Bootstrap resampling-based small sample modeling stability evaluation method and system

Abstract

The application discloses a small sample modeling stability evaluation method and system based on Bootstrap resampling, and particularly relates to the technical field of computer and data intelligence, and the method comprises the following steps: completing data preprocessing and stable stage identification under a unified time base, and forming a segmented set; taking the average block length as the decision quantity to optimize SBB to construct a sample space, and determining the optimal block length in combination with the variance consistency and nominal coverage consistency criteria; performing resampling training around three scales of short, medium and long, and collecting layered indexes such as prediction, parameters and features; completing stability calculation and empirical coverage calibration based on scale-in statistics and scale-weighted mixing, and outputting a pseudo-stationary diagnosis score; finally, engineering judgment and rollback optimization are performed according to the coverage, correlation retention and risk threshold. The system records random seeds, block metadata and model version generation evidence pointers, has traceable and retestable characteristics, and is suitable for scenes such as production lines, network traffic and finance.

Description

Technical Field

[0001] This invention relates to the field of computer and data intelligence technology, and more specifically, to a method and system for evaluating the stability of small-sample modeling based on Bootstrap resampling. Background Technology

[0002] With the rapid development of the Internet of Things (IoT), Industrial Internet, and Fintech, modeling and analysis based on multi-source time series data has become crucial for achieving automated orchestration and intelligent decision-making. However, in real-world business scenarios, the sample size available for modeling is often limited, and the data simultaneously exhibits complex statistical characteristics such as autocorrelation, seasonality, and heteroscedasticity. When the operating environment includes strong boundary conditions such as shift changes, batch replacements, and transaction day divisions, traditional bootstrap methods based on the independent and identically distributed (IOD) assumption struggle to retain the correlation structure of the data at key lags, leading to distorted model stability assessments.

[0003] Existing block self-help methods, such as moving block self-help, cyclic block self-help, or stationary block self-help, while considering data correlation to some extent, rely heavily on subjective experience to set their block length parameters, lacking a data-driven selection mechanism. This easily leads to two risks: first, excessively short block lengths may fail to effectively preserve medium- to long-term correlation structures, causing correlation disruption; second, excessively long block lengths may cross intrinsic data inflection points or strong boundaries, introducing trend leakage and creating pseudo-trends that did not originally exist. These problems ultimately manifest as a significant discrepancy between the nominal coverage and empirical coverage of the model's evaluation confidence interval, and may even result in seemingly good but ultimately untrue pseudo-stationarity.

[0004] Therefore, there is an urgent need for a method and system that can automatically identify stable phases and relevant scales under a unified time base and fixed sampling step size, construct a sample space based on the optimal average block length, conduct multi-scale resampling training, and form an engineered judgment and repeatable data chain through empirical coverage calibration and pseudo-stationarity diagnosis. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a method and system for evaluating the stability of small-sample modeling based on Bootstrap resampling to address the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] The stability assessment method for small-sample modeling based on Bootstrap resampling includes the following steps:

[0008] The original time series data is preprocessed and stable phases are identified to obtain relevant structural information about these stable phases.

[0009] Based on the relevant structural information of the stable phase, the average block length is used as the decision quantity, and the variance consistency and nominal coverage consistency are the dual objectives. The optimal average block length is selected by minimizing the comprehensive cost function. Based on this, a resampling sample space based on the Bootstrap of stationary blocks is constructed according to the principles of intra-segment block extraction, inter-segment splicing and order preservation.

[0010] Resampling and model training were performed around at least two different correlation scales, and stratified statistics of predicted output, model parameters and diagnostic indicators were collected.

[0011] The stratified statistics under different correlation scales are weighted and fused to form a mixed distribution. The confidence intervals obtained based on the mixed distribution are calibrated by empirical coverage, and the key lag autocorrelation difference, trend slope difference and slice consistency quantity are synthesized to calculate the pseudo-stationary diagnostic score.

[0012] Based on the calibrated confidence interval coverage, relevant structure preservation, and pseudo-stationarity diagnostic score, the system outputs an engineering assessment of model stability and recommendations for handling such situations.

[0013] In a preferred embodiment, preprocessing the original time series data and identifying stable phases includes: calculating the autocorrelation function of the stable phase to obtain the correlation half-life and integral autocorrelation time; extracting the seasonal cycle using mutual information spectrum or periodogram; and locating change points using a combination of KPSS and ADF test with windowed CUSUM or PELT algorithm to form a segment set.

[0014] In a preferred embodiment, constructing a resampling sample space based on a stable block Bootstrap includes: strictly restricting the construction and splicing of blocks to a single sub-segment of the segment set obtained by variable point positioning, and prioritizing the alignment of the start and end positions of the blocks with the strong boundaries defined by the business rules; when no significant correlation or seasonality is detected in the stable phase, automatically reverting to traditional independent resampling with replacement.

[0015] In a preferred embodiment, resampling is performed around at least two different correlation scales, including using the optimal average block length as a mesoscale benchmark and selecting shorter and longer scales in its neighborhood, corresponding to short-term lags, dominant correlations, and seasonal effects, respectively.

[0016] In a preferred embodiment, in weighted fusion, the weights of different scales are calculated based on the comprehensive cost function value corresponding to each scale when determining the optimal average block length, and the scale with the lower cost is assigned a higher weight.

[0017] In a preferred embodiment, empirical coverage calibration of the confidence interval is achieved by adjusting the interval half-width using a scaling factor. The scaling factor is calculated based on the deviation between the empirical coverage and the nominal coverage, so that the calibrated empirical coverage falls within a preset tolerance band.

[0018] In a preferred embodiment, the pseudo-stationary diagnostic score is obtained by weighted synthesis of key lag autocorrelation difference, trend slope difference, and slice consistency quantity.

[0019] In a preferred embodiment, the engineering determination of model stability includes: when the empirical coverage falls into a preset tolerance zone, the autocorrelation difference at the key lag is lower than a preset threshold, and the pseudo-stationary diagnostic score is lower than a preset upper bound, it is determined to be stable; otherwise, a rollback optimization mechanism is triggered, which includes adjusting the optimal average block length, refining the segment set, or switching the heteroscedasticity robustness processing method.

[0020] In a preferred embodiment, the rollback optimization mechanism makes targeted adjustments based on the unmet judgment conditions: when the correlation maintenance is not up to standard or the pseudo-stationary diagnostic score exceeds the threshold, the average block length is reduced and the alignment of the block start and end with the strong boundary is strengthened; when the coverage is low but the correlation maintenance is up to standard, the block length and segmentation remain unchanged, the heteroscedasticity robustness mechanism is switched or strengthened and the interval half-width is expanded.

