending to a higher dimension When the dimension is 1, the newly added coordinate components are: Define the ratio:

[0054] like (default If a point is a false nearest neighbor, then that neighbor is a false nearest neighbor. The proportion of false nearest neighbors... This represents the proportion of false nearest neighbors to the total number of neighbors. (Embedding dimension) Pick The smallest dimension that first falls below the preset threshold (default 5%). The candidate range is (default ).

[0055] Among them, R tol The relative tolerance threshold for false nearest neighbor detection (default 15), m max A is the upper limit of the candidate embedding dimension (default 8). tol This is the absolute tolerance threshold (default 2).

[0056] Step S213: Construct the embedding vector.

[0057] In a definite and For the observation sequence structure 3D delayed embedding vector:

[0058] in, For the first Observations over a single trading day (e.g., logarithmic returns). To delay time, For embedded dimensions, To reconstruct the first phase space Each point. All embedded vectors constitute the reconstructed phase space trajectory matrix. ,in To reconstruct the number of points in phase space.

[0059] The phase space nearest neighbor search is accelerated using a kd-tree data structure, and a Theiler temporal isolation window (window width set by default) is used. (Or the average period of the sequence) excludes points that are temporally close to the reference point to avoid misjudging time correlation as spatial proximity.

[0060] Step S22, the first stability indicator—the maximum Lyapunov index (MLE).

[0061] Combination Figure 2 As shown, the first stability index is the maximum Lyapunov exponent. By tracking the distance between nearest neighbor pairs in the reconstructed phase space as the number of evolution steps, the average logarithmic divergence curve is obtained. Linear fitting is then performed within the linear scaling region of this curve, and the resulting slope is the index. The specific calculation steps are as follows: Step S221, nearest neighbor search.

[0062] For each reference point in the reconstructed phase space ( Search for its nearest neighbor in the kd-tree. (Theiler window excludes time neighbors), record the initial distance. .

[0063] Step S222, trajectory tracking and divergence measurement.

[0064] For each reference point, track its time with its nearest neighbor. Separation distance after step:

[0065] in, Evolutionary steps (unit: trading days) Maximum number of evolutionary steps (default) ), For reference point Its nearest neighbor is The Euclidean distance of the steps. Assume exponential divergence. Taking the logarithm, we get .

[0066] Step S223, logarithmic divergence curve.

[0067] Take the sample average of the logarithmic distances to all valid reference points:

[0068] in, For at any time There is still a set of reference points that can be effectively tracked. Let its number of elements be , For the first The average logarithmic divergence of the steps. Due to Approximate constant, Approximately .

[0069] Step S224, linear scaling region fitting.

[0070] exist about Identify the scaling region on the curve, i.e. Intervals that approximate straight lines. The automatic scaling region identification method is: traverse all possible intervals. Perform least squares linear regression on each interval and select the coefficient of determination for the fit. The highest interval is designated as the scaling region. A linear fit is performed within this scaling region, and the slope is the MLE estimate.

[0071] in, Sampling period (daily frequency) (Trading day) For automatically detected linear scaling regions, This represents the slope of the linear regression. This index quantitatively characterizes the rate of trajectory divergence. The system is characterized to enter a chaotic divergent state (risk phase region). Characterize the stability of the system (stable phase region). Characterizes critical edge states.

[0072] Step S23, the second stability index—the drift growth rate gV of the Lyapunov function.

[0073] The second stability metric is the drift growth rate of the Lyapunov function. The trend of stress energy variation is measured by constructing a quadratic Lyapunov function system. The specific calculation steps are as follows: Step S231, local Jacobian matrix estimation.

[0074] Reconstructing phase space trajectories With sliding window (window length) (Default 15) Regarding state transition relationships Local least squares estimation is performed to obtain the local Jacobian matrix at each step. Specifically, in the context of Within the central window, the independent variable matrix With the dependent variable matrix Perform ordinary least squares regression ,in , .

[0075] Among them, X cur The independent variable matrix is ​​composed of phase space points within the window; X next The dependent variable matrix is ​​composed of the corresponding next-step phase space points; X cur The transpose is denoted as ; The lower bound of the window; The upper bound of the window; Estimate the sliding window length for Jacobi (default 15); Let M be the local Jacobian matrix at step t (m×m dimensional); M is the number of points in the reconstructed phase space, and m is the embedding dimension.

[0076] Step S232, solve for the common Lyapunov matrix P. This is done using the mean of all Jacobian matrices during the training period. As a representative ( (For the training period length, see the definition of training period in step S3), solve the discrete Lyapunov equations:

[0077] in, The average Jacobian matrix during the training period ( ), The public Lyapunov matrix to be found is ( (symmetric positive definite) Given a positive definite matrix (the identity matrix is ​​taken by default). In the formula express transpose multiplied by Multiply by .like Non-Shull stability (i.e., spectral radius) ), then first Damping is Then solve it again to ensure It is positive definite and finite. The solution method is a direct method (such as the Bartels-Stewart algorithm).

[0078] Step S233: Calculate the stress energy V and the drift dV.

[0079] With fixed and time-varying Calculate the stress energy and its drift at each step:

[0080]

[0081] in, For the first Stress energy of step (scalar) ), For the first The phase space state vector of the step ( dimension), For the drift matrix ( In the formula Representing vectors transpose, express transpose multiplied by Multiply by . This indicates an increase in stress energy (system deterioration). This indicates a reduction in stress energy (system self-healing).

