Theoretically consistent time variable parameter autoregression inflation rate prediction method

Abstract

The invention provides a theoretically consistent time variable parameter autoregressive inflation rate prediction method, and aims at providing an improved time variable parameter distribution vector autoregressive model (TC-TVP-DVAR) for overcoming the defects of an existing economic prediction model in the aspects of dynamics, uncertainty and theoretical consistency. By introducing theoretical consistency priori, reinforcement learning driven adaptive parameter optimization mechanism and high-dimensional distribution feature modeling, the method can dynamically capture the change trend of the inflation rate, and effectively model and quantify tail risks under different economic conditions. Specifically, according to the method, time-varying parameters and high-dimensional distribution modeling are combined, and the dynamic relation of economic variables is described; self-adaptive parameter optimization is realized by utilizing reinforcement learning; and the uncertainty is quantified through Bayesian inference, so that the prediction precision and stability of the model are remarkably improved. The method has theoretical consistency and high robustness, and a more reliable tool with explanatory force is provided for prediction of the inflation rate.

Description

Technical Field

[0001] The invention relates to forecasting inflation rate by using theoretical consistency and time-varying parameter autoregressive model, and solves the problems of dynamic modeling and tail risk characterization of macroeconomic variable forecasting by constructing multiple modules. Background Art

[0002] The current macroeconomic variable forecasting models mainly use time series methods, such as autoregression models, vector autoregression (VAR) models, and state space models. These models are used to deal with the dynamic relationship between various economic variables and analyze the changes of variables at different time points and their mutual influence. However, these models have limitations in dealing with nonlinear relationships between economic variables and tail risks under extreme economic conditions, and often only provide a single deterministic forecast result.

[0003] Uncertainty estimation is an important indicator in economic forecasting and decision support, which usually includes the inherent uncertainty of the model itself and the randomness introduced by the data. Current methods usually describe the uncertainty of the model by constructing confidence intervals or adopting the probability distribution of error terms. However, these methods fail to fully capture the complex interdependence between macroeconomic variables, especially the tail risk measurement in extreme cases.

[0004] In addition, traditional forecasting methods lack the ability to model nonlinear relationships between economic variables in high-dimensional space. As the complexity of economic systems increases, the interactions between economic variables become more difficult to capture, especially when faced with extreme economic scenarios, traditional models often have difficulty providing reliable tail risk characterizations. This greatly reduces the robustness and accuracy of forecast results in response to economic crises, policy making, and other situations. At the same time, traditional models perform poorly in dealing with dynamic changes in the macroeconomic environment. The parameters of most models remain fixed after training, lack flexibility, and cannot be adjusted in real time according to new economic data, resulting in a decline in the model's forecasting performance when the economic environment changes.

[0005] Therefore, there is an urgent need for a forecasting model that can simultaneously capture the complex dynamic nonlinear relationship between macroeconomic variables, effectively deal with tail risks, and have dynamic adaptability, so as to improve the accuracy and robustness of inflation rate forecasts. Summary of the invention

[0006] In view of the shortcomings and challenges of existing macroeconomic variable prediction models, this paper proposes a theoretically consistent time-varying parameter autoregressive inflation rate prediction method (TC-TVP-DVAR). TC-TVP-DVAR captures the dynamic changes of macroeconomic variables by constructing a time-varying parameter autoregressive module, combines a theoretical consistency prior module to ensure that parameter estimation conforms to economic theory, introduces a high-dimensional distribution modeling module to characterize the distribution characteristics of economic variables at different time points, and uses an adaptive parameter optimization module to optimize model parameters in real time. Finally, the credibility of the prediction results is quantified through an uncertainty quantification module, thereby improving the accuracy and robustness of the prediction.

[0007] A method for predicting inflation rate using time-varying autoregressive parameters consistent with theory of the present invention comprises the following steps:

[0008] S1: The present invention proposes a theoretically consistent time-varying parameter autoregressive TC-TVP-DVAR model for predicting inflation rate, which includes the following components:

[0009] The time-varying parameter autoregression module dynamically captures the changes in macroeconomic variables based on time series data and uses the time-varying parameter method to model the dynamic characteristics of the variables to describe the long-term trend of the inflation rate;

[0010] The theoretical consistency prior module combines the recognized constraints in economic theory to impose a priori constraints on the time-varying parameter model. Through the theoretical consistency prior, the parameter estimation in the model is more reasonable and consistent with the economic explanation, which helps to improve the reliability and interpretability of the model;

[0011] High-dimensional distribution modeling module, which is used to perform high-dimensional modeling of the distribution characteristics of macroeconomic variables at different time points. It introduces a distribution embedding layer and an adaptive weight adjustment mechanism to capture the distribution characteristics of the inflation rate and its changes under extreme economic conditions, and improve the overall forecasting ability of inflation.

[0012] The adaptive parameter optimization module, based on the reinforcement learning mechanism, performs real-time adaptive updates on the weights of various macro variables. Through historical data feedback, it continuously optimizes the weights of parameters to ensure that the model can respond flexibly in different economic cycles and improve the accuracy of predictions.

[0013] The uncertainty quantification module embeds the Bayesian inference mechanism in the model, quantifies the uncertainty of the predicted value output by the model, provides prediction credibility analysis, and enables the model to identify and quantify the uncertainty factors in the prediction, thereby improving the stability of the overall prediction.

[0014] S2: Based on the time-varying parameter autoregressive module, combined with the theoretical consistency prior module, the dynamic relationship between macroeconomic variables is established; the dynamic changes between variables are captured through time-varying parameters, and the parameters are ensured to be consistent with economic theory through theoretical prior constraints, which enhances the explanatory power of the model and completes the reasonable modeling of the relationship between variables;

[0015] S3: After the dynamic relationship is established, the high-dimensional distribution modeling module is used to comprehensively model the distribution characteristics of various economic variables, so as to capture the complex changes of inflation rate under different economic scenarios. This module can refine the model's understanding of economic fluctuations, especially the accurate characterization of tail risks under extreme economic conditions;

[0016] S4: Based on the high-dimensional distribution modeling results, the adaptive parameter optimization module is used to further dynamically optimize the model parameters. The reinforcement learning mechanism dynamically adjusts the weights of each macro variable through real-time feedback, so that the model can flexibly respond to the changing economic background and improve the overall prediction accuracy;

[0017] S5: In the model output stage, combined with the uncertainty quantification module, the credibility of each prediction output is quantitatively evaluated through Bayesian inference, and the quantitative results are fed back to the parameter optimization module, so that the model can dynamically identify and reduce the uncertainty in the prediction, thereby improving the robustness of the overall model and the reliability of the prediction results;

[0018] S6: Finally, by designing a multi-objective loss function, we jointly optimize the accuracy of time-varying parameter estimation, the goodness of fit of high-dimensional distribution modeling, and the confidence level of uncertainty quantification. During model training, we ensure that multiple objectives are optimized in a balanced manner, so that an effective combination is formed between the modules, further improving the accuracy and stability of inflation rate forecasts.