[0021] In a preferred embodiment, the following modules are included:

[0022] The data preprocessing and stable sample extraction module is used to preprocess the raw time series data and identify stable phases in order to obtain relevant structural information of the stable phase.

[0023] The Bootstrap sample space construction module is used to construct a resampling sample space based on the relevant structural information of the stable phase, with the average block length as the decision quantity and variance consistency and nominal coverage consistency as dual objectives. It selects the optimal average block length by minimizing the comprehensive cost function, and constructs the resampling sample space based on the Bootstrap of the stationary block according to the principles of intra-segment block extraction, inter-segment concatenation and order preservation.

[0024] The model training and stratified index collection module is used to resample and train the model around at least two different correlation scales, and to collect stratified statistics of predicted output, model parameters and diagnostic indicators.

[0025] The stability calculation and coverage calibration module is used to weight and fuse stratified statistics under different correlation scales to form a mixed distribution, perform empirical coverage calibration on the confidence intervals obtained based on the mixed distribution, and synthesize key lag autocorrelation difference, trend slope difference and slice consistency quantity to calculate pseudo-stationary diagnostic score.

[0026] The stability assessment and judgment module is used to output engineering judgment results and handling suggestions on model stability based on the calibrated confidence interval coverage, relevant structure retention, and pseudo-stationarity diagnostic score.

[0027] The technical effects and advantages of this invention are as follows:

[0028] This invention identifies stable phases under a unified time base and fixed sampling step size, and constructs a stable block Bootstrap sample space that follows the principles of intra-segment block extraction, inter-segment splicing, and order preservation. This allows for the simultaneous preservation of short-term lags, dominant correlations, and seasonal structures during resampling, avoiding correlation disruptions and trend leakage caused by blocks crossing change points and strong boundaries, thus improving the authenticity and verifiability of stability assessments from the source.

[0029] This invention takes variance consistency and nominal coverage consistency as dual objectives, establishes a comprehensive cost function around the average block length and adaptively selects the block length; further, it performs parallel resampling and uniform training at three relevant scales (short, medium and long), so that the stability measure comes from multi-perspective data evidence rather than a single parameter, thereby significantly reducing the sensitivity of the evaluation results to the block length setting and human experience.

[0030] In the hierarchical statistics fusion stage, this invention uses the scale weight derived from the cost function to weight and mix the statistics under different correlation scales, and uses the empirical coverage rate to perform proportional calibration on the nominal confidence interval, so that the interval estimation still maintains frequency consistency under the conditions of limited samples, correlation and heteroscedasticity, and reduces the engineering risks of excessively narrow intervals and artificially high confidence.

[0031] To prevent pseudo-stationarity where indicators look good but are not genuine, this invention integrates a pseudo-stationarity diagnostic score composed of key lag autocorrelation difference, trend slope difference, and slice consistency. It outputs engineered conclusions based on confluence criteria: coverage meets standards, correlation maintains standards, and pseudo-stationarity is controlled. When criteria mismatch occurs, clear handling suggestions are provided, elevating stability assessment from simply presenting results to an executable closed loop of diagnosis, correction, and reassessment.

[0032] Regarding online correction, this invention provides a low-cost rollback path: when coverage is insufficient, heteroscedasticity robustness is prioritized and the interval is expanded; when correlation is insufficient or there are signs of trend leakage, the block length is reduced and the alignment of the block start and end points with strong boundaries is strengthened. This strategy ensures statistical consistency while maintaining ease of implementation, facilitating rapid iteration and replay verification.

[0033] This invention solidifies random seeds, block metadata, and model versions throughout the entire process, generating uniquely locatable evidence pointers to ensure the traceability, verifiability, and comparability of conclusions. When no significant correlation or seasonality is detected, the algorithm automatically reverts to independent resampling, ensuring the consistency of the method's closed-loop under different data forms and avoiding the usage risks caused by unclear application boundaries.

[0034] At the application level, this invention can be directly mapped to scenarios with strong boundaries such as production line monitoring, network traffic, and finance, even under conditions of heteroscedasticity and volatility aggregation. It can still maintain the robustness of interval estimation and standard error, significantly reduce the cost of manual adjustment and trial and error, improve the reliability and consistency of stability assessment before going live, thereby increasing the success rate of model deployment and enhancing the operability and interpretability of monitoring during operation. Attached Figure Description

[0035] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings;

[0036] Figure 1 This is a flowchart illustrating the stability evaluation method for small sample modeling based on Bootstrap resampling according to the present invention.

[0037] Figure 2 This is a schematic diagram of the structure of the small sample modeling stability evaluation system based on Bootstrap resampling of the present invention. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Example 1: The present invention provides a small sample modeling stability evaluation method based on Bootstrap resampling, such as... Figure 1 As shown, it includes the following steps:

[0040] Step 1: Data preprocessing and stable sample extraction;

[0041] First, the original multi-source time series are subjected to integrity verification and consistency processing, which includes timestamp alignment, robust repair of missing and outliers, and unification and standardization of dimensions to make each feature comparable under the same statistical scale. Then, based on business rules and statistical tests, the stable phase is defined, that is, the period in which the mean, variance and autocorrelation structure do not undergo significant structural changes within a given observation window.

[0042] While obtaining samples from the stable phase, quantitative diagnosis is conducted on the relevant scales and potential segments within this phase: First, the relevant half-life is calculated based on the autocorrelation function (ACF) of the stable phase. Autocorrelation time with integral .in , This represents the sample autocorrelation coefficient at lag X in this stage, summed at... The sequence is terminated according to a conservative truncation rule when it is sufficiently close to zero or near zero for the first time, in order to measure the effective independent length of the sequence and the cumulative effect of the associated tail; while Then depict The minimum hysteresis corresponding to the decay to a preset threshold z1 (e.g., z1=0.5) is used as an intuitive reference for the block length dimension. Secondly, to identify the source of periodic correlation, the system extracts the seasonal cycle using mutual information spectrum or periodogram within the same stable phase, prioritizing the selection of the most significant peak from candidate frequency bands (e.g., shifts, daily cycles, or weekly cycles) consistent with the business rhythm; if there are competing peaks from nearby neighbors, the fitting residuals of cross-validation and the information criterion are used as parallel adjudicators to ensure that the selection of the dominant seasonal cycle can explain the main energy peak without excessively following random noise. Thirdly, to handle the common operating conditions of slow drift superimposed with short-term correlation, the system further performs non-stationary segmentation on the stable phase: without changing the unified caliber, the joint test of KPSS and ADF is used to identify signs of unit root or variance drift, and the change point is located using windowed CUSUM or PELT based on the cost function to form a segment set. Each sub-segment can be statistically approximated as a weakly stationary process, used for independent block extraction and splicing during subsequent blockization; if batch switching, shift handover, or medical follow-up nodes are known on the engineering side, then such strong boundaries are directly incorporated. To avoid structural damage caused by block crossings, the above processing is accompanied by evidentiary and traceability requirements: the system uses a fixed random seed and algorithm version, persists data snapshots, parameter sets for cleaning and repair operations, and calculation methods for key statistics, generating uniquely indexable evidence pointers to ensure the reproducibility of the results of step one under different environments. Through this step, the system produces cleaned, standardized, and consistent stable phase samples, and provides data within the same phase. , Seasonal cycles and segmented sets Quantitative estimates of these quantities will serve as direct inputs to candidate block lengths and block boundaries when constructing the Bootstrap sample space.