[0082] Step S234, drift growth rate gV.

[0083] The relative rate of change of drift is taken as the second stability index:

[0084] in, For the first The drift growth rate of the step (dimensionless scalar). and The first Step and the first The amount of drift in a step, For numerically stable small constants (default) ( ), to prevent the denominator from being zero. The shift from negative to positive indicates that stress energy changes from "decreasing / slowly increasing" to "accelerated accumulation," which is a precursor signal of instability acceleration. This index quantitatively characterizes the drift trend of stable energy.

[0085] Step S24, the third stability metric—False Nearest Neighbor Ratio (FNN).

[0086] The third stability metric is the spurious nearest neighbor ratio at a fixed embedding dimension. The dynamic drift over time is used to characterize the change in phase space structure stability. The specific calculation method is as follows: using a sliding window... (Default 120 trading days) Scroll along the time axis, and calculate the fixed dimension within each window using the FNN method described in step S21. The spurious nearest neighbor ratio is used to obtain the first... The rolling FNN value of the step . An increase in the stability index indicates that the phase space structure is collapsing or distorting, and the system complexity undergoes a step change, often corresponding to a phase transition (such as the collapse of a low-dimensional stable attractor into a high-dimensional chaotic attractor). This index quantitatively characterizes the dynamic changes in the stability of the phase space structure.

[0087] Step S3, stability fusion.

[0088] Combination Figure 3As shown, the first, second, and third stability indices are uniformly represented as a single risk quantity, namely the Unified Stability Risk Index (USRI)—a unified stability risk representation that maps the instability information of the three dimensions of local trajectory divergence, system energy drift, and phase space structure changes to a unified value. The single risk level within the range.

[0089] Specifically, it is implemented through the following steps: Step S31, standardization.

[0090] Calculate the mean of the three stability indices on the training period prefix. with standard deviation ( (corresponding to MLE, gV, and FNN respectively), and z-score normalization is performed:

[0091] in, For the first Class stability index in the first The original value of the step ( For MLE, For drift growth rate, (for spurious nearest neighbor ratios) and The first The mean and standard deviation of the class indicator during the training period. For the first Class indicators in the first Standardization is a measure of the steps. Standardization makes the mean of each indicator 0 and the standard deviation 1, thus eliminating dimensional differences.

[0092] Step S32, logistic normalization. Apply logistic (sigmoid) normalization to the standardized quantity, mapping it to... :

[0093] in, For the sigmoid function, For standardized quantities, For the first Class indicators in the first Normalized value of the step. After normalization, the normal period (Due to the standardization of the training period mean) , The further it deviates from the normal range, the closer it is to 0 or 1; the larger the value, the more dangerous it is.

[0094] Step S33, weighted fusion.

[0095] The three types of normalized indicators are merged into a unified stability risk index according to their weights:

[0096] in, For the first The unified stability risk index of the step, with a value range of 100%. ; The combined weights of the three types of indicators, For MLE weights, For gV weights, These are the weights of the FNN, and their values ​​range from [value range missing]. , ; For the first Class indicators in the first The sigmoid normalized value of the step, with a range of values ​​of 1. ; For the first Class indicators in the first The standardized quantity of the step, with a value range of 1000. , This is a discrete-time index (trading day), with a value range of [value range missing]. .

[0097] Unified Stability Risk Index This is a unified measure of the distance between the system and the instability boundary; the larger the value, the higher the risk.

[0098] In a preferred embodiment of the present invention, the weights are dynamic weights, adaptively determined based on the statistical discriminancy of the three types of stability indicators during the training period. Specifically, the discriminancy is measured by the variance of the normalized sequence of each indicator during the training period—the larger the variance, the more drastic the fluctuation of the indicator during the training period, and the stronger its ability to distinguish between normal and dangerous states, thus requiring a higher weight. The dynamic weight calculation formula is as follows:

[0099] in, For the first The variance of the normalized index during the training period. This sets the lower limit for the weights (default 0.1) to prevent a single metric from being completely overwhelmed and degraded. The numerator is calculated from the variance. The larger value, with the denominator being the sum of the corresponding values ​​of the three categories of indicators, ensures... This mechanism automatically adjusts the contribution of each indicator under different market environments and sample periods: when an indicator has low discriminative power (small variance) in a certain market, its weight is automatically limited to avoid low-quality indicators dragging down the integration.

[0100] Step S4: Tiered early warning.

[0101] Combination Figure 5 As shown, a graded early warning signal is output based on the unified stability risk index. In a preferred embodiment of the present invention, the graded early warning adopts an adaptive threshold and confirmation window mechanism, specifically including the following sub-steps: Step S41, adaptive threshold determination.

[0102] The adaptive threshold is determined based on the distribution quantile of the Uniform Stability Risk Index (USRI) during the training period. Specifically, all USRI values ​​are collected during the training period. Calculate its four quantiles as the four thresholds for green / yellow / orange / red:

[0103] in, For the first percentile function This is the set of all USRI values ​​during the training period, with the four quantiles set by default. (Green warning line) (Yellow police line) (Orange alert line) (Red Alert Line). This mechanism adaptively calibrates the warning level according to the overall risk level of the market environment: the threshold automatically moves up when the overall USRI is high in a bull market and automatically moves down when the threshold is low in a bear market, rather than using a fixed threshold.