[0019] According to a specific implementation of the embodiment of the present invention, the specific steps of S2 are:

[0020] S21: Construction of a time-varying parameter autoregressive model. A time-varying parameter autoregressive model is constructed to describe the dynamic impact of macroeconomic variables (interest rates, money supply, unemployment rate, etc.) on the inflation rate. The mathematical expression of the model is:

[0021] y t =X t β t +ε t

[0022] Among them, y t represents the target variable inflation rate at time t; X t represents the input feature matrix at time t, including macroeconomic variables; β trepresents the time-varying parameter vector, which represents the dynamic impact of each economic variable at time t; ε t is the error term, which is assumed to have a mean of 0 and a variance of σ 2 Normal distribution of

[0023] S22: Introduction of theoretical consistency priors to ensure that the time-varying parameter β t In line with the rationality of economic theory, the theoretical consistency prior distribution P(β t ); Theoretical consistency prior is based on constraints in economics, such as the impact of interest rates on inflation should be negative: β1<0, and the Bayesian method is used to estimate time-varying parameters. The update formula of the posterior distribution is:

[0024] P(β t |y t ,X t )∝P(y t |X t ,β t )P(β t )

[0025] Among them, P(β t |y t ,X t ) represents the posterior distribution of the time-varying parameter; P(y t |X t ,β t ) represents the likelihood function, which indicates the probability of observing data under given parameters and input features; P(β t ) represents the theoretical consistency prior distribution, which is used to constrain the reasonable range of parameters;

[0026] Choice of prior distribution: theoretical consistency: a priori choose normal distribution or other distribution forms that are consistent with economic theory;

[0027] Selection basis: The normal distribution is suitable for modeling the fluctuations of most economic variables, but for scenarios where extreme values ​​may exist, the heavy-tailed t distribution can be selected to cope with the impact of extreme values;

[0028] S23: Bayesian update of parameters using observed data y t And the input feature matrix X t , by maximizing the posterior distribution P(β t |y t ,X t ) to get the updated time-varying parameters:

[0029]

[0030] in, Denotes the updated time-varying parameters. In order to perform Bayesian update of parameters, variational inference is used to approximate the posterior distribution to improve computational efficiency. Variational inference transforms the complex posterior distribution into a solvable optimization problem, making parameter estimation more accurate and efficient. In variational inference, a tractable distribution q(β t ) to approximate the true posterior distribution P(β t |y t ,X t ). Optimize q(β) by minimizing the Kullback-Leibler (KL) divergence between the two t ),Right now:

[0031]

[0032] Among them, KL divergence measures the difference between two probability distributions. Minimizing this divergence means that q(β t ) is as close to the true posterior distribution as possible;

[0033] By optimizing the variational lower bound ELBO, we find a parameterized form that can effectively approximate the posterior distribution, making the calculation more feasible. The updated parameters will be verified for theoretical consistency in S24 to ensure that they meet the economic constraints.

[0034] S24: Theoretical consistency verification, verifying the updated time-varying parameters Whether the theoretical consistency constraint is met, for the interest rate parameter β1, it should satisfy: β1<0; if not, it is necessary to return to S22 or S23 to readjust the prior distribution and perform iterative updates;

[0035] S25: Establishment of dynamic relationship: after the time-varying parameter estimation is completed, the updated parameters are used Establish the dynamic relationship between macroeconomic variables; this dynamic relationship describes the impact of macroeconomic variables on inflation rate at different time points, ensuring the rationality and interpretability of the model in a dynamic environment; mathematical representation of the dynamic relationship:

[0036]

[0037] in, represents the updated time-varying parameter at time t+1; X t+1 Represents the input feature matrix at time t+1. Implementation details of dynamic relations: updated time-varying parameters The results will be dynamically updated based on the parameters at the previous time point to capture the time-varying characteristics of macroeconomic variables, so that the model can maintain rationality and accuracy in different economic environments. Through such dynamic adjustments, the model can take into account historical information and current economic conditions at each time step to ensure the stability and reliability of the forecast results.

[0038] Model rationality guarantee: When making the next prediction, the model will use the parameter update results of the historical time point and ensure a smooth transition of the parameters through the weighted average method to avoid prediction errors caused by sudden changes.

[0039] According to a specific implementation of the embodiment of the present invention, the specific steps of S3 are:

[0040] S31: Extract high-dimensional distribution features. Extract high-dimensional distribution features of historical data of each economic variable and construct feature embedding vectors. Assume that the input feature matrix is ​​X t , perform high-dimensional feature embedding and obtain the embedding vector Z t , the mathematical expression of high-dimensional embedding is:

[0041] Z t =f embed (X t )

[0042] Among them, f embed Represents a high-dimensional feature embedding function, which is used to map the input feature matrix into a high-dimensional space. t The embedding vector representing time t contains the high-dimensional representation of the input features; the specific implementation of the high-dimensional feature embedding function is:

[0043] High-dimensional feature embedding function f embed The deep neural network DNN is used for implementation; specifically, the function contains multiple layers of fully connected layers, each of which is accompanied by a nonlinear activation function ReLU to enhance the nonlinear expression ability of the features; the mathematical expression is:

[0044] Z t =f embed (X t )=φ L (φ L-1 (…φ1(X t W1+b1)…)W L-1 +b L-1 )W L +b L

[0045] Among them, φ i represents the activation function of the i-th layer, ReLU function: φ(x)=max(0,x); W i and b iRepresent the weight matrix and bias vector of the i-th layer respectively, L represents the total number of layers, and the final Z t It is a high-dimensional embedding vector after multi-layer mapping;

[0046] S32: Distribution modeling, using high-dimensional embedding vectors Z t Model the distribution of economic variables at different time points; by introducing a distribution embedding layer, capture the distribution characteristics of economic variables in high-dimensional space and establish the correlation between economic variables;

[0047] The mathematical expression of the modeling process is:

[0048] P(Y t |Z t ) = g dist (Z t )

[0049] Among them, P(Y t |Z t ) represents the given embedding vector Z t The target variable Y under the condition t The distribution of g dist Represents the distribution modeling function, which is used to describe the impact of high-dimensional embedding vectors on the target variable;

[0050] S33: Tail risk characterization, characterizing tail risks under extreme economic conditions, ensuring the robustness of the model under different economic scenarios, using the tail characteristics of the distribution to quantify risks, especially modeling possible extreme situations in high-dimensional space;

[0051] The mathematical expression of risk characterization is:

[0052] R t =h tail (Z t )