[0043] Step 2: Construct the Bootstrap sample space;

[0044] Building upon the stable phase identification and related structural diagnosis described in Step 1, this step aims to construct a resampling sample space that maximizes the preservation of sequence correlation and ensures reproducibility, using the average block length as a unified decision metric. The system prioritizes the Stationary Block Bootstrap (SBB) as the optimal solution, while also accommodating Moving Blocks (MBB) and Circular Blocks (CBB) for comparative verification under specific operating conditions. To avoid subjective parameter setting, this step does not directly set the continuation probability of the SBB; instead, it uses the average block length L as the core parameter, ensuring that the SBB parameters satisfy… ,in This represents the Bernoulli trial probability of whether to start a new block at each position.

[0045] Candidate average block lengths are automatically generated from the relevant scale and seasonal information obtained in step one, supplemented by statistical calibration with dual objectives of trend leakage and coverage. Specifically, the system first uses integral autocorrelation time... A finite number of candidate L values ​​are generated based on the seasonal cycle, and each candidate is independently evaluated within an approximately stationary sub-segment; to suppress cross-segment contamination and trend leakage, blocks are strictly limited to a segmented set. Within a single sub-segment, the system constructs and splices blocks, prioritizing alignment of the block start and end points with strong boundaries such as batch switching, shift handover, or follow-up nodes. Subsequently, the system quantitatively compares candidate Ls using variance consistency and nominal coverage consistency as dual objectives. To estimate the variance of the target statistic obtained through block bootstrapping for a given L, This is the reference variance obtained based on consistent estimates of heteroscedasticity and autocorrelation (e.g., HAC / NW) or block censoring by Jackknife. nominal confidence level Given the empirical coverage, the system minimizes the following formula to select the optimal block length: .

[0046] in, Here, ω represents the overall cost function; ω∈[0,1] is the trade-off coefficient between the two objectives, used to balance the importance of variance consistency and coverage consistency. In a preferred embodiment, ω can be set to 0.5 by default to achieve equal weighting; if the business scenario places more emphasis on the accuracy of variance estimation, ω can be appropriately increased, such as ω = 0.7, and conversely, if the accuracy of interval coverage is more important, ω can be appropriately decreased, such as ω = 0.3. The significance level is indicated by .

[0047] The reference variance The preferred method is to use the heteroscedastic autocorrelation consistent (HAC) estimator, specifically the Newey-West estimator. The empirical coverage... The Monte Carlo simulation is used to calculate the following: Based on the current candidate block length L, B1 bootstrap resamplings are performed (e.g., B1 = 1000). Each resampling constructs a nominal 1-α confidence interval. The proportion of these intervals that cover the true parameters (or baseline model point estimates) is the empirical coverage.

[0048] The first term of the objective function encourages consistency between the resampling variance and the robust reference variance, while the second term ensures that the confidence intervals constructed using the nominal confidence level have empirically correct coverage performance. This is achieved by solving the above problem on the candidate set. And based on this, determine the probability of SBB continuing to be a block. To further reduce the risk of trend leakage and avoid structural bias caused by crossing significant seasonal scales, the system applies an engineering boundary to L, ensuring that it does not exceed a certain proportion of the upper limit of the segment length and does not exceed twice the seasonal scale. When no significant correlation or seasonality is detected during the stable phase, the system automatically reverts to traditional independent resampling with replacement to maintain method closure and statistical consistency.

[0049] After determining the optimal parameters, the sample space is constructed according to the principles of intra-segment block selection, inter-segment concatenation, order preservation, and traceability of evidence. Taking SBB as an example, the system randomly selects the starting point of the block in a uniform distribution within each sub-segment and generates random block lengths according to a geometric distribution, ensuring that each block falls completely within the current sub-segment. If a random block crosses a sub-segment boundary, it is truncated, and the next block is opened using the same rules until a resampled sequence equivalent to the original sample length is accumulated within each sub-segment. To preserve the correlation structure of the original sequence at critical lags and match the business rhythm, the starting point of the block is preferentially aligned with the allowable set near these boundaries when shifts / batch / outpatient time periods exist, avoiding frequent truncation in high-uniformity intervals that could destroy short-term correlations. For the control settings of MBB or CBB, the system uses the same... As a block length parameter, resampling sequences are generated within the segment using either sliding window or cyclic block sampling methods to support subsequent methodological sensitivity analysis and robustness comparisons. The entire resampling process uses a fixed random seed and records block metadata; the block metadata includes scale, segment identifier, L, and so on. The start and end positions of blocks and truncation conditions are used to generate uniquely indexable evidence pointers under the joint constraints of model version and data snapshot, thereby ensuring the repeatability of sample space construction and audit traceability.

[0050] To facilitate subsequent cross-scale fusion and coverage calibration, this step retains a sample pool corresponding to several nearest neighbor values ​​in the optimal block length neighborhood. This reduces the sensitivity of single block length estimation errors to the final stability evaluation. This sample pool does not alter the core conclusion of this step but provides alternative evidence for nominal coverage calibration in step four and engineering arbitration in step five. When the target application exhibits significant heteroscedasticity but the correlation structure is clear, this step maintains the block structure and parameters unchanged, only applying heteroscedasticity robustness to the residual weights or statistics in subsequent steps. This clearly limits the responsibility for relevance preservation to the sample space construction stage. Through this mechanism, the system completes the entire chain of sample space construction—from relevance scale identification to adaptive parameter determination, and then to intra-segment consistency constraints and evidence-based output—in a data-driven manner, laying a robust statistical foundation for subsequent model training, hierarchical index collection, and cross-scale fusion.