[0104] Step S42, mapping of four-level early warning levels.

[0105] Combination Figure 6 As shown, the USRI value at each step is mapped to a discrete warning level:

[0106] in, The adaptive threshold determined in step S41, For the first The initial warning level (0–4 integers) is set. If adjacent quantiles are equal, resulting in a non-strictly increasing threshold, then the latter is increased. Forced increment.

[0107] Step S43, confirm the window mechanism.

[0108] To suppress false alarms caused by single spikes, a confirmation window mechanism is adopted: confirmation windows are only issued when the original warning level is within a certain range. One cycle (default) The warning level will be upgraded to the level corresponding to the threshold only if the corresponding threshold condition is met continuously within a certain number of trading days. The confirmation level is the minimum value of the original levels within the confirmation window (conservative strategy).

[0109] in, To confirm the window length (default 3). For the first The initial warning level of the step, For the first The final confirmation of the alert level is then determined. This mechanism ensures that the alert level is only upgraded if the USRI remains consistently above the threshold throughout the entire window, thus "diluting" daily spikes and effectively reducing the false alarm rate.

[0110] A second aspect of the present invention provides a financial systemic risk stability fusion early warning system for configuring and implementing the method of the first aspect described above.

[0111] like Figure 7 , 8 As shown, the system includes: The data acquisition module is used to acquire financial time series data, perform preprocessing, and output the observation series. The stability analysis module, connected to the data acquisition module, is used to analyze the observation sequence and output a first stability index, a second stability index, and a third stability index. The risk fusion module, connected to the stability analysis module, is used to normalize the three types of stability indicators and then fuse them into a unified stability risk index according to their weights. The graded early warning module is connected to the risk fusion module and is used to output graded early warning signals based on the unified stability risk index.

[0112] The backtesting calibration module, connected to the graded early warning module, is used to backtest the early warning signal based on historical risk events, and accordingly adaptively calibrate the weights and graded thresholds.

[0113] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the first method of the present embodiment.

[0114] The present invention will now be described in further detail. A preferred embodiment of the stability fusion analysis framework described in this invention is implemented in Python within the Lyapunov RiskEngine and driven by a real data validation pipeline. In this preferred embodiment, phase space reconstruction is achieved using time-delayed embedding (the delay time is determined by the first local minimum of the average mutual information, and the embedding dimension is determined by the minimum dimension when the false nearest neighbor ratio drops to a threshold). Nearest neighbor search is accelerated using a kd-tree data structure and time nearest neighbors are excluded using a Theiler temporal isolation window. The maximum Lyapunov exponent is obtained through linear fitting within the scaling region. The aforementioned known algorithms are all specific means of implementing the stability index and do not constitute the source of inventiveness of the independent claims of this invention. All the following embodiments use real A-share daily market data collected via the akshare interface from the Shanghai Composite Index (sh000001) or the CSI 300 Index (sh000300) as the sole input, and all samples are real market data.

[0115] The embodiments of the present invention employ the following methods: Figure 9 Default parameters (corresponding to the Engine Config data class, determined by daily frequency tuning of A-shares).

[0116] This invention uses dynamic weights and adaptive thresholds by default, rather than fixed values. The dynamic weights are adaptively determined based on the discriminancy (variance) of each stability index during the training period; the adaptive thresholds are determined based on the distribution quantiles (0.50, 0.75, 0.90, 0.97) of the unified stability risk index during the training period. This is the fundamental feature that distinguishes this invention from fixed-parameter methods.

[0117] Regarding the calculation method for the first stability index: One preferred implementation of the first stability index is the scaling region estimation of the maximum Lyapunov exponent, the core steps of which are (the algorithm is known and will not be derived): Step 1: Phase space reconstruction.

[0118] The delay time determined in step S21 With Embedded Dimension scalar observation sequence Execution time delay embedding yields the reconstructed phase space trajectory matrix. Each of its actions is a 3D phase space point .

[0119] Step 2, nearest neighbor search. An index is built on the phase space point set using a kd-tree data structure, and for each reference point... Search its nearest neighbors The search is performed using a Theiler time-domain isolation window (the window width is equal to the average period of the sequence or...). Exclude points that are temporally close to the reference point to avoid misclassifying time-related points as spatial neighbors. Record the initial distance. .

[0120] Step 3, Trajectory Tracking and Divergence Measurement. For each reference point, track its distance to its nearest neighbor along the time axis as the number of evolution steps increases. Changes, calculation , ( (Maximum number of evolutionary steps).

[0121] Step 4, logarithmic divergence curve. For all valid reference points at time... The logarithmic distance is taken as the sample average to obtain the mean logarithmic divergence curve. .

[0122] Step 5: Automatic identification of the scale region. Traversal. All possible intervals on the curve Perform least squares linear regression on each interval and select the coefficient of determination for the fit. The highest interval is designated as the linear scaling region. The minimum length constraint for the scaling region is... .

[0123] Step six: Perform linear fitting to calculate MLE. In the scaling region... Internal about Perform linear regression, and divide the resulting slope by the sampling period. This is the estimate of the maximum Lyapunov exponent. . Figure 3 The process is illustrated with an auxiliary diagram.

[0124] A method for integrating and classifying the unified stability risk index.