[0053] Among them, R t represents the tail risk measure at time t, h tail represents the tail risk characterization function, which is used to describe the extreme risk characteristics in the embedded vector;

[0054] S34: Dynamic update of distribution characteristics

[0055] As time goes by, the economic scenario may change, so it is necessary to dynamically update the high-dimensional distribution features. At each time step t, according to the new input feature matrix X t+1 For the high-dimensional embedding vector Z t+1 Updates are made to ensure that the model can capture changes in economic scenarios in real time;

[0056] Z t+1 =fembed (X t+1 )

[0057] According to a specific implementation of the embodiment of the present invention, the specific steps of S4 are:

[0058] S41: Introduction of reinforcement learning mechanism The reinforcement learning mechanism is used to optimize the weights of time-varying parameters in real time, making the model flexible in different economic environments; suppose state S t Represents the economic environment at time t, including high-dimensional distribution characteristics Z t and the current parameter value, reinforcement learning is done through the strategy function π(S t ) Dynamically adjust model parameters to maximize the objective function;

[0059] S42: Definition of immediate reward function, define the immediate reward function R t , used to measure the economic environment S t The model prediction effect under . The immediate reward function is defined as:

[0060]

[0061] in, Represents the loss function, used to calculate the predicted value and the true value y t The goal of the reward function is to minimize the prediction error and thus maximize the immediate reward;

[0062] S43: Strategy update and parameter optimization, using the policy gradient method in reinforcement learning to update the policy function π(S t ) is optimized, and the mathematical expression of parameter update is:

[0063]

[0064] Among them, θ t Represents the model parameters at time t; α represents the learning rate, which is used to control the step size of the update; Represents the gradient of the immediate reward, which is used to guide the direction of parameter optimization;

[0065] S44: Weight adaptive adjustment: At each time step t, the reinforcement learning mechanism adaptively adjusts the weights of each macro variable according to the current economic environment and reward function; through the strategy function π(S t ) outputs the optimal weight combination β t , the model can optimize the influence of each variable; the optimal weight combination β t Represents the dynamic weight of each macro variable, which is determined by the policy function according to the current state S tIt is calculated based on historical feedback data, so as to achieve precise control of the influence of each variable;

[0066] S45: Continuous iteration of dynamic optimization. The dynamic optimization process of the reinforcement learning mechanism is continuously iterative. Each input of new economic data will trigger the re-optimization of parameters. The continuous iterative optimization process enables the model to adapt to changes in the economic environment in real time, ensuring high prediction accuracy in a constantly changing context.

[0067] According to a specific implementation of the embodiment of the present invention, the specific steps of S5 are:

[0068] S51: Introduction of Bayesian inference, output for each prediction To quantify uncertainty, use the Bayesian inference method to obtain the credible interval of the predicted distribution. Indicates that given the input feature matrix X t and the time-varying parameter β t The goal of Bayesian inference is to quantify the uncertainty of the prediction by calculating the variance of the predicted distribution.

[0069] S52: Uncertainty quantification, prediction output To quantify uncertainty, we calculate the mean and variance of the posterior distribution to obtain a credible interval for the prediction:

[0070]

[0071] in, represents the mean of the prediction distribution, representing the most likely prediction value, Represents the variance of the prediction distribution, quantifying the uncertainty of the prediction results;

[0072] S53: Credibility assessment based on posterior distribution Calculate the credibility of the predicted output and obtain the predicted credible interval The credible interval is used to measure the prediction stability of the model in the current economic environment;

[0073] S54: The quantification results are fed back to the parameter optimization module to quantify the uncertainty results Feedback to the adaptive parameter optimization module to guide the model's parameter adjustment in subsequent steps. For predictions with large variance, the reinforcement learning mechanism will increase attention to the corresponding variables and reduce uncertainty by adjusting weights;

[0074] S55: Dynamic identification and reduction of uncertainty. At each time step t, the high uncertainty factors in the model are dynamically identified based on the uncertainty quantification results. The weights of the high uncertainty factors are adjusted through the adaptive parameter optimization module, thereby reducing the uncertainty in the prediction and improving the overall robustness of the model and the reliability of the prediction.

[0075] According to a specific implementation of the embodiment of the present invention, the specific steps of S6 are:

[0076] S61: Construction of a multi-objective loss function. A loss function containing multiple optimization objectives is constructed to jointly optimize various parts of the model. The mathematical expression of the multi-objective loss function is:

[0077] L=λ1L param +λ2L dist +λ3L uncertainty

[0078] Among them, L param Represents the loss function of time-varying parameter estimation, which measures the accuracy of the model in time-varying parameter estimation. dist Represents the loss function of high-dimensional distribution modeling, which measures the model's fit in capturing the distribution characteristics of economic variables. uncertainty represents the loss function for uncertainty quantification, which measures the confidence level of the predicted distribution. λ1,λ2,λ3 represent the weight coefficients of the loss function, which are used to control the importance of each objective in the joint optimization.

[0079] S62: Weight adjustment of loss function. During the model training process, according to the optimization requirements of each target, the weight coefficients λ1, λ2, λ3 of the loss function are dynamically adjusted to ensure balanced optimization of the model at different training stages. The mathematical expression of weight adjustment is:

[0080]

[0081] in, represents the weight of the loss function at time step t, α represents the learning rate, which is used to control the step size of weight adjustment, Represents the gradient of the loss function with respect to the weight;

[0082] S63: Joint optimization process, the multi-objective loss function is optimized by gradient descent method, and the model parameters are jointly updated so that each module can work together under the same optimization goal. The parameters of the time-varying parameter estimation module, the high-dimensional distribution modeling module and the uncertainty quantification module are jointly updated during the optimization process. The specific parameter update formula is:

[0083]

[0084] Among them, θ trepresents all model parameters at time step t, including time-varying parameters, high-dimensional embedding parameters, and uncertainty quantization parameters. η represents the learning rate, which is used to control the step size of parameter update. Represents the effective combination of multi-objective loss functions between model modules: ensuring that the time-varying parameter estimation, high-dimensional distribution modeling, and uncertainty quantification modules cooperate with each other in the joint optimization process to form an effective combination. The embedding result Z of the high-dimensional distribution modeling module t As the input of the time-varying parameter estimation module, the consistency of embedded features is maintained during the optimization process. The feedback results of the uncertainty quantification module are used to guide the adjustment of time-varying parameters. The reinforcement learning mechanism dynamically adjusts the weights of each macro variable according to the uncertainty quantification results. Through multi-objective optimization, the data flow between modules is smooth, information sharing is sufficient, and a unified prediction framework is formed.

