GARCH-MIDAS-BiGRU bitcoin volatility prediction method based on nonlinear dimension reduction

Abstract

The invention provides a GARCH-MIDAS-BiGRU (Gaussian Autoregressive Receiving Channel-MIDAS-BiGRU) Bitcoin fluctuation rate prediction method based on nonlinear dimensionality reduction. According to the method, firstly, a nonlinear dimension reduction technology t-SNE is used for carrying out dimension reduction processing on macroeconomic variables, and low-dimensional features are extracted, so that data redundancy is reduced, and the training efficiency of a model is improved; and then, combining bitcoin price data and the dimension-reduced macroeconomic variables, constructing a multi-factor GARCH-MIDAS model, effectively processing data of different frequencies, and capturing changes of long-term and short-term fluctuation rates. And finally, introducing a BiGRU neural network to further enhance the processing capability of the model on the time sequence data, and better capturing the nonlinear relationship and complex dynamic characteristics in the data. Through the comprehensive method, the accuracy and the reliability of predicting the fluctuation ratio of the Bitcoin can be improved, and a more effective risk management tool is provided for investors.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of bitcoin volatility prediction, in particular to a GARCH-MIDAS-BiGRU bitcoin volatility prediction method based on nonlinear dimension reduction BACKGROUND

[0002] As a kind of cryptocurrency, bitcoin has attracted the attention of global investors since its inception due to its unique decentralized nature and potential high returns. However, the sharp fluctuations in the price of bitcoin have also made it a high-risk investment asset. Such fluctuations are not only caused by the market supply and demand relationship of bitcoin, but also influenced by macroeconomic environment, market sentiment, policy changes, and technological development. The complex price dynamics make the risk of the bitcoin market significantly higher than that of traditional financial markets, and investors face great uncertainty. Therefore, accurate prediction of bitcoin volatility is of great significance for investors' risk management and investment decisions.

[0003] Regarding the research on bitcoin volatility prediction, in traditional econometric models, handling mixed-frequency data usually involves converting data of different frequencies to the same frequency for analysis and modeling. For high-frequency data, the mean or sum is usually calculated to convert it to low-frequency data. Although this approach is simple, it may ignore the volatility information in high-frequency data, causing information loss of high-frequency sequences, and thus leading to sample reduction. For low-frequency data, it is transformed into high-frequency data through interpolation method. For this reason, Engle et al. proposed the GARCH-MIDAS model, which decomposes the volatility into long-term trend component and short-term volatility component, and uses MIDAS to model the long-term trend component, so that it can describe the long-term impact of low-frequency macro variables on high-frequency asset returns.

[0004] Chinese and foreign scholars have also made good progress in mixed-frequency prediction of bitcoin volatility. Conrad et al. used the GARCH-MIDAS model to analyze the determinants of long-term bitcoin volatility from the perspective of the U.S. stock market and global economic activity. Walther et al. used GARCH-MIDAS to study the impact of various exogenous factors on bitcoin volatility, and found that the global economic activity index has a better prediction effect on cryptocurrency volatility than EPU. Yang Jiemeng et al. used the GARCH-MIDAS model to find that the EPU index of China, the United States and other five countries significantly affects the long-term volatility of bitcoin, and the empirical results show that the U.S. EPU is highly positively correlated, the Chinese and German EPU are generally negatively correlated, and the model with EPU has better volatility prediction accuracy.

[0005] Currently, univariate mixed frequency models based on a single variable are mostly used in the field of Bitcoin volatility prediction. These models often ignore other influencing factors such as macroeconomic variables when processing Bitcoin price data. However, Bitcoin price volatility is actually the result of the combined action of multiple factors. As the number of factors considered increases, the non-linear relationship between variables becomes increasingly complex. Traditional mixed frequency data models can capture linear trends, but their explanatory power is clearly insufficient when faced with such complex non-linear relationships. SUMMARY

[0006] The present application aims to address the deficiencies in the background art by providing a GARCH-MIDAS-BiGRU Bitcoin volatility prediction method based on nonlinear dimensionality reduction. The method uses t-SNE to reduce the dimensionality of macroeconomic variables and extract low-dimensional features. It combines Bitcoin price data and reduced macroeconomic variables to construct a multi-factor GARCH-MIDAS model, effectively handling data of different frequencies and capturing changes in long-term and short-term volatility. The BiGRU neural network is introduced to further enhance the model's ability to process time series data, better capturing non-linear relationships and complex dynamic characteristics in the data.

[0007] To achieve the above-mentioned purpose, the present application provides a GARCH-MIDAS-BiGRU Bitcoin volatility prediction method based on nonlinear dimensionality reduction, comprising the following steps:

[0008] S1: Collecting original data of Bitcoin and macroeconomic variables;

[0009] S2: Preprocessing the original data;

[0010] S3: Building a multi-factor GARCH-MIDAS model with five different weight functions, using Bitcoin returns as high-frequency independent variables and macroeconomic variables as low-frequency dependent variables.