[0125] The core steps of stability fusion and hierarchical early warning are detailed below, with a focus on dynamic weighting and adaptive threshold mechanisms: Step 1: Calculate the first and third stability indices in a rolling manner.

[0126] With sliding window (Default 120 trading days) Scroll along the time axis, and within each window, calculate the first stability index MLE using the Rosenstein method described in step S22 and the third stability index FNN using the method described in step S24 to obtain the daily MLE sequence. With FNN sequences .

[0127] Step two, calculate the second stability index. Using the method described in step S23, based on the fixed common matrix... Time-varying Jacobian matrix Calculate stress energy With drift Then take the drift growth rate The daily gV sequence was obtained. .

[0128] Step 3: Standardization and normalization during the training period. The average value of each indicator in the first 50% of the training period is used. with standard deviation Perform z-score standardization on the entire sequence, then apply sigmoid normalization to obtain three normalized index sequences. (MLE) (gV) (FNN), all Standardization uses only training-period statistics to prevent future information leaks.

[0129] in, 1, k (MLE) is the normalized maximum Lyapunov exponent, representing the normalized value of the trajectory divergence rate; 2, k (gV) is the normalized Lyapunov function drift growth rate, which characterizes the normalized value of the system's energy drift; 3, k (FNN) is the normalized spurious nearest neighbor ratio, representing the normalized value of the phase space structure stability. All three values ​​are ∈ (0,1), and the larger the value, the more dangerous the structure.

[0130] Step 4: Determine dynamic weights. Using the dynamic weight formula from step S3, calculate the weights based on the variances of the three normalized indices during the training period. (satisfy , ).

[0131] Step 5, weighted fusion. Calculate the Uniform Stability Risk Index (USRI) and truncate it to... Interval.

[0132] Step 6, Adaptive Threshold Determination. Using the method described in step S41, calculate the four quantiles (50%, 75%, 90%, 97%) of the USRI distribution during the training period as the four-level thresholds for green / yellow / orange / red. .

[0133] Step 7, Four-level threshold mapping and confirmation window. Following step S41, each USRI is mapped to the original warning level, and then the confirmation window mechanism (window length) is implemented in step S43. The lowest level within the window is taken as the final confirmed warning level, and four warning signals are output: 0 / 1=green, 2=yellow, 3=orange, 4=red.

[0134] The output mapping for the Level 4 warning level is as follows, where the threshold is... The adaptive threshold is determined based on the distribution quantiles of the unified stability risk index during the training period, such as... Figure 10 As shown.

[0135] Example 1: Data Analysis of the Shanghai Composite Index from 2007 to 2008 This embodiment uses the peak of the Shanghai Composite Index in 2007 and the subsequent decline in 2008 as real crisis events to verify the forward-looking early warning capability of the stability fusion analysis framework of this invention in real A-share market conditions.

[0136] (1) Authentic data sources and windows.

[0137] This data was collected from the Shanghai Stock Exchange Composite Index (SSEC) on real trading days via the akshare API's `stock_zh_index_daily(symbol="sh000001")`, covering the period from January 1, 2006 to June 30, 2009. It includes data from the SSEC peaking at 6124 points on October 16, 2007, and the subsequent decline in 2008. The benchmark crisis event was defined as October 16, 2007 (the day the SSEC peaked).

[0138] (2) Data preprocessing. Calculate the logarithmic return rate using the closing price series. After removing the first missing term, we get A logarithmic return sample is used as the observation sequence obtained in step S1.

[0139] (3) Engine Fitting (Step S2). The phase space reconstruction parameters are estimated using the Lyapunov RiskEngine on the training prefix (train_frac=0.5): , The global first stability metric (maximum Lyapunov exponent) is estimated during the training phase. The scale region is Coefficient of determination Public Lyapunov matrix Zhengding.

[0140] (4) Dynamic Weights and Adaptive Thresholds (Steps S3 and S4). After enabling dynamic weights and adaptive thresholds, the dynamic weights of the three stability indices are approximately... Adaptive threshold is These values ​​are all adaptively determined based on training data, rather than being fixed values.

[0141] (5) Forward-looking verification. Prior to the event date of October 16, 2007, the first stability metric... It turned positive 309 trading days in advance (mle_positive_before_event=True, mle_lead_days=309), and the Unified Stability Risk Index (USRI) also crossed the adaptive threshold before the event (lri_rose_before_event=True), indicating that the invention captured the system instability signal about 1.2 years before the bubble peaked.

[0142] (6) Backtesting. Backtesting was conducted with a confirmed orange alert (level ≥ 2) and a lead window of 80 trading days for evaluation: Hit rate. (100% hit rate), confirmed alerts 16 trading days in advance, false alarm rate False detection probability Peirce Skills Rating The overall warning distribution across the region is as follows: 612 green warnings, 147 yellow warnings, 45 orange warnings, and 42 red warnings.

[0143] (7) Conclusion. This embodiment shows that before the Shanghai Composite Index peaked in 2007, the first stability indicator turned positive 309 trading days in advance, and the orange alert was triggered 16 trading days in advance. The PSS=0.973 is significantly better than the random level (0), which verifies the forward-looking early warning capability of the stability fusion analysis framework of this invention for real bubble-crash crisis.

[0144] Example 2: Shanghai Composite Index 2015 Data This embodiment uses 2015 A-share data to verify the early warning capability of the present invention for real and rapid risks.