[0085] S65: Evaluation and verification of forecast results: Evaluate the forecast results of the jointly optimized model, verify its accuracy and stability in inflation rate forecasting, and evaluate the forecasting effect of the model under different economic backgrounds by comparing with historical data. Specifically: Use indicators such as mean square error (MSE) and root mean square error (RMSE) to evaluate the deviation between the forecast value and the actual value:

[0086]

[0087] Among them, y i represents the actual value at the i-th time point, represents the predicted value at the i-th time point, and N represents the number of predicted time points. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 Flow chart of the basic steps of the TC-TVP-DVAR model of this method

[0089] Figure 2 Basic flow chart of the TC-TVP-DVAR model of this method

[0090] Figure 3 High-dimensional distribution modeling architecture diagram for this method DETAILED DESCRIPTION

[0091] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below with reference to examples and drawings.

[0092] As attached Figure 1 As shown, a theoretically consistent method for predicting inflation rate with time-varying parameter autoregression of the present invention comprises the following steps:

[0093] S1: The present invention proposes a theoretically consistent time-varying parameter autoregressive TC-TVP-DVAR model for predicting inflation rate, which includes the following components:

[0094] The time-varying parameter autoregression module dynamically captures the changes in macroeconomic variables based on time series data and uses the time-varying parameter method to model the dynamic characteristics of the variables to describe the long-term trend of the inflation rate;

[0095] The theoretical consistency prior module combines the recognized constraints in economic theory to impose a priori constraints on the time-varying parameter model. Through the theoretical consistency prior, the parameter estimation in the model is more reasonable and consistent with the economic explanation, which helps to improve the reliability and interpretability of the model;

[0096] High-dimensional distribution modeling module, which is used to perform high-dimensional modeling of the distribution characteristics of macroeconomic variables at different time points. It introduces a distribution embedding layer and an adaptive weight adjustment mechanism to capture the distribution characteristics of the inflation rate and its changes under extreme economic conditions, and improve the overall forecasting ability of inflation.

[0097] The adaptive parameter optimization module, based on the reinforcement learning mechanism, performs real-time adaptive updates on the weights of various macro variables. It continuously optimizes the parameter weights through historical data feedback to ensure that the model can respond flexibly in different economic cycles and improve the accuracy of predictions.

[0098] The uncertainty quantification module embeds the Bayesian inference mechanism in the model, quantifies the uncertainty of the predicted value output by the model, provides prediction credibility analysis, and enables the model to identify and quantify the uncertainty factors in the prediction, thereby improving the stability of the overall prediction.

[0099] S2: Based on the time-varying parameter autoregressive module, combined with the theoretical consistency prior module, the dynamic relationship between macroeconomic variables is established; the dynamic changes between variables are captured through time-varying parameters, and the parameters are ensured to be consistent with economic theory through theoretical prior constraints, which enhances the explanatory power of the model and completes the reasonable modeling of the relationship between variables;

[0100] S3: After the dynamic relationship is established, the high-dimensional distribution modeling module is used to comprehensively model the distribution characteristics of various economic variables, so as to capture the complex changes of inflation rate under different economic scenarios. This module can refine the model's understanding of economic fluctuations, especially the accurate characterization of tail risks under extreme economic conditions;

[0101] S4: Based on the high-dimensional distribution modeling results, the adaptive parameter optimization module is used to further dynamically optimize the model parameters. The reinforcement learning mechanism dynamically adjusts the weights of each macro variable through real-time feedback, so that the model can flexibly respond to the changing economic background and improve the overall prediction accuracy;

[0102] S5: In the model output stage, combined with the uncertainty quantification module, the credibility of each prediction output is quantitatively evaluated through Bayesian inference, and the quantitative results are fed back to the parameter optimization module, so that the model can dynamically identify and reduce the uncertainty in the prediction, thereby improving the robustness of the overall model and the reliability of the prediction results;

[0103] S6: Finally, by designing a multi-objective loss function, we jointly optimize the accuracy of time-varying parameter estimation, the goodness of fit of high-dimensional distribution modeling, and the confidence level of uncertainty quantification. During model training, we ensure that multiple objectives are optimized in a balanced manner, so that an effective combination is formed between the modules, further improving the accuracy and stability of inflation rate forecasts.

[0104] According to a specific implementation of the embodiment of the present invention, the specific steps of S2 are:

[0105] S21: Construction of a time-varying parameter autoregressive model. A time-varying parameter autoregressive model is constructed to describe the dynamic impact of macroeconomic variables (interest rates, money supply, unemployment rate, etc.) on the inflation rate. The mathematical expression of the model is:

[0106] y t =X t β t +ε t

[0107] Among them, y t represents the target variable inflation rate at time t; X t represents the input feature matrix at time t, including macroeconomic variables; β t represents the time-varying parameter vector, which represents the dynamic impact of each economic variable at time t; ε t is the error term, which is assumed to have a mean of 0 and a variance of σ 2 Normal distribution of

[0108] S22: Introduction of theoretical consistency priors to ensure that the time-varying parameter β t In line with the rationality of economic theory, the theoretical consistency prior distribution P(β t ); Theoretical consistency prior is based on the constraints in economics. The impact of interest rates on inflation should be negative: β1<0. The Bayesian method is used to estimate the time-varying parameters. The update formula of the posterior distribution is:

[0109] P(β t |y t ,X t )∝P(y t |X t ,β t )P(βt )

[0110] Among them, P(β t |y t ,X t ) represents the posterior distribution of the time-varying parameter; P(y t |X t ,β t ) represents the likelihood function, which indicates the probability of observing data under given parameters and input features; P(β t ) represents the theoretical consistency prior distribution, which is used to constrain the reasonable range of parameters;

[0111] Choice of prior distribution: theoretical consistency: a priori choose normal distribution or other distribution forms that are consistent with economic theory;

[0112] Selection basis: The normal distribution is suitable for modeling the fluctuations of most economic variables, but for scenarios where extreme values ​​may exist, the heavy-tailed t distribution can be selected to cope with the impact of extreme values;

[0113] S23: Bayesian update of parameters using observed data y t And the input feature matrix X t , by maximizing the posterior distribution P(β t |y t ,X t ) to get the updated time-varying parameters:

[0114]

[0115] in, Denotes the updated time-varying parameters. In order to perform Bayesian update of parameters, variational inference is used to approximate the posterior distribution to improve computational efficiency. Variational inference transforms the complex posterior distribution into a solvable optimization problem, making parameter estimation more accurate and efficient. In variational inference, a tractable distribution q(β t ) to approximate the true posterior distribution P(β t |y t ,X t ), optimize q(β t ),Right now:

[0116]

[0117] Among them, KL divergence measures the difference between two probability distributions. Minimizing this divergence means that q(β t ) is as close to the true posterior distribution as possible;

[0118] By optimizing the variational lower bound ELBO, we find a parameterized form that can effectively approximate the posterior distribution, making the calculation more feasible. The updated parameters will be verified for theoretical consistency in S24 to ensure that they meet the economic constraints.