[0051] Step 3: Model training and hierarchical metric collection;

[0052] Having determined the optimal average block length and continuation probability in step two, this step simultaneously constructs resampled datasets across short, medium, and long correlation scales. Under the constraints of a unified model configuration and random seeds, repeated training and evaluation are performed to obtain stratified statistics that can be used for subsequent stability calculations and coverage calibration. To balance correlation retention and estimated variance, the system uses the optimal block length... As a mesoscale benchmark, two scales, shorter and longer, are set within its neighborhood, so that the three scales correspond to different sensitivities to short-term lags, dominant correlations, and seasonal effects, respectively. Each scale is used in a segmented ensemble. Blocking and splicing are performed independently within each segment, and blocks are not allowed to cross segment boundaries. When there are batch switching, shift handover, or follow-up nodes, the start and end of the block are preferentially aligned with the strong boundary of that type, thereby avoiding the destruction of autocorrelation patterns at structural transitions. For residual weak drift, the system first detrends the sequence within the segment, completes resampling, and then reinjects the original trend term, or adopts a slowly changing continuation block probability within the segment to approximate the assumption of local stationarity, but does not change the overall parameter caliber determined in step two.

[0053] After fixing the sample space, the system independently repeats the complete training process for each resampled sequence. The model type, feature engineering, hyperparameters, and optimization strategies remain consistent with the baseline training, and a clear distinction is made between the randomness introduced by resampling and the randomness introduced by the trainer itself: unless otherwise stated, the latter is masked by fixing the random seed of the trainer to attribute uncertainty to variations in the data layer. For any resampling experiment b, the system records the prediction results. Parameter vector Feature subset and performance metrics consistent with the objective function ;in This can be understood as the time-by-time output of the validation set or replay samples under a unified time base. This represents the parameter estimates or their functional mappings corresponding to the interpretable portion of the model. This refers to the set of variables adopted by the feature selection model during this training iteration. These are scalar metrics that align with business objectives, such as mean squared error, absolute error quantiles, log-likelihood, or classification discriminant. To ensure the robustness of coverage assessment and subsequent quantile calibration, the number of resampling operations at all three scales is sufficiently large in engineering practice (e.g., a total of no less than 1,500 times), and evidentiary fields such as scale identifier, segment identifier, block start and end positions, truncation conditions, and random seed are retained in the metadata to support traceability and verifiability.

[0054] Considering the prevalence of heteroscedasticity in scenarios such as industrial production lines, medical follow-ups, and network traffic, the system employs a residual reweighting mechanism, such as wild / bootstrap-t, to construct statistics without altering the block structure. Let the residuals obtained from the baseline model under a unified caliber be denoted as... Introduce independent and identically distributed weights into the resampled sequence. (For example, using Rademacher ±1 weights or normal weights with zero mean and unit variance), then weight the residuals. As input for constructing bootstrap statistics or correcting standard errors; if t-type calibration is used, the standardized quantity obtained by subtracting the baseline point estimate from the resampling estimate is used as the central statistic, thus achieving approximately unbiased interval coverage even in the presence of conditional heteroscedasticity. The above processing only affects the generation and calibration method of the statistics, without making any secondary adjustments to the block length and continuation probability, ensuring clear boundaries of responsibility for correlation retention and variance robustness.

[0055] To support the subsequent hierarchical aggregation of stability metrics, this step simultaneously collects metric distributions at three levels. The first level targets the predicted output, where the system forms a time-by-time distribution. The empirical distribution, with its quantiles, variance, and bandwidth, serves as a direct characterization of prediction uncertainty. When necessary, the quantile curve is post-processed with order-preserving or monotonicity constraints to ensure compatibility with physical or business boundaries. The second layer addresses parameters and features, using... The covariance structure characterizes parameter stability and uses characteristic selection frequencies. The robustness of variable j in selection is described by B, where B is the number of resamplings at this scale, and 1 / {⋅} is the indicator function; when the model is not explicitly sparse, it can be... This can be interpreted as the probability of effective contribution, which is equivalent to obtaining the absolute value of the thresholded parameter or a saliency mask based on the importance of permutation. The third level addresses the risks of correlation maintenance and trend leakage by systematically comparing the autocorrelation differences between the resampled sequence and the original sequence at key lags, and generating a diagnostic metric for subsequent threshold determination; if the autocorrelation of the original sequence at lag n is denoted as... The corresponding quantity of the resampled sequence is Then the single diagnostic difference is defined as Under typical operating conditions The system covers three scales: short-term, dominant, and seasonal. Simultaneously, it fits linear or piecewise linear trends to the resampled sequences, extracts slope statistics, and compares them with the corresponding quantities in the original sequences in a standardized manner to indicate whether trend leakage occurs due to excessively long blocks. For applications with shift or batch slices, the variance or mean difference of each slice is also archived as a consistency indicator, thus enabling the differentiation of pseudo-stability situations where the overall structure is stable but the slices are distorted during subsequent arbitration.

[0056] Through the above process, step three, without changing the model form and training interface, completed multi-scale parallel training driven by block resampling, and formed a hierarchical indicator set that can be used for statistical inference and engineering arbitration in three dimensions: predicted output, parameters and features, and correlation and trend diagnosis. These indicators have sufficient sample support and evidential metadata within the scale, and comparable dimensions and calibers between scales, providing complete, traceable and reproducible experimental input for the cross-scale fusion and coverage calibration in step four.

[0057] Step 4: Stability calculation and coverage calibration;

[0058] Based on the resampling results obtained in Step 3 across the three relevant scales, this step performs intra-scale aggregation and inter-scale fusion of stratified indicators such as predicted output, parameter estimation, and feature selection according to a unified statistical standard. Nominal confidence intervals are then calibrated based on empirical coverage, ultimately forming a set of stability measures that can be used for engineering decision-making and forensic verification. To avoid bias caused by a single long-term selection, this step treats different scales as three complementary perspectives on the same underlying uncertainty. First, empirical distributions are obtained within each scale, then data-driven weights are used to mix them across scales. The resulting mixed distribution then serves as the direct source for all intervals and statistical conclusions.

[0059] Within the scale, the system records in step three. Using the sample as an example, prediction intervals, parameter intervals, and performance intervals are calculated according to the percentile method and bias correction rules, and frequency estimates of feature selection stability are provided. All statistics within the scale adopt the same validation criteria and scoring set as the baseline to avoid introducing additional variance due to changes in evaluation criteria. When the prediction interval needs to maintain monotonicity or physical boundaries, the quantile curves within the scale are subjected to ordination preservation processing, but the confidence level of the quantiles themselves is not changed.