[0145] (1) Source and Window of Real Data. The Shanghai Composite Index was collected via the akshare interface, covering the period from January 1, 2014 to June 30, 2016, including the peak of the Shanghai Composite Index at 5178 points on June 12, 2015 and the subsequent sharp decline. The benchmark crisis event was defined as June 12, 2015.

[0146] (2) Data preprocessing. Same as in Example 1, calculate the logarithmic rate of return. A sample of log-returns.

[0147] (3) Engine Fitting (Step S2). The engine configuration is the same as in Example 1. The training-period prefix (train_frac=0.5) is estimated as follows: , Global first stability index Scale area Coefficient of determination , Zhengding.

[0148] (4) Dynamic weights and adaptive thresholds (steps S3 and S4). After enabling dynamic weights and adaptive thresholds, the dynamic weights are approximately... Adaptive threshold is All values ​​are adaptively determined based on training period data.

[0149] (5) Forward-looking verification. Prior to the event date of June 12, 2015, the first stability metric... The event turned positive 198 trading days in advance (mle_positive_before_event=True, mle_lead_days=198), and the USRI also crossed the adaptive threshold before the event, indicating that the invention captured the instability signal about 9.5 months before the peak in 2015.

[0150] (6) Backtesting. Backtesting was conducted after confirming the orange alert and setting the lead_window to 60 trading days for evaluation: Hit rate. (100% hit rate), confirmed alerts are triggered on average 0 trading days in advance (triggered on the day of the crash), false alarm rate. False detection probability Peirce Skills Rating The overall warning distribution across the region is as follows: 350 green warnings, 163 yellow warnings, 69 orange warnings, and 26 red warnings.

[0151] (7) Conclusion. This embodiment shows that the first stability indicator turned positive 198 trading days before the Shanghai Composite Index peaked in 2015, confirming that the orange alert was triggered on the day of the crash, with PSS=0.969, which verifies the forward-looking early warning capability of the stability fusion analysis framework of this invention for real leveraged stock market crashes.

[0152] Example 3: The 2020 Global Liquidity Shock on the CSI 300 Index This embodiment uses the exogenous shock of the global liquidity crisis in March 2020 to the A-share market as a real crisis event to verify the early warning capability of the present invention for real exogenous liquidity shocks.

[0153] (1) Source and Window of Real Data. Real market data for the CSI 300 Index was collected via the akshare API stock_zh_index_daily(symbol="sh000300"), covering the period from January 1, 2019 to June 30, 2021, encompassing the impact of the global liquidity crisis in March 2020 on the A-share market. The benchmark crisis event was defined as March 23, 2020 (global liquidity bottom).

[0154] (2) Data preprocessing. As before, calculate the logarithmic rate of return. A sample of log-returns.

[0155] (3) Engine Fitting (Step S2). The engine configuration is the same as before, and the training-period prefix (train_frac=0.5) is estimated as follows. , Global first stability index Scale area Coefficient of determination , Zhengding.

[0156] (4) Dynamic weights and adaptive thresholds (steps S3 and S4). After enabling dynamic weights and adaptive thresholds, the dynamic weights are approximately... Adaptive threshold is All values ​​are adaptively determined based on training period data.

[0157] (5) Forward-looking verification. Prior to the event date of March 23, 2020, the first stability metric... The positive turnaround time (mle_positive_before_event=True, mle_lead_days=175) and the fact that the USRI also crossed the adaptive threshold before the event indicate that the invention captured the instability signal approximately 8 months before the bottom of the exogenous liquidity shock.

[0158] (6) Backtesting. Backtesting was conducted after confirming the orange alert and setting the lead_window to 50 trading days for evaluation: Hit rate. (100% hit rate), confirmed alerts are issued on average one trading day in advance, with a low false alarm rate. False detection probability Peirce Skills Rating The overall warning distribution across the region is as follows: 351 green warnings, 130 yellow warnings, 97 orange warnings, and 26 red warnings.

[0159] (7) Conclusion. This embodiment shows that before the bottom of the global liquidity shock in the CSI 300 index in 2020, the first stability indicator turned positive 175 trading days in advance, the orange alert was triggered 1 trading day in advance, and PSS=0.975, which verifies the forward-looking early warning capability of the stability fusion analysis framework of this invention for real exogenous liquidity shocks.

[0160] Summary of Implementation Examples The verification metrics of the above three embodiments are summarized as follows: Figure 11 (The advance period is in trading days; all data comes from real market data of the Shanghai Composite Index (sh000001) and the CSI 300 Index (sh000300) collected by akshare; dynamic weights and adaptive thresholds are determined adaptively based on training period data).

[0161] The three examples collectively demonstrate that in three real A-share crises—the Shanghai Composite Index crises of 2007 and 2015, and the CSI 300 Index crises of 2020—the first stability indicator (the maximum Lyapunov index) turned positive before the events (175–309 trading days in advance), achieving a 100% hit rate for all three crises, and the Peirce skill score was consistently high. The range was confirmed to be 0–16 trading days in advance for orange alerts. The above results validate the effectiveness of the stability fusion analysis framework of this invention on real market data: the first stability indicator turning positive precedes the occurrence of a catastrophe, providing a rigorous criterion at the dynamic system level for forward-looking early warning; dynamic weights and adaptive thresholds enable the fusion contribution and grading thresholds of the three stability indicators to adaptively calibrate with the market environment, maintaining robust early warning effectiveness under different crisis types (endogenous bubbles, leveraged stock market crashes, and exogenous liquidity shocks).