[0119] S24: Theoretical consistency verification, verifying the updated time-varying parameters Whether the theoretical consistency constraint is met, for the interest rate parameter β1, it should satisfy: β1<0; if not, it is necessary to return to S22 or S23 to readjust the prior distribution and perform iterative updates;

[0120] S25: Establishment of dynamic relationship: after the time-varying parameter estimation is completed, the updated parameters are used Establish the dynamic relationship between macroeconomic variables; this dynamic relationship describes the impact of macroeconomic variables on inflation rate at different time points, ensuring the rationality and interpretability of the model in a dynamic environment; mathematical representation of the dynamic relationship:

[0121]

[0122] in, represents the updated time-varying parameter at time t+1; X t+1 Represents the input feature matrix at time t+1; implementation details of dynamic relationships: updated time-varying parameters The results will be dynamically updated based on the parameters at the previous time point to capture the time-varying characteristics of macroeconomic variables, so that the model can maintain rationality and accuracy in different economic environments. Through such dynamic adjustments, the model can take into account historical information and current economic conditions at each time step to ensure the stability and reliability of the forecast results.

[0123] Model rationality guarantee: When making the next prediction, the model will use the parameter update results of the historical time point and ensure a smooth transition of the parameters through the weighted average method to avoid prediction errors caused by sudden changes.

[0124] As attached Figure 3 As shown, according to a specific implementation of an embodiment of the present invention, the specific steps of S3 are:

[0125] S31: Extract high-dimensional distribution features. Extract high-dimensional distribution features of historical data of each economic variable and construct feature embedding vectors. Assume that the input feature matrix is ​​X t , perform high-dimensional feature embedding and obtain the embedding vector Z t ;

[0126] The mathematical expression of high-dimensional embedding is:

[0127] Z t =fembed (X t )

[0128] Among them, f embed Represents a high-dimensional feature embedding function, which is used to map the input feature matrix into a high-dimensional space; Z t The embedding vector representing time t contains a high-dimensional representation of the input features;

[0129] High-dimensional feature embedding function f embed The deep neural network DNN is used for implementation; specifically, the function contains multiple layers of fully connected layers, each of which is accompanied by a nonlinear activation function ReLU to enhance the nonlinear expression ability of the features; the mathematical expression is:

[0130] Z t =f embed (X t )=φ L (φ L-1 (…φ1(X t W1+b1)…)W L-1 +b L-1 )W L +b L

[0131] Among them, φ i represents the activation function of the i-th layer, ReLU function: φ(x)=max(0,x); W i and b i Represent the weight matrix and bias vector of the i-th layer respectively, L represents the total number of layers, and the final Z t It is a high-dimensional embedding vector after multi-layer mapping;

[0132] S32: Distribution modeling, using high-dimensional embedding vectors Z t Model the distribution of economic variables at different time points; by introducing a distribution embedding layer, capture the distribution characteristics of economic variables in high-dimensional space and establish the correlation between economic variables;

[0133] The mathematical expression of the modeling process is:

[0134] P(Y t |Z t ) = g dist (Z t )

[0135] Among them, P(Y t |Z t ) represents the given embedding vector Z t The target variable Y under the condition t The distribution of g dist Represents the distribution modeling function, which is used to describe the impact of high-dimensional embedding vectors on the target variable;

[0136] S33: Tail risk characterization, characterizing tail risks under extreme economic conditions, ensuring the robustness of the model under different economic scenarios, using the tail characteristics of the distribution to quantify risks, especially modeling possible extreme situations in high-dimensional space;

[0137] The mathematical expression of risk characterization is:

[0138] R t =h tail (Z t )

[0139] Among them, R t represents the tail risk measure at time t, h tail represents the tail risk characterization function, which is used to describe the extreme risk characteristics in the embedded vector;

[0140] S34: Dynamic update of distribution features. As time goes by, the economic scenario may change. Therefore, it is necessary to dynamically update the high-dimensional distribution features. At each time step t, according to the new input feature matrix X t+1 For the high-dimensional embedding vector Z t+1 Updates are made to ensure that the model can capture changes in economic scenarios in real time;

[0141] Z t+1 =f embed (X t+1 )

[0142] According to a specific implementation of the embodiment of the present invention, the specific steps of S4 are:

[0143] S41: Introduction of reinforcement learning mechanism The reinforcement learning mechanism is used to optimize the weights of time-varying parameters in real time, making the model flexible in different economic environments; suppose state S t Represents the economic environment at time t, including high-dimensional distribution characteristics Z t and the current parameter value, reinforcement learning is done through the strategy function π(S t ) Dynamically adjust model parameters to maximize the objective function;

[0144] S42: Definition of immediate reward function, define the immediate reward function R t , used to measure the economic environment S t The model prediction effect under this condition; the immediate reward function is defined as:

[0145]

[0146] in, Represents the loss function, used to calculate the predicted value and the true value yt The goal of the reward function is to minimize the prediction error and thus maximize the immediate reward;

[0147] S43: Strategy update and parameter optimization, using the policy gradient method in reinforcement learning to update the policy function π(S t ) is optimized, and the mathematical expression of parameter update is:

[0148]

[0149] Among them, θ t Represents the model parameters at time t; α represents the learning rate, which is used to control the step size of the update; Represents the gradient of the immediate reward, which is used to guide the direction of parameter optimization;

[0150] S44: Weight adaptive adjustment: At each time step t, the reinforcement learning mechanism adaptively adjusts the weights of each macro variable according to the current economic environment and reward function; through the strategy function π(S t ) outputs the optimal weight combination β t , the model can optimize the influence of each variable; the optimal weight combination β t Represents the dynamic weight of each macro variable, which is determined by the policy function according to the current state S t It is calculated based on historical feedback data, so as to achieve precise control of the influence of each variable;

[0151] S45: Continuous iteration of dynamic optimization. The dynamic optimization process of the reinforcement learning mechanism is continuously iterative. Each input of new economic data will trigger the re-optimization of parameters. The continuous iterative optimization process enables the model to adapt to changes in the economic environment in real time, ensuring high prediction accuracy in a constantly changing context.

[0152] According to a specific implementation of the embodiment of the present invention, the specific steps of S5 are:

[0153] S51: Introduction of Bayesian inference, output for each prediction To quantify uncertainty, use the Bayesian inference method to obtain the credible interval of the predicted distribution. Indicates that given the input feature matrix X t and the time-varying parameter β t The goal of Bayesian inference is to quantify the uncertainty of the prediction by calculating the variance of the predicted distribution.