[0060] After completing intra-scale statistics, the system proceeds to inter-scale fusion: Let the cost function obtained in step two be denoted as... ,in The average block length at the k-th scale (short, medium, and long correspond to k∈{s,m,l}, respectively) is represented by... The relative merits of each factor are used as the quantitative basis for the credibility of the scale, and weights are constructed accordingly. In the formula, >0 represents a temperature parameter used to control the sharpness of the weights, for example... Set to All The median; when Smaller, with weights concentrated on less costly scales, when A larger value results in a more even distribution across the three scales. The empirical distributions within a scale are weighted and mixed across scales using the aforementioned weights: for any scalar statistic (such as time-by-time prediction, overall performance, or parameter components), the mixed distribution is the weighted sum of the empirical distributions at the three scales; for feature selection stability, let... Let represent the selection frequency of feature j at the k-th scale, then the mixing frequency... As a robust measure of this feature across scales, once the mixture distribution is determined, the system directly provides the mixture quantiles and mixture variances for the prediction interval, parameter interval, and performance interval, thus avoiding the fragility of drawing conclusions based on a single scale.

[0061] To ensure that the frequency coverage properties of the interval are consistent with the nominal confidence level, this step constructs the nominal confidence level under the mixed distribution. Experience coverage assessment and calibration are performed within the interval. Experience coverage. This is approximated by resampling with in-segment reservations / block-on-block additions, evaluating whether the interval constructed according to the mixed distribution can cover the target quantity with the desired frequency under the current sample size and related structure. and Deviation exceeding the tolerance zone At this time, the system performs proportional calibration on the half-width of the interval: the center of the nominal interval is denoted as... (For example, median or unbiased point estimation of a mixed distribution), if the original half-width is h, then the calibrated half-width is taken as h. ;in, Insufficient coverage (interval expansion). The coverage is too wide (interval shrinkage); The value of is determined by the principle of minimizing coverage deviation, so that the empirical coverage after calibration falls within . The target interval is determined by maintaining the relative order and monotonicity of the quantiles on both sides, ensuring that the interval does not cross or anomalously shrink. The calibration operation only applies to the scale of the interval and does not change the shape of the mixed distribution itself, thus not disrupting the bias-variance tradeoff previously obtained through weighted fusion.

[0062] The scaling factor This is determined through an iterative calibration process, with the following specific steps:

[0063] Step a1: Initialization = 1.0.

[0064] Step a2: Use the current Adjust all nominal 1-α confidence intervals constructed under the mixed distribution to obtain the calibrated intervals.

[0065] Step a3: Re-evaluate the empirical coverage of the calibrated intervals using the reserved validation set or by adding blocks to blocks and resampling. .

[0066] Step a4: Determine: Does it fall within the tolerance zone [1-α-ε, 1-α+ε]? If so, output the current value. If not, update according to the following rules. :like <1-α-ε (insufficient coverage), then let = + δ; δ is the step size, for example, δ = 0.05. If >1-α+ε (overcovering), then let = - δ.

[0067] Step a5: Repeat steps a2 to a4 until... Falling into the tolerance zone or reaching the maximum number of iterations (e.g., 100 times). Final solidification. This value will be used for calibration in all subsequent intervals.

[0068] Considering that the goal of block resampling is not only to obtain intervals and variances, but also to test whether correlations are preserved and trends are introduced, this step, while completing interval calibration, uniformly quantifies the risk of pseudo-stationarity and outputs a diagnostic score.

[0069] The system will calculate the key lag autocorrelation difference in step three. Diagnostic parameters such as trend slope difference and slice consistency (shift / batch) are calculated as expected within the scale and as expected between scales. Weighted, then standardized and weighted synthesized to obtain ,in, This represents the weighted sum of the absolute autocorrelation differences over several key lags (usually n∈{1,s,2s}); This represents the standardized difference between the resampled sequence and the original sequence under a mixed distribution in terms of linear or piecewise linear slope. It represents a comprehensive measure of variance ratios or mean differences after shift, batch, or follow-up slices; , , ≥0 represents the component weight, satisfying + + =1, for example =0.3, =0.4, =0.3. The higher this score, the greater the risk of visually appealing but ultimately unrealistic results caused by improper blockization or cross-segment splicing.

[0070] After completing inter-scale fusion, coverage calibration, and pseudo-stationarity diagnosis, the system outputs all results in a unified structured format, including point estimates and calibrated intervals under mixed distributions, variances and quantiles of various stability indices, characteristic mixing frequencies, and coverage reports (including...). , , , )as well as It is composed of its decomposed components. This step involves simultaneous curing. , , , , The final value and generation process are related to step two. Together with the resampling metadata from step three, this forms a uniquely indexable evidence pointer. At this point, the stability measurement completes a closed loop from intra-scale statistics to inter-scale fusion, and then to coverage calibration and risk diagnosis, providing sufficient and reliable quantitative evidence for the engineering threshold determination and automatic backoff in step five.

[0071] Step 5: Stability assessment and determination;

[0072] After completing the cross-scale fusion and coverage calibration in step four, this step uses a unified statistical caliber to verify the compliance of the resulting mixed distribution in a frequency sense, and combines three types of diagnostic quantities—relevant preservation, trend leakage, and slice consistency—to form the final engineering judgment and handling recommendations.

[0073] First, the system reads the point and interval estimates corresponding to the business objective on the mixed distribution, and sets the nominal confidence level to... The calibrated interval is checked for consistency with its empirical coverage report. If the coverage... Already fallen If the tolerance band is found, the interval is considered to have a correct frequencyological interpretation under the current sample size and correlation structure. If the interval still deviates from the tolerance band but does not exceed the acceptable upper limit, the system retains the deviation and marks it in the handling suggestion as requiring continued calibration during the runtime, without further scaling of the interval, to avoid over-correction introducing secondary bias during the data-scarce phase. Coverage verification is a necessary but not sufficient condition for the final conclusion, because the goal of resampling also includes the requirement of retaining true correlations rather than spurious stationarity. Therefore, the system weights the diagnostic values ​​obtained in steps three and four according to their scale. Perform a hybrid approach to obtain the correlation retention and trend leakage measures at key lags, and compare these with a threshold related to business rhythm: the correlation difference at short-term lags satisfies... And the dominant seasonal lag satisfies At that time, the relevant retention was recorded as meeting the standard; among which and Let represent the autocorrelation differences of the resampled sequence relative to the original sequence at lags of 1 and lag s, respectively. and An engineering threshold set after balancing design verification capability with acceptable false alarm rate, for example and This can be determined using Monte Carlo simulation at a 5% significance level; for engineering practice, a default setting of 0.1 is acceptable. Simultaneously, a pseudo-stationary diagnostic score is calculated by combining the difference in the mixed trend slope with the slice consistency measure. It should not exceed the preset upper limit; A higher value indicates a higher risk of visually appealing but ultimately unsatisfactory results due to improper blockization or cross-segment splicing. If the threshold is exceeded, the coverage rate should not be directly judged as stable even if it meets the standard.