[0162] Synergistic effect verification: The 1+1+1>3 effect of fusing three types of stability indices To verify the synergistic effect of the "fusion of three types of stability indicators" compared to any single indicator, and to prove that each type of indicator has an irreplaceable contribution, two new scenarios were added to the above three embodiments: the Shanghai Stock Exchange in 2018 due to the trade war and the CSI 300 in 2022 due to the adjustment. This resulted in a total of five real A-share crisis scenarios (all using the same engine configuration and real market data from akshare). Risk indices were independently constructed using a single stability indicator and backtested (single indicator experiment). Then, an ablation experiment was conducted on the fused unified stability risk index USRI. The results are as follows (lead time unit is trading days): (1) Single-index experiment—each index issues an early warning separately, such as Figure 12 As shown.

[0163] (2) Ablation experiment – ​​Remove one type of index from the fusion USRI, such as Figure 13 As shown.

[0164] Each type of indicator has its own "home field" (complementarity): the first indicator (trajectory divergence) performed best in the 2020 exogenous shock (PSS 0.980, 2 days ahead); the second indicator (energy drift) is the most robust (5 / 5 hit rate alone, and the longest lead time in 2015 and 2018); the third indicator (structural stability) had the highest PSS in 2015 (PSS 0.980) and 2018 (PSS 0.983), and the longest lead time in 2007 (75 days). The three types of indicators capture different forms of instability from the dimensions of trajectory, energy, and structure, respectively, and each has an irreplaceable "home field," proving that the three describe different dimensions of the instability process rather than redundant information—this is the physical basis for "1+1+1>3".

[0165] Each type of indicator has a "blind spot," which is addressed through fusion (core evidence that 1+1+1>3): Single-indicator experiments show that the first indicator (MLE) alone underreported the 2018 trade war (PSS= 0.017), the third indicator (structural stability) alone failed to report the 2020 global liquidity shock (PSS= 0.027) – This means that each individual indicator has its own types of crises that cannot be predicted; while the fused USRI, through the complementarity between indicators, maintains a 5 / 5 hit rate and no catastrophic underreporting across the five types of heterogeneous crises, which is significantly better than MLE alone (4 / 5) and structural indicators alone (4 / 5). This is "1+1+1>3" – the overall coverage and robustness of the fused indicator are better than any single indicator, and crises missed by any single indicator can be supplemented by the other indicators.

[0166] Ablation experiments demonstrate that each type of indicator is indispensable: after removing the third indicator (structural stability) from the merged USRI, the 2018 trade war changed from a hit (PSS 0.972) to a miss (PSS = The value of 0.025 indicates that structural indicators were indispensable for the 2018 type of crisis. After removing the first indicator (MLE), the PSS of the 2020 global liquidity shock decreased from 0.977 to 0.951, and the 2007 bubble decreased from 0.971 to 0.962, indicating that the trajectory divergence indicator made a significant contribution to these two types of crises. The second indicator (energy drift) was the only indicator that achieved a 5 / 5 hit, forming a robust foundation for the integration. Removing any one of the three indicators led to a decrease in the early warning effectiveness or underreporting of specific crises, proving that each type of indicator makes an irreplaceable contribution to the overall integration.

[0167] Furthermore, dynamic weights and adaptive thresholds ensure that the aforementioned synergistic effect holds true adaptively under different market conditions: dynamic weights are determined based on the discriminative power of each indicator during the training period. When an indicator has low discriminative power in a certain market (such as the structural indicators in 2020), its contribution is automatically limited, avoiding low-quality indicators from dragging down the fusion; adaptive thresholds are calibrated and graded based on the USRI distribution during the training period. The combination of these two factors ensures that the synergistic effect of "1+1+1>3" holds true robustly under five different crisis types (endogenous bubbles, leveraged stock market crashes, exogenous liquidity shocks, trade frictions, and policy adjustments).

[0168] This invention has significant industrial applicability. The stability fusion analysis framework can be deployed in the risk control centers of stock exchanges, central clearing institutions, macro-prudential regulatory departments, and large financial institutions to monitor multi-source financial time series in real-time or near real-time at daily or even minute-level frequencies. In this preferred embodiment, the nearest neighbor search for phase space reconstruction uses a kd-tree data structure and excludes temporal nearest neighbors using a Theiler window, with a single-window incremental computation complexity of O(n). The stability index calculations for each reference point are independent of each other and can be executed in high parallel on GPUs or distributed computing clusters, meeting the latency requirements of high-frequency monitoring scenarios.

[0169] This invention has been validated using real data from Chinese A-share markets (SSE Composite Index sh000001, CSI 300 sh000300, collected from real exchange data via the AKShare interface), covering three real crises in 2007, 2015, and 2020. The accuracy rate for all three types of crises reached 100%. The first stability indicator turned positive 175–309 trading days in advance, the orange alert confirmation period was 0–16 trading days in advance, and the Peirce skill score was [not specified]. The range indicates that the stability fusion analysis framework possesses implementable early warning capabilities in real regulatory scenarios. The hierarchical early warning mechanism with dynamic weights and adaptive thresholds can be directly integrated with macro-prudential hierarchical response plans, providing interpretable and quantifiable decision support for the pre-identification, in-process intervention, and post-event attribution of systemic risks, and possesses the engineering conditions for large-scale implementation in financial regulatory infrastructure.