[0154] S52: Uncertainty quantification, prediction output To quantify uncertainty, we calculate the mean and variance of the posterior distribution to obtain a credible interval for the prediction:

[0155]

[0156] in, represents the mean of the prediction distribution, representing the most likely prediction value, Represents the variance of the prediction distribution, quantifying the uncertainty of the prediction results;

[0157] S53: Credibility assessment based on posterior distribution Calculate the credibility of the predicted output and obtain the predicted credible interval The credible interval is used to measure the prediction stability of the model in the current economic environment;

[0158] S54: The quantification results are fed back to the parameter optimization module to quantify the uncertainty results Feedback to the adaptive parameter optimization module to guide the model's parameter adjustment in subsequent steps. For predictions with large variance, the reinforcement learning mechanism will increase attention to the corresponding variables and reduce uncertainty by adjusting weights;

[0159] S55: Dynamic identification and reduction of uncertainty. At each time step t, the high uncertainty factors in the model are dynamically identified based on the uncertainty quantification results. The weights of the high uncertainty factors are adjusted through the adaptive parameter optimization module, thereby reducing the uncertainty in the prediction and improving the overall robustness of the model and the reliability of the prediction.

[0160] According to a specific implementation of the embodiment of the present invention, the specific steps of S6 are:

[0161] S61: Construction of a multi-objective loss function. A loss function containing multiple optimization objectives is constructed to jointly optimize various parts of the model. The mathematical expression of the multi-objective loss function is:

[0162] L=λ1L param +λ2L dist +λ3L uncertainty

[0163] Among them, L param Represents the loss function of time-varying parameter estimation, which measures the accuracy of the model in time-varying parameter estimation. dist Represents the loss function of high-dimensional distribution modeling, which measures the model's fit in capturing the distribution characteristics of economic variables. uncertainty represents the loss function for uncertainty quantification, which measures the confidence level of the predicted distribution. λ1,λ2,λ3 represent the weight coefficients of the loss function, which are used to control the importance of each objective in the joint optimization.

[0164] S62: Weight adjustment of loss function. During the model training process, according to the optimization requirements of each target, the weight coefficients λ1, λ2, λ3 of the loss function are dynamically adjusted to ensure balanced optimization of the model at different training stages. The mathematical expression of weight adjustment is:

[0165]

[0166] in, represents the weight of the loss function at time step t, α represents the learning rate, which is used to control the step size of weight adjustment, Represents the gradient of the loss function with respect to the weight;

[0167] S63: Joint optimization process, the multi-objective loss function is optimized by gradient descent method, and the model parameters are jointly updated so that each module can work together under the same optimization goal. The parameters of the time-varying parameter estimation module, the high-dimensional distribution modeling module and the uncertainty quantification module are jointly updated during the optimization process. The specific parameter update formula is:

[0168]

[0169] Among them, θ t represents all model parameters at time step t, including time-varying parameters, high-dimensional embedding parameters, and uncertainty quantization parameters. η represents the learning rate, which is used to control the step size of parameter update. Represents the effective combination of multi-objective loss functions between model modules: ensuring that the time-varying parameter estimation, high-dimensional distribution modeling, and uncertainty quantification modules cooperate with each other in the joint optimization process to form an effective combination. The embedding result Z of the high-dimensional distribution modeling module t As the input of the time-varying parameter estimation module, the consistency of embedded features is maintained during the optimization process. The feedback results of the uncertainty quantification module are used to guide the adjustment of time-varying parameters. The reinforcement learning mechanism dynamically adjusts the weights of each macro variable according to the uncertainty quantification results. Through multi-objective optimization, the data flow between modules is smooth, information sharing is sufficient, and a unified prediction framework is formed.

[0170] S65: Evaluation and verification of forecast results: Evaluate the forecast results of the jointly optimized model, verify its accuracy and stability in inflation rate forecasting, and evaluate the forecasting effect of the model under different economic backgrounds by comparing with historical data. Specifically: Use indicators such as mean square error (MSE) and root mean square error (RMSE) to evaluate the deviation between the forecast value and the actual value:

[0171]

[0172] Among them, y i represents the actual value at the i-th time point, represents the predicted value at the i-th time point, and N represents the number of predicted time points.

Claims

1. A theoretically consistent time-varying parameter autoregressive inflation rate forecasting method characterized by The following steps are involved: S1: The present invention proposes a theoretically consistent time-varying parameter autoregressive TC-TVP-DVAR model for predicting inflation rate, which includes the following components: The time-varying parameter autoregression module dynamically captures the changes in macroeconomic variables based on time series data and uses the time-varying parameter method to model the dynamic characteristics of the variables to describe the long-term trend of the inflation rate; The theoretical consistency prior module combines the recognized constraints in economic theory to impose a priori constraints on the time-varying parameter model. Through the theoretical consistency prior, the parameter estimation in the model is more reasonable and consistent with the economic explanation, which helps to improve the reliability and interpretability of the model. High-dimensional distribution modeling module, which is used to perform high-dimensional modeling of the distribution characteristics of macroeconomic variables at different time points. It introduces a distribution embedding layer and an adaptive weight adjustment mechanism to capture the distribution characteristics of the inflation rate and its changes under extreme economic conditions, and improve the overall forecasting ability of inflation. The adaptive parameter optimization module, based on the reinforcement learning mechanism, performs real-time adaptive updates on the weights of various macro variables. Through historical data feedback, it continuously optimizes the weights of parameters to ensure that the model can respond flexibly in different economic cycles and improve the accuracy of predictions. The uncertainty quantification module embeds the Bayesian inference mechanism in the model to quantify the uncertainty of the predicted value output by the model, provide prediction credibility analysis, and enable the model to identify and quantify the uncertainty factors in the prediction, thereby improving the stability of the overall prediction; S2: Based on the time-varying parameter autoregressive module, combined with the theoretical consistency prior module, the dynamic relationship between macroeconomic variables is established; the dynamic changes between variables are captured through time-varying parameters, and the parameters are ensured to be consistent with economic theory through theoretical prior constraints, which enhances the explanatory power of the model and completes the reasonable modeling of the relationship between variables; S3: After the dynamic relationship is established, the high-dimensional distribution modeling module is used to comprehensively model the distribution characteristics of various economic variables, so as to capture the complex changes of inflation rate under different economic scenarios. This module can refine the model's understanding of economic fluctuations, especially the accurate characterization of tail risks under extreme economic conditions; S4: Based on the high-dimensional distribution modeling results, the adaptive parameter optimization module is used to further dynamically optimize the model parameters. The reinforcement learning mechanism dynamically adjusts the weights of each macro variable through real-time feedback, so that the model can flexibly respond to the changing economic background and improve the overall prediction accuracy; S5: In the model output stage, combined with the uncertainty quantification module, the credibility of each prediction output is quantitatively evaluated through Bayesian inference, and the quantitative results are fed back to the parameter optimization module, so that the model can dynamically identify and reduce the uncertainty in the prediction, thereby improving the robustness of the overall model and the reliability of the prediction results; S6: Finally, by designing a multi-objective loss function, we jointly optimize the accuracy of time-varying parameter estimation, the goodness of fit of high-dimensional distribution modeling, and the confidence level of uncertainty quantification. During model training, we ensure that multiple objectives are optimized in a balanced manner, so that an effective combination is formed between the modules, further improving the accuracy and stability of inflation rate forecasts.