[0074] Under the joint constraints of coverage, relevance preservation, and spurious stationarity risk, the system determines that the system has achieved stable passage, and archives all evidentiary metadata used to generate this conclusion, including the data used. Three-scale weights Interval calibration coefficient The key quantiles and variances of the mixture distribution, the characteristic mixing frequencies and their threshold caliber, and , , The final values ​​and calculation methods. If the coverage meets the standard and only one of the related maintenance or pseudo-stationary risks slightly exceeds the limit, the calibration is considered passed. The system's handling recommendations require retaining the current block length and segmentation settings, and only retesting and updating on a rolling basis according to the established cycle during operation. and At the same time, stricter online monitoring thresholds are introduced for out-of-bounds items. If any key indicator significantly exceeds the limit, it is judged as failing and triggers rollback and re-optimization: when the relevant remains substandard or When the threshold is exceeded and there are signs of trend leakage, the system returns to step two in the candidate set. Shrink the average block length within the neighborhood (and refine the segment set if necessary). It also strengthens the alignment of block start and end points with strong boundaries to reduce distortion caused by cross-trend stitching; when coverage is low but correlation remains up to standard, the system maintains... and The process remains unchanged, except that the heteroscedasticity robustness mechanism is switched or strengthened in the pipeline during steps three and four, and updated. The coverage area is then expanded outwards, and subsequently reassessed until the coverage rate enters the tolerance zone.

[0075] Without altering the three consensus thresholds mentioned above, a scenario-based arbitration priority is introduced to provide a definite handling direction in boundary situations. For production lines, priority is given to ensuring that short-term lag-related factors remain consistent with batch / shift slices. Approaching the threshold and coverage is When both standards are met, it is permissible to maintain the same level of compliance. In cases where the boundary effect can be mitigated by increasing the alignment strength between the start and end points of blocks and shift handover; for time-series medical follow-up, priority should be given to ensuring the maintenance of autocorrelation and coverage corresponding to the follow-up period, when When the threshold is approaching and the short-term lag margin is large, it is recommended to appropriately relax the monitoring threshold for short-term lag, tighten the threshold for seasonal lag, and maintain [the appropriate level of lag]. Unchanged; for network traffic, priority is given to correlation maintenance and heteroscedasticity robustness with daily / weekly seasonal lags. When there is slight under-coverage but sufficient correlation maintenance, it is preferable to increase... Instead of readjusting the block length, the interval should be expanded outwards to avoid disrupting the peak and trough structure.

[0076] This step generates a monitoring baseline and reassessment trigger conditions during the operational period while outputting stability conclusions. The monitoring baseline is derived from the critical quantiles and standard deviations of a mixed distribution and mapped to a control band rolling over a unified time base; the trigger conditions are determined by coverage deviation, , and The out-of-bounds event definition, and its relationship with the data access layer version number, random seed, and segment set. With block parameters The evidence pointers are written together. In this way, if abnormal fluctuations occur during operation, the system can quickly replay to the judgment state of this step without changing the evidence chain, locate whether it is a mismatch of the coverage mechanism or a mismatch of the relevant maintenance, and then backtrack to step four or step two for correction with minimal cost.

[0077] Example 2 illustrates the application of the small-sample modeling stability assessment method based on block resampling in the financial field. Data sources include multi-source time series from both the transaction and event sides, such as minute-level market data and trading volume sequences organized with a unified time base and fixed sampling step size, order book aggregation features, fund flow indicators, and announcement streams and financial event streams aligned with the transaction calendar. First, complete integrity checks, timestamp alignment, robust repair of missing and outlier values, and dimensional unification are performed according to the criteria in Step 1. Under the same statistical scale, periods where the mean, variance, and autocorrelation structures do not undergo significant structural changes are selected as stable phases, and segment sets are formed by combining KPSS / ADF and windowed CUSUM or PELT positioning. Strong boundaries in the financial scenario are directly incorporated into the segment set to constrain subsequent block extraction and splicing. Typical strong boundaries include trading day switching, opening auction, closing settlement, midday market closure, delivery / settlement periods, before and after holidays, and before and after major announcements. To measure short-term and seasonal correlations, the correlation half-life, integral autocorrelation time, and seasonal cycles (such as intraday and intraweek cycles) consistent with business rhythms are extracted based on the autocorrelation function and mutual information spectrum during the stable phase. The random seed, algorithm version, data snapshot, and key statistical criteria are solidified to generate evidence pointers, ensuring that they are verifiable and traceable.

[0078] In step two, the average block length L is used as the unified decision metric to preferentially adopt the stationary block bootstrap (SBB). Candidate Ls are generated using integral autocorrelation time and seasonal cycles. The sample space is constructed according to the principles of intra-segment block selection, inter-segment concatenation, order preservation, and evidence traceability. The start and end points of blocks must strictly fall within the same sub-segment, prioritizing alignment with strong financial boundaries and prohibiting crossing trading days and market closure points to suppress trend leakage and structural biases caused by cross-institutional switching. The optimal L is selected from the candidate set through a dual-objective cost function of variance consistency and nominal coverage consistency. In engineering, constraints are imposed on L, which do not exceed a certain proportion of the sub-segment length and do not exceed twice the seasonal scale. When no significant correlation or seasonality is detected in the stable phase, it automatically reverts to traditional independent resampling with replacement to maintain the consistency of the closed-loop method. The metadata of the resampled blocks and the data / model version are written into the evidence pointer. The block metadata includes scale, sub-segment identifier, L, continuation probability, block start and end points, and truncation status.

[0079] In step three, resampled datasets are constructed in parallel across short, medium, and long correlation scales, and training and evaluation are repeated. The model form remains consistent with the baseline, attributing uncertainty only to resampled perturbations on the data side. For regression or ranking tasks such as quantitative stock selection or market microstructure factors, performance indicators consistent with business objectives, as well as parameter vectors and feature selection frequencies, are recorded. For classification tasks such as credit risk or anti-fraud, scalar indicators such as AUC, KS, F1, and threshold sensitivity curves are recorded. Considering the heteroscedasticity and volatility clustering of financial time series, wild / bootstrap-t reweighting mechanisms are used to construct statistics without changing the block structure, ensuring the robustness of interval estimation and standard error under conditional heteroscedasticity. Simultaneously, correlation preservation and trend leakage diagnostics are collected: the autocorrelation difference between the resampled and original sequences at key lags is compared, and the pseudo-stationary risk introduced by excessively long blocks is identified by comparing piecewise linear slopes; the metric differences of slices such as opening / midday / closing, before / after announcements, and before / after holidays are archived for subsequent arbitration.