[0170] Compared with the prior art, this embodiment has the following advantages: (1) Stability analysis – from wave analysis to dynamic stability analysis Existing technologies analyze fluctuations (second-order moments), and their mathematical essence is modeling the statistical moments of the return distribution, only answering "how much market volatility there is." This invention analyzes stability (dynamic divergence), and its mathematical essence is characterizing the divergence rate of orbits in phase space, the drift of stable energy, and the stability of the phase space structure, answering "how far is the system from the instability boundary?" This represents a fundamental shift from a statistical paradigm to a dynamical paradigm. Specifically, this invention quantitatively characterizes the orbit divergence rate using a first stability index (maximum Lyapunov exponent), quantitatively characterizes the stable energy drift using a second stability index (Lyapunov function drift growth rate), and quantitatively characterizes the phase space structure stability using a third stability index (spurious nearest neighbor ratio drift)—all three indices originate from dynamical system stability theory, not statistical moment theory.

[0171] (2) Risk integration – Unified integration of three types of stability indicators Existing technologies either use a single volatility indicator for early warning or simply weight multiple statistical indicators, lacking a fusion approach from a multi-dimensional, complementary perspective of dynamic stability. This invention, for the first time, integrates a first stability indicator characterizing trajectory divergence rate, a second stability indicator characterizing stable energy drift, and a third stability indicator characterizing phase space structural stability into a unified stability risk index. These three indicators respectively characterize system instability from the trajectory, energy, and structural dimensions, and are complementary: trajectory divergence captures the emergence of chaos, energy drift captures stable energy trends, and structural stability captures phase space topological changes. The resulting technical effect is that instability signals that any single indicator might miss can be detected by the others, and the unified stability risk index more comprehensively and robustly characterizes the system's distance from the instability boundary than any single indicator. This is the "1+1+1>3" synergistic effect: the three indicators complement each other, making the overall robustness of the integration better than any single indicator. As verified by real A-share data, each single indicator has blind spots (such as the structural stability indicator being missed by the global liquidity shock in 2020), while the integration maintains a 3 / 3 hit rate and has no catastrophic underreporting.

[0172] (3) Dynamic early warning - hierarchical early warning based on dynamic weights and adaptive thresholds Existing technologies often employ fixed weights and thresholds, making it difficult to adapt to different market environments. This invention adopts a tiered early warning mechanism with dynamic weights and adaptive thresholds: weights are adaptively determined based on the discriminative power of each indicator during the training period—indicators with higher discriminative power contribute more to the fusion process, allowing the fusion weights to automatically adjust according to the information content of the indicators in different market environments; tiered thresholds are determined based on the distribution quantiles of a unified stability risk index during the training period—allowing the four-level thresholds (green / yellow / orange / red) to adaptively calibrate with the overall market risk level. The combination of these two mechanisms, supplemented by a confirmation window mechanism to suppress fluctuations, enables this invention to maintain robust tiered early warning performance across different markets and sample periods. This is the fundamental feature that distinguishes this invention from fixed-parameter methods.

[0173] In summary, the core innovations of this invention can be summarized as follows: replacing fluctuation analysis with stability analysis; replacing simple weighting of single indicators or statistical indicators with the unified fusion of three types of stability indicators; and replacing fixed parameter early warning with hierarchical early warning based on dynamic weights and adaptive thresholds. These three elements work together to form a stability fusion analysis framework, overcoming the fundamental deficiency of existing technologies that can only analyze fluctuations and not stability.

[0174] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the invention. Therefore, any equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A method for early warning of systemic financial risk stability, characterized in that, Includes the following steps: Step S1: Obtain the financial time series and preprocess the time series to obtain the observation series; Step S2: Perform stability analysis on the observation sequence to obtain a first stability index, a second stability index, and a third stability index characterizing the dynamic characteristics of the system. Step S3: The first stability index, the second stability index, and the third stability index are uniformly represented as a single risk quantity, and a unified stability risk index is formed. Step S4: Output a graded early warning signal based on the unified stability risk index; Step S3 includes the following sub-steps: Step S31: Calculate the mean and standard deviation of the first stability index, the second stability index and the third stability index on the training period prefix, and perform z-score standardization on each; Step S32: Apply logistic normalization to each standardized index and map it to the (0, 1) interval; Step S33: The three normalized indicators are merged according to their weights into the unified stability risk index.

2. The financial systemic risk stability fusion early warning method according to claim 1, characterized in that, The preprocessing in step S1 includes the following sub-steps in sequence: Step S11, missing value imputation, using forward filling or linear interpolation to complete the missing values ​​in the sequence; Step S12, outlier removal: outliers are identified and removed using the three-standard-deviation criterion or the interquartile range criterion. The removed outliers are then filled in using the missing value imputation method. Step S12, frequency domain alignment, resample sequences with different sampling frequencies to the same frequency; Step S12, normalization processing: z-score standardization is performed on each source sequence to make the mean of each sequence 0 and the standard deviation 1, thus eliminating the difference in dimensions. Step S13, Multi-source fusion: When it is necessary to perform cross-asset or cross-market fusion monitoring on multi-source financial time series, the standardized multi-source series are fused into a single scalar observable by principal component analysis to obtain the first principal component, or by equal weight or inverse variance weighted average, and then the scalar observable is used as the observation series for stability analysis.