[0011] S4: Constructing a BiGRU neural network to further improve the accuracy of volatility prediction.

[0012] Further, in step S1, collecting historical data of Bitcoin and macroeconomic indicators refers to obtaining historical data of macroeconomic indicators from 2015 to 2023 from http: / / www.policyuncertainty.com, including Economic Policy Uncertainty Index (EPU), Geopolitical Risk Index (GPR), Market Volatility Index (VIX), Economic Uncertainty Index (EUI), and Global Economic Policy Uncertainty Index (GEPU). The daily closing price historical data of Bitcoin from 2015 to 2023 is obtained from Bitfinex API.

[0013] Further, the data preprocessing in step S2 includes the following steps:

[0014] S21: Log return transformation of Bitcoin price data. To calculate the daily return of Bitcoin, we use the closing price to calculate the log return. The specific formula is:

[0015]

[0016] where r i,t represents the return of Bitcoin on the i i,t th day in the t i,t-1 th month, P i represents the closing price of Bitcoin on the t i th day, and P j represents the closing price of Bitcoin on the previous trading day.

[0017] S22: tSNE feature extraction;

[0018] Dimensionality reduction of original high-dimensional data using t-SNE algorithm. In this study, we choose to map it to a two-dimensional space, which can convert the complex features of the original data into a visual form while preserving the key information. The t-SNE algorithm consists of two steps: first, calculate the similarity between data points in high-dimensional space and convert these similarities into probability distributions; then, define another probability distribution in low-dimensional space and use optimization methods such as gradient descent to minimize the KL divergence between the two probability distributions, thereby mapping high-dimensional data to low-dimensional space. The formula of tSNE algorithm is as follows:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] where σ i is the standard deviation of the Gaussian distribution centered at x i (x j ) in high-dimensional space, and n is the total number of data points.

[0025] S23: Data normalization;

[0026] Unify the value range between different features to eliminate the influence of dimension difference and numerical difference between different features on model training. Use the max-min normalization method to process the macroeconomic data and Bitcoin return data after tSNE dimensionality reduction, which linearly maps the data between the specified minimum and maximum values, and the formula is:

[0027]

[0028] where x' is the normalized data, x is the value of the original data, x max and x min are the maximum and minimum values of the original data, respectively.

[0029] After the experimental prediction, the inverse normalization operation should be performed, and the inverse normalization formula is as follows:

[0030] x = x' · (x max -x min )+x min

[0031] Further, in step S3, the bitcoin yield is taken as a high-frequency independent variable, and macroeconomic variables are taken as low-frequency dependent variables, and a multi-factor GARCH-MIDAS model with five different weight functions is constructed, including the following steps:

[0032] S31: Construct a GARCH-MIDAS model;

[0033] The GARCH-MIDAS model captures the short-term and long-term fluctuations of financial data, effectively combining high-frequency market fluctuations with low-frequency macroeconomics. The structure of the model is as follows:

[0034]

[0035] h i,t = τ t g i,t

[0036] where N t is the number of trading days in month t, and the total number of monthly observations is The total number of observation months is T, and ε i,t obeys the conditional standard normal distribution, i.e. ε i,t |ψ i-1,t ~N(0,1), indicating the information set available on the i-1 day of month t. The volatility is composed of two components: the long-term component τ t and the short-term component g i,t . g i,t obeys the GARCH(1,1) process:

[0037] g i,t = (1-α-β) + α(r i-1,t -μ) 2 / τ t + βg i-1,t

[0038] where α>0, β>0, α+β<1, and E t-1(g i,t ) is equal to its unconditional expectation, i.e. E t-1 (g i,t ) = 1. Referring to the MIDAS regression approach, the long-term volatility τ t is expressed as:

[0039]

[0040] where m is a constant, θ is the slope coefficient, is a reflection of the MIDAS structure, K is the maximum lag order of the low-frequency variable, RV t-k is the realized volatility, φ k (ω1,ω2) is defined as the weight equation of MIDAS.

[0041] Five restrictive weight functions are adopted, namely Beta weight function, Almon weight function, exponential Almon weight function, Gompertz weight function and Log-Cauchy weight function

[0042] S32: Constructing a multi-factor GARCH-MIDAS model;

[0043] The above single-factor GARCH-MIDAS model only considers historical volatility data and fails to incorporate the influence of other exogenous low-frequency variables. The multi-factor GARCH-MIDAS model is expressed as:

[0044]

[0045] S33: Parameter estimation and model validation;

[0046] The maximum likelihood estimation (MLE) is used to estimate the model parameters, and the Akaike information criterion (AIC) and Bayesian information criterion (BIC) are used to evaluate the goodness of fit of the model. The specific formulas are as follows:

[0047] AIC = 2k - 2ln(L)

[0048] BIC = kln(n) - 2ln(L)

[0049] where k is the number of model parameters, L is the maximum value of the likelihood function, and n is the sample size.