[0080] In step four, empirical distributions are first formed at the three scales. Then, weights are constructed based on the relative merits of the cost function from step two, and a weighted mixture is performed across scales. The prediction interval, parameter interval, and performance interval are directly given from the mixed distribution. The nominal confidence interval is proportionally calibrated using empirical coverage to achieve the target coverage under the current sample size and relevant structure. Simultaneously, diagnostic quantities such as key lag autocorrelation difference, trend slope difference, and slice consistency are expected within the scale and weighted across scales to form a pseudo-stationary diagnostic score. This score is used to quantify the risk of poorly presented but unreliable results due to inappropriate blockization or cross-segment splicing. All statistics and calibration methods are consistent with those in the preceding steps and are archived in conjunction with the evidence metadata.

[0081] In step five, based on the conjunctive criteria of coverage meeting the target, correlation maintenance meeting the target, and spurious stationarity risk being controlled, engineering judgment and handling suggestions are formed: When coverage meets the target but correlation maintenance is insufficient or the spurious stationarity score exceeds the threshold, L is preferentially contracted and segments are refined to make the block start and end more closely aligned with the opening and closing windows and announcement windows; when correlation maintenance is sufficient but coverage is low, L and segments remain unchanged, and the statistical caliber of heteroscedasticity robustness is switched or enhanced and the interval half-width is expanded; when only a slight deviation occurs in individual slices, such as before or after holidays or during earnings season, the calibration is judged to be passed, the current parameters are maintained, and the online monitoring threshold and reassessment frequency are tightened during operation. Finally, the point estimate and calibration interval under the mixed distribution, cross-scale stability index, feature mixing frequency and coverage report are output, and the operation monitoring baseline and trigger conditions are generated. Together with the data / model version, segment set and block parameters, they are solidified as evidence pointers to support subsequent evidence playback and minimum cost backoff mechanism. This embodiment does not require changes to the core process and unified standards of the method. By simply mapping strong boundaries, candidate scales, and performance indicators to financial transaction and compliance scenarios, a closed loop can be completed from sample space construction, hierarchical indicator collection, cross-scale fusion to engineering judgment, proving that the method is also applicable to the financial field.

[0082] Example 3: The design of the small sample modeling stability evaluation system based on Bootstrap resampling of the present invention is based on the method in Example 1, specifically as follows... Figure 2 The following modules are shown:

[0083] Module M101: Data preprocessing and stable sample extraction module;

[0084] Specifically, it is used for: performing integrity verification and consistency processing on original multi-source time series, including timestamp alignment, robust repair of missing and outliers, and dimensional unification and standardization; jointly defining stable phases based on business rules and statistical tests; and calculating the correlation half-life based on the autocorrelation function of the stable phase. Autocorrelation time with integral Seasonal cycles are extracted using mutual information spectra or periodograms; change points are located using a joint KPSS and ADF test combined with windowed CUSUM or PELT algorithms to form segmented sets. This module uses a fixed random seed and algorithm version, persists data snapshots and key statistics, and generates uniquely indexable evidence pointers. The output of this module is a preprocessed stable-phase sample and its associated quantitative estimates, providing input for subsequent modules.

[0085] Module M102: Bootstrap sample space construction module;

[0086] It uses the average block length L as a unified decision metric and preferentially employs the stationary block bootstrap (SBB) scheme to construct the resampling sample space. Specifically, the module is used to: automatically generate candidate L values ​​based on the output of module M101; and minimize the comprehensive cost function with both variance consistency and nominal coverage consistency as dual objectives. To select the optimal block length and the corresponding continuation block probability The construction and splicing of blocks are strictly restricted to segmented sets. Within a single subsegment, prioritizing alignment with known strong boundaries; resampling is implemented following the principles of intra-segment block extraction, inter-segment concatenation, order preservation, and evidence traceability, with a fixed random seed and recording all block metadata to generate evidence pointers. This module is also responsible for automatically reverting to traditional sampling with replacement when no significant correlation is detected.

[0087] Module M103: Model training and hierarchical metric collection module;

[0088] It constructs resampling datasets in parallel across short, medium, and long correlation scales. Specifically, the module is used to: independently train the model for each resampling sequence under a unified model configuration and random seed constraints; and record the prediction output of each experiment. Parameter vector Feature subset and performance metrics The statistical construction employs mechanisms such as wild / bootstrap-t to robustly handle heteroscedasticity; the distribution of indicators is collected simultaneously at three levels: predicted output, parameters and features, and correlation and trend diagnosis, specifically including the formation of... Empirical distribution, calculation of feature selection frequency And calculate the autocorrelation difference at key lags. And the difference in trend slope. All collected indicators are associated with metadata such as scale identifiers and segment identifiers to ensure traceability.

[0089] Module M104: Stability Calculation and Coverage Calibration Module;

[0090] Its core function is to achieve intra-scale aggregation and inter-scale fusion, and to calibrate the confidence intervals. Specifically, the module is used to: first, form an empirical distribution within the scale of the results output by module M103 at the three scales; then, based on the cost function values ​​obtained from module M102... Through the weighting formula Calculate the weights for each scale, and then construct a weighted mixture distribution; based on this mixture distribution, directly provide the prediction interval, parameter interval, and performance interval; evaluate the nominal value under the mixture distribution. Interval experience coverage When the deviation exceeds At the same time, proportional calibration is performed on the interval half-width; simultaneously, the key lag autocorrelation difference, trend slope difference, and slice consistency quantity are synthesized, and the pseudo-stationary diagnostic score is calculated. The final output includes all calibrated stability metrics and related parameters.

[0091] Module M105: Stability assessment and judgment module;

[0092] As a decision engine, it makes the final determination based on the output of module M104. Specifically, this module is used to verify whether the experience coverage falls within the tolerance zone. ; Check whether the relevant retention meets the standard (i.e. and ; Determine the diagnostic score for pseudo-stationarity Whether it falls below the preset upper limit. Based on the satisfaction of these three constraints, a final judgment is given as stable pass, calibration pass, or failure, and corresponding handling suggestions or rollback optimization mechanisms are triggered. The module also generates the runtime monitoring baseline and trigger conditions, and archives all judgment conclusions, parameters, and evidence metadata.