3. The financial systemic risk stability fusion early warning method according to claim 1, characterized in that, Step S2 includes the following steps: By reconstructing the phase space of the observation sequence, the one-dimensional scalar projection is restored to a high-dimensional phase space trajectory. The phase space reconstruction is achieved using a time-delay embedding method, including the following steps: Step S211, determine the delay time The delay time The average mutual information function of the observed sequence is determined by the first local minimum value of the average mutual information function, which is: in, To estimate the number of boxes using mutual information, for Falling into Column and number The joint probability of a row-joint histogram. and These are the marginal probabilities, Measured and The strength of the nonlinear dependency between them, and the delay time Pick about The value corresponding to the first local minimum; Step S212: Determine the embedding dimension m, which is determined by the false nearest neighbor method, taking the minimum dimension when the proportion of false nearest neighbors first drops below a preset threshold; Step S213, construct the embedding vector with the delay time With the embedding dimension m, construct an m-dimensional delayed embedding vector for the observation sequence: ,in, Let be the observation value on the t-th trading day. To reconstruct the t-th point in the phase space, all embedded vectors form the reconstructed phase space trajectory matrix. ,in M represents the number of reconstructed phase space points, and N represents the length of the observation sequence.

4. The financial systemic risk stability fusion early warning method according to claim 3, characterized in that, In step S2, the first stability index is the maximum Lyapunov exponent. By tracking the distance changes of the nearest neighbor pairs in the reconstructed phase space with the number of evolution steps, the average logarithmic divergence curve is obtained. Linear fitting is performed in the linear scaling region of the curve, and the resulting slope is the first stability index. The second stability index is the drift growth rate of the Lyapunov function, which measures the trend of stress energy change in the system by constructing a quadratic Lyapunov function. The third stability index is the dynamic drift of the false nearest neighbor ratio over time under a fixed embedding dimension. The false nearest neighbor ratio under a fixed embedding dimension is calculated in each window by sliding a window along the time axis to obtain the rolling false nearest neighbor ratio value, which is used to characterize the change in the stability of the phase space structure.

5. The financial systemic risk stability fusion early warning method according to claim 4, characterized in that, In step S2, the calculation steps for the first stability index include: Step S221, for each reference point in the reconstructed phase space ( Search for its nearest neighbor in the kd-tree. Record the initial distance ; Step S222: For each reference point, track its time with its nearest neighbor. Separation distance after step: , in, For the number of evolutionary steps, The maximum number of evolutionary steps, For reference point Its nearest neighbor is The Euclidean distance of the step; Step S223: Take the sample average of the logarithmic distances for all valid reference points: in, For at any time There is still a set of reference points that can be effectively tracked. Let its number of elements be , For the first The mean logarithmic divergence of the steps; Step S224, in about Identify linear scaling regions on the curve and traverse all possible intervals. Perform least squares linear regression on each interval and select the coefficient of determination for the fit. The highest interval is used as the scaling region. Linear fitting is performed within the scaling region, and the slope is calculated: in, The sampling period is For automatically detected linear scaling regions, This represents the slope of the linear regression.

6. The financial systemic risk stability fusion early warning method according to claim 1, characterized in that, In step S4, the graded early warning adopts an adaptive threshold and confirmation window mechanism. The adaptive threshold is determined based on the distribution quantile of the unified stability risk index during the training period, and includes the following steps: Step S41: Collect all uniform stability risk index values ​​during the training period and calculate their multiple quantiles as warning thresholds at each level; Step S42: Map the unified stability risk index value of each step to a discrete early warning level; Step S43: Using a confirmation window mechanism, the warning level will be upgraded to the level corresponding to the threshold only if the original warning level continuously meets the corresponding threshold condition for h consecutive cycles.

7. A system using the financial systemic risk stability fusion early warning method according to any one of claims 1-6, characterized in that, include: The data acquisition module is used to acquire financial time series data, perform preprocessing, and output the observation series. The stability analysis module, connected to the data acquisition module, is used to analyze the observation sequence and output a first stability index, a second stability index, and a third stability index. The risk fusion module, connected to the stability analysis module, is used to normalize the three types of stability indicators and then fuse them into a unified stability risk index according to their weights. The graded early warning module is connected to the risk fusion module and is used to output graded early warning signals based on the unified stability risk index.

8. The system according to claim 7, characterized in that, It also includes a backtesting calibration module, which is connected to the graded early warning module, and is used to backtest the early warning signal based on historical risk events, and accordingly to adaptively calibrate the weight and graded threshold.

9. The system according to claim 7, characterized in that, The weights are dynamic weights, adaptively determined based on the statistical discriminant power of the three stability indices during the training period. The discriminant power is measured by the variance of the normalized sequence of each index during the training period. The dynamic weight calculation formula is as follows: in, Let be the variance of the i-th type of normalized index during the training period. is the lower bound of the weight, j is the index of the summation of the indicator categories, and j = 1, 2, 3 correspond to the first stability indicator, the second stability indicator, and the third stability indicator, respectively.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the financial systemic risk stability fusion early warning method as described in any one of claims 1 to 6.

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