2. A theoretically consistent time-varying parameter autoregressive inflation rate forecasting method according to claim 1, characterized in that The specific method of step S2 is: S21: Construction of a time-varying parameter autoregressive model. A time-varying parameter autoregressive model is constructed to describe the dynamic impact of macroeconomic variables (interest rates, money supply, unemployment rate, etc.) on the inflation rate. The mathematical expression of the model is: y t =X t b t +e t Among them, y t represents the target variable inflation rate at time t; X t represents the input feature matrix at time t, including macroeconomic variables; β t represents the time-varying parameter vector, which represents the dynamic impact of each economic variable at time t; ε t is the error term, which is assumed to have a mean of 0 and a variance of σ 2 Normal distribution of S22: Introduction of theoretical consistency priors to ensure that the time-varying parameter β t In line with the rationality of economic theory, the theoretical consistency prior distribution P(β t ); Theoretical consistency prior is based on the constraints in economics. The impact of interest rates on inflation should be negative: β1<0. The Bayesian method is used to estimate the time-varying parameters. The update formula of the posterior distribution is: P(β t |y t ,X t )∝P(y t |X t ,b t )P(β t ) Among them, P(β t |y t ,X t ) represents the posterior distribution of the time-varying parameter; P(y t |X t ,β t ) represents the likelihood function, which indicates the probability of observing data under given parameters and input features; P(β t ) represents the theoretical consistency prior distribution, which is used to constrain the reasonable range of parameters; Selection of prior distribution: Theoretical consistency: Normal distribution or other distribution forms that are consistent with economic theory are selected a priori; Selection basis: Normal distribution is suitable for volatility modeling of most economic variables, but for scenarios where extreme values ​​may exist, heavy-tailed t distribution can be selected to cope with the impact of extreme values; S23: Bayesian update of parameters using observed data y t And the input feature matrix X t , by maximizing the posterior distribution P(β t |y t ,X t ) to obtain the updated time-varying parameters; in, represents the updated time-varying parameters. In order to perform Bayesian update of parameters, the variational inference method is used to approximate the posterior distribution to improve computational efficiency. Variational inference transforms the complex posterior distribution into a solvable optimization problem, making parameter estimation more accurate and efficient. In variational inference, a tractable distribution q(β t ) to approximate the true posterior distribution P(β t |y t ,X t ), optimize q(β t ),Right now: Among them, KL divergence measures the difference between two probability distributions. Minimizing this divergence means that q(β t ) is as close to the true posterior distribution as possible; By optimizing the variational lower bound ELBO, we find a parameterized form that can effectively approximate the posterior distribution, making the calculation more feasible. The updated parameters will be verified for theoretical consistency in S24 to ensure that they meet the economic constraints. S24: Theoretical consistency verification, verifying the updated time-varying parameters Whether the theoretical consistency constraint is met, for the interest rate parameter β1, it should satisfy: β1<0; if not, it is necessary to return to S22 or S23 to readjust the prior distribution and perform iterative updates; S25: Establishment of dynamic relationship: after the time-varying parameter estimation is completed, the updated parameters are used Establish the dynamic relationship between macroeconomic variables; this dynamic relationship describes the impact of macroeconomic variables on inflation rate at different time points, ensuring the rationality and interpretability of the model in a dynamic environment; mathematical representation of the dynamic relationship: in, represents the updated time-varying parameter at time t+1; X t+1 Represents the input feature matrix at time t+1; implementation details of dynamic relationships: updated time-varying parameters The results will be dynamically updated based on the parameters at the previous time point to capture the time-varying characteristics of macroeconomic variables, so that the model can maintain rationality and accuracy in different economic environments. Through such dynamic adjustments, the model can take into account historical information and current economic conditions at each time step to ensure the stability and reliability of the forecast results. Model rationality guarantee: When making the next prediction, the model will use the parameter update results of the historical time point and ensure a smooth transition of the parameters through the weighted average method to avoid prediction errors caused by sudden changes.