[0093] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0094] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0095] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0096] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0097] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A small-sample modeling stability assessment method based on Bootstrap resampling, applied to the financial field, characterized by: Includes the following steps: Under a unified time base and fixed sampling step size, the raw time series data of the financial transaction side and the event side are preprocessed and stable phases are identified to obtain relevant structural information of the stable phase. The raw time series data includes at least minute-level market data and trading volume series, order book aggregation features, fund flow indicators, and announcement streams or financial report event streams aligned with the trading calendar. Based on the relevant structural information of the stable phase, the following are identified as strong boundaries and segmented sets: trading day switching, opening auction, midday break, closing clearing, delivery or settlement period, before and after holidays, and before and after major announcements. The average block length is used as the decision quantity, and variance consistency and nominal coverage consistency are the dual objectives. The optimal average block length is selected by minimizing the comprehensive cost function. Based on this, a resampling sample space based on the Bootstrap of stable blocks is constructed according to the principles of intra-segment block extraction, inter-segment splicing and order preservation, and prohibition of blocks from crossing the strong boundaries. Resampling and model training were performed around at least two different correlation scales, and stratified statistics of predicted output, model parameters and diagnostic indicators were collected. The stratified statistics under different correlation scales are weighted and fused to form a mixed distribution. The confidence intervals obtained based on the mixed distribution are calibrated by empirical coverage, and the key lag autocorrelation difference, trend slope difference and slice consistency quantity are synthesized to calculate the pseudo-stationary diagnostic score. Based on the calibrated confidence interval coverage, relevant structure preservation, and pseudo-stationarity diagnostic score, an engineered judgment result on model stability is output, and a backoff optimization mechanism is triggered according to the judgment result to automate the computer modeling process.

2. The method for evaluating the stability of small-sample modeling based on Bootstrap resampling according to claim 1, characterized in that: Preprocessing the raw time series data and identifying stable phases includes: aligning timestamps on a unified time base according to the trading calendar, robustly repairing missing and outlier values, and unifying dimensions; calculating the autocorrelation function of the stable phase to obtain the correlation half-life and integral autocorrelation time; extracting seasonal cycles using mutual information spectra or periodograms; and locating change points using a combination of KPSS and ADF joint tests and windowed CUSUM or PELT algorithms to form a segmented set.

3. The method for evaluating the stability of small-sample modeling based on Bootstrap resampling according to claim 1, characterized in that: Constructing a resampling sample space based on a stable block Bootstrap involves: strictly restricting the construction and splicing of blocks to a single sub-segment of the segment set obtained through variable point positioning, and prioritizing the alignment of the start and end positions of blocks with strong boundaries, which at least include trading day switching, opening auction, midday break, closing clearing, settlement or delivery periods, before and after holidays, and before and after major announcements; when no significant correlation or seasonality is detected during the stable phase, it automatically reverts to traditional independent resampling with replacement.

4. The method for evaluating the stability of small-sample modeling based on Bootstrap resampling according to claim 1, characterized in that: Resampling is performed around at least two different correlation scales, including using the optimal average block length as a mesoscale benchmark and selecting shorter and longer scales in its neighborhood, corresponding to short-term lag, dominant correlation, and intraday or weekly seasonality consistent with business rhythms, respectively.

5. The method for evaluating the stability of small-sample modeling based on Bootstrap resampling according to claim 1, characterized in that: In weighted fusion, the weights of different scales are calculated based on the comprehensive cost function value corresponding to each scale when determining the optimal average block length, and the scale with the lower cost is assigned a higher weight.

6. The method for evaluating the stability of small-sample modeling based on Bootstrap resampling according to claim 1, characterized in that: Empirical coverage calibration of the confidence interval is achieved by adjusting the half-width of the interval using a scaling factor. The scaling factor is calculated based on the deviation between the empirical coverage and the nominal coverage, so that the calibrated empirical coverage falls within a preset tolerance band.

7. The method for evaluating the stability of small-sample modeling based on Bootstrap resampling according to claim 1, characterized in that: The pseudo-stationary diagnostic score was obtained by weighted synthesis of key lag autocorrelation difference, trend slope difference, and slice consistency.

8. The method for evaluating the stability of small-sample modeling based on Bootstrap resampling according to claim 1, characterized in that: The engineering determination of model stability includes: when the empirical coverage falls into the preset tolerance zone, the autocorrelation difference at the key lag is lower than the preset threshold, and the pseudo-stationary diagnostic score is lower than the preset upper bound, it is determined to be stable; otherwise, a rollback optimization mechanism is triggered, which includes adjusting the optimal average block length, refining the segment set, or switching the heteroscedasticity robustness processing method.

9. The method for evaluating the stability of small-sample modeling based on Bootstrap resampling according to claim 8, characterized in that: The rollback optimization mechanism makes targeted adjustments based on the judgment conditions that are not met: when the correlation maintenance is not up to standard or the pseudo-stationary diagnostic score exceeds the threshold, the average block length is reduced and the alignment of the block start and end with the strong boundary is strengthened. The strong boundary includes at least the trading day switch, opening auction, midday break and closing settlement; when the coverage is low but the correlation maintenance is up to standard, the block length and segmentation remain unchanged, the heteroscedasticity robustness mechanism is switched or strengthened and the interval half-width is expanded.

10. A small-sample modeling stability evaluation system based on Bootstrap resampling, characterized in that, The evaluation system is used to implement the method according to any one of claims 1-9, and includes the following modules: The data preprocessing and stable sample extraction module is used to preprocess the original time series data and identify stable phases under a unified time base and fixed sampling step size, so as to obtain the relevant structural information of the stable phase. The Bootstrap sample space construction module is used to construct a resampling sample space based on the relevant structural information of the stable phase, with the average block length as the decision quantity and variance consistency and nominal coverage consistency as dual objectives. It selects the optimal average block length by minimizing the comprehensive cost function, and constructs the resampling sample space based on the Bootstrap of the stationary block according to the principles of intra-segment block extraction, inter-segment concatenation and order preservation. The model training and stratified index collection module is used to resample and train the model around at least two different correlation scales, and to collect stratified statistics of predicted output, model parameters and diagnostic indicators. The stability calculation and coverage calibration module is used to weight and fuse stratified statistics under different correlation scales to form a mixed distribution, perform empirical coverage calibration on the confidence intervals obtained based on the mixed distribution, and synthesize key lag autocorrelation difference, trend slope difference and slice consistency quantity to calculate pseudo-stationary diagnostic score. The stability assessment and judgment module is used to output an engineered judgment result on the stability of the model based on the calibrated confidence interval coverage, the relevant structure retention, and the pseudo-stationarity diagnostic score. Based on the judgment result, a backoff optimization mechanism is triggered to automate the computer modeling process.

Images