3. A theoretically consistent time-varying parameter autoregressive inflation rate forecasting method according to claim 1, characterized in that The specific method of step S3 is: S31: Extract high-dimensional distribution features. Extract high-dimensional distribution features of historical data of each economic variable and construct feature embedding vectors. Assume that the input feature matrix is ​​X t , perform high-dimensional feature embedding and obtain the embedding vector Z t ; The mathematical expression of high-dimensional embedding is: Z t =f embed (X t ) Among them, f embed Represents a high-dimensional feature embedding function, which is used to map the input feature matrix into a high-dimensional space. t The embedding vector representing time t contains a high-dimensional representation of the input features; High-dimensional feature embedding function f embed It is implemented using a deep neural network DNN; specifically, the function contains multiple fully connected layers, each of which is accompanied by a nonlinear activation function ReLU to enhance the nonlinear expression ability of the features; Mathematically expressed as: Z t =f embed (X t )=φ L (φ L-1 (…φ1(X t W1+b1)…)W L-1 +b L-1 )W L +b L Among them, φ i represents the activation function of the i-th layer, ReLU function: φ(x)=max(0,x); W i and b i Represent the weight matrix and bias vector of the i-th layer respectively, L represents the total number of layers, and the final Z t It is a high-dimensional embedding vector after multi-layer mapping; S32: Distribution modeling, using high-dimensional embedding vectors Z t Model the distribution of economic variables at different time points; by introducing a distribution embedding layer, capture the distribution characteristics of economic variables in high-dimensional space and establish the correlation between economic variables; The mathematical expression of the modeling process is: P(Y t |Z t )=g dist (Z t ) Among them, P(Y t |Z t ) represents the given embedding vector Z t The target variable Y under the condition t The distribution of g dist Represents the distribution modeling function, which is used to describe the impact of high-dimensional embedding vectors on the target variable; S33: Tail risk characterization, characterizing tail risks under extreme economic conditions, ensuring the robustness of the model under different economic scenarios, using the tail characteristics of the distribution to quantify risks, especially modeling possible extreme situations in high-dimensional space; The mathematical expression of risk characterization is: R t =h tail (Z t ) Among them, R t represents the tail risk measure at time t, h tail represents the tail risk characterization function, which is used to describe the extreme risk characteristics in the embedded vector; S34: Dynamic update of distribution features. As time goes by, the economic scenario may change. Therefore, it is necessary to dynamically update the high-dimensional distribution features. At each time step t, according to the new input feature matrix X t+1 For the high-dimensional embedding vector Z t+1 Updates are made to ensure that the model can capture changes in economic scenarios in real time: Z t+1 =f embed (X t+1 )。 4. A theoretically consistent time-varying parameter autoregressive inflation rate forecasting method according to claim 1, characterized in that The specific method of step S4 is: S41: Introduction of reinforcement learning mechanism The reinforcement learning mechanism is used to optimize the weights of time-varying parameters in real time, making the model flexible in different economic environments; suppose state S t Represents the economic environment at time t, including high-dimensional distribution characteristics Z t and the current parameter value, reinforcement learning is done through the strategy function π(S t ) Dynamically adjust model parameters to maximize the objective function; S42: Definition of immediate reward function, define the immediate reward function R t , used to measure the economic environment S t The model prediction effect under this condition; the immediate reward function is defined as: in, Represents the loss function, used to calculate the predicted value and the true value y t The goal of the reward function is to minimize the prediction error and thus maximize the immediate reward; S43: Strategy update and parameter optimization, using the policy gradient method in reinforcement learning to update the policy function π(S t ) is optimized, and the mathematical expression of parameter update is: Among them, θ t Represents the model parameters at time t; α represents the learning rate, which is used to control the step size of the update; Represents the gradient of the immediate reward, which is used to guide the direction of parameter optimization; S44: Weight adaptive adjustment: At each time step t, the reinforcement learning mechanism adaptively adjusts the weights of each macro variable according to the current economic environment and reward function; through the strategy function π(S t ) outputs the optimal weight combination β t , the model can optimize the influence of each variable; the optimal weight combination β t Represents the dynamic weight of each macro variable, which is determined by the policy function according to the current state S t It is calculated based on historical feedback data, so as to achieve precise control of the influence of each variable; S45: Continuous iteration of dynamic optimization. The dynamic optimization process of the reinforcement learning mechanism is continuously iterative. Each input of new economic data will trigger the re-optimization of parameters. The continuous iterative optimization process enables the model to adapt to changes in the economic environment in real time, ensuring high prediction accuracy in a constantly changing context.

5. A theoretically consistent time-varying parameter autoregressive inflation rate forecasting method according to claim 1, characterized in that The specific method of step S5 is: S51: Introduction of Bayesian inference, output for each prediction To quantify uncertainty, use the Bayesian inference method to obtain the credible interval of the predicted distribution. Indicates that given the input feature matrix X t and the time-varying parameter β t The goal of Bayesian inference is to quantify the uncertainty of the prediction by calculating the variance of the predicted distribution. S52: Uncertainty quantification, prediction output Quantify uncertainty and calculate the mean and variance of the posterior distribution to obtain a credible interval for the prediction; in, represents the mean of the prediction distribution, representing the most likely prediction value, Represents the variance of the prediction distribution, quantifying the uncertainty of the prediction results; S53: Credibility assessment based on posterior distribution Calculate the credibility of the predicted output and obtain the predicted credible interval The credible interval is used to measure the prediction stability of the model in the current economic environment; S54: The quantification results are fed back to the parameter optimization module to quantify the uncertainty results Feedback to the adaptive parameter optimization module to guide the model's parameter adjustment in subsequent steps. For predictions with large variance, the reinforcement learning mechanism will increase attention to the corresponding variables and reduce uncertainty by adjusting weights; S55: Dynamic identification and reduction of uncertainty. At each time step t, the high uncertainty factors in the model are dynamically identified based on the uncertainty quantification results. The weights of the high uncertainty factors are adjusted through the adaptive parameter optimization module, thereby reducing the uncertainty in the prediction and improving the overall robustness of the model and the reliability of the prediction.

6. A theoretically consistent time-varying parameter autoregressive inflation rate forecasting method according to claim 1, characterized in that The specific method of step S6 is: S61: Construction of a multi-objective loss function. A loss function containing multiple optimization objectives is constructed to jointly optimize various parts of the model. The mathematical expression of the multi-objective loss function is: L=λ1L param +λ2L dist +λ3L uncertainty Among them, L param Represents the loss function of time-varying parameter estimation, which measures the accuracy of the model in time-varying parameter estimation. dist Represents the loss function of high-dimensional distribution modeling, which measures the model's fit in capturing the distribution characteristics of economic variables. uncertainty represents the loss function for uncertainty quantification, which measures the confidence level of the predicted distribution. λ1,λ2,λ3 represent the weight coefficients of the loss function, which are used to control the importance of each objective in the joint optimization. S62: Weight adjustment of loss function. During the model training process, according to the optimization requirements of each target, the weight coefficients λ1, λ2, λ3 of the loss function are dynamically adjusted to ensure balanced optimization of the model at different training stages. The mathematical expression of weight adjustment is: in, represents the weight of the loss function at time step t, α represents the learning rate, which is used to control the step size of weight adjustment, Represents the gradient of the loss function with respect to the weight; S63: Joint optimization process, the multi-objective loss function is optimized by gradient descent method, and the model parameters are jointly updated so that each module can work together under the same optimization goal. The parameters of the time-varying parameter estimation module, the high-dimensional distribution modeling module and the uncertainty quantification module are jointly updated during the optimization process. The specific parameter update formula is: Among them, θ t represents all model parameters at time step t, including time-varying parameters, high-dimensional embedding parameters, and uncertainty quantization parameters. η represents the learning rate, which is used to control the step size of parameter update. Represents the effective combination of multi-objective loss functions between model modules; ensures that the time-varying parameter estimation, high-dimensional distribution modeling and uncertainty quantification modules cooperate with each other in the joint optimization process to form an effective combination, and the embedding result Z of the high-dimensional distribution modeling module t As the input of the time-varying parameter estimation module, the consistency of embedded features is maintained during the optimization process. The feedback results of the uncertainty quantification module are used to guide the adjustment of time-varying parameters. The reinforcement learning mechanism dynamically adjusts the weights of each macro variable according to the uncertainty quantification results. Through multi-objective optimization, the data flow between modules is smooth, information sharing is sufficient, and a unified prediction framework is formed. S65: Evaluation and verification of forecast results. Evaluate the forecast results of the jointly optimized model to verify its accuracy and stability in inflation rate forecasting. By comparing with historical data, evaluate the forecasting effect of the model under different economic backgrounds. Specifically, use indicators such as mean square error (MSE) and root mean square error (RMSE) to evaluate the deviation between the forecast value and the actual value: Among them, y i represents the actual value at the i-th time point, represents the predicted value at the i-th time point, and N represents the number of predicted time points.

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