[0050] Calculate the prediction error of each model for comparison, including MSE, RMSE, and MAE.

[0051] Further, in step S4, a BiGRU neural network is constructed to further improve the accuracy of volatility prediction. The specific steps are as follows:

[0052] S41: Data preparation;

[0053] The past n-day Bitcoin logarithmic return rate, the reduced macroeconomic variables and the conditional volatility output by the optimal GARCH-MIDAS model are taken as input features.

[0054] S42: model construction;

[0055] The GRU network operation mechanism can be described by the following mathematical expressions:

[0056] r t = sigma(W rx x t +W rh h t-1 +b r )

[0057] z t = sigma(W zx x t +W zh h t-1 +b z )

[0058] h' t = tanh(W hx x t +W hr r t h t-1 +b h )

[0059] h t = (1-z t )h t-1 +z t h' t

[0060] wherein r t is the output signal of the reset gate at time t; z t is the output signal of the update gate at time t; W rx is the reset gate weight vector; W zx is the update gate weight vector; W hx is the input layer to the hidden layer vector; W rh is the hidden layer to the reset gate weight vector; W zh is the hidden layer to the update gate weight vector; W hr is the hidden layer state vector; b r , b z , b h are the corresponding bias vectors. Sigma represents the sigmoid function; tanh represents the activation function.

[0061] Based on the GRU network, a bidirectional learning strategy is introduced, that is, the BiGRU network can be obtained. By processing the sequence information in the forward direction (from front to back) and the reverse direction (from back to front) at the same time, the model can comprehensively consider the context information and improve the understanding depth of the sequence data. Specifically to the bitcoin volatility prediction problem, the influence factor data before and after the corresponding time point of the volatility data to be predicted can be used for prediction. The operation mechanism of the BiGRU network can be described by the following mathematical expressions:

[0062] h q (t)=T G (x(t),h q (t-1))

[0063] h h (t)=T G (x(t),h h (t-1))

[0064] h(t)=f(W q h q (t)+W h h h (t)+b o )

[0065] Wherein, T G represents the output of the GRU network; h q (t) and h h (t) represent the forward hidden layer state and the backward hidden layer state transmitted at t time respectively; W q and W h represent the forward hidden layer weight vector and the backward hidden layer weight vector respectively; b o represents the bias vector matrix of the hidden layer.

[0066] S43: model training and evaluation;

[0067] The number of neurons in the input layer hidden layer of the BiGRU network is set to 250, the number of network training iterations is set to 100, the mean absolute error is used as the loss function, and the Aadm optimization algorithm is used to update the weight matrix and bias matrix of the neurons, and the optimal prediction state of the network is obtained through optimization iteration. The output of the model is the prediction value sequence of the bitcoin volatility in the future 30 days, and each prediction value corresponds to the volatility prediction result of the future one day. By calculating the mean square error (MSE), the root mean square error (RMSE) and the mean absolute error (MAE) between the prediction value and the actual value, the accuracy of the model prediction is quantitatively evaluated.

[0068] Compared with the prior art, the significant advantages of the present application are as follows:

[0069] 1. The present application effectively handles the high-dimensional characteristics of macroeconomic variables by introducing the nonlinear dimensionality reduction technique t-SNE. Traditional methods can usually only capture linear relationships, while the present application can deeply explore the complex nonlinear relationships between variables, while reducing data redundancy through dimensionality reduction, improving the training efficiency and prediction performance of the model. This capture of nonlinear features and dimensionality reduction optimization significantly enhances the model's ability to adapt to complex economic environments.

[0070] 2. The present application innovatively combines the multi-factor GARCH-MIDAS model, which can handle data of different frequencies simultaneously. This mixed frequency data modeling method not only makes full use of the information of various data, but also effectively solves the time mismatch problem of different frequency data through MIDAS regression technology, improving the model's explanatory power and prediction accuracy.

[0071] 3. In order to effectively handle the complex dynamic characteristics of time series data and capture long-term dependencies in the data, the present application further introduces BiGRU neural networks, combining deep learning techniques with traditional econometric models. This fusion not only retains the interpretability of traditional models, but also enhances the predictive power of the model through deep learning techniques, significantly improving the accuracy and robustness of Bitcoin volatility prediction. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 The method flowchart of the present application. DETAILED DESCRIPTION

[0073] The specific embodiments of the present application will be described in detail below with reference to the accompanying drawings. Those skilled in the art can easily understand other advantages and effects of the present disclosure based on the information disclosed in the present specification. It should be particularly noted that the embodiments described herein are only some embodiments of the present disclosure. The present application can also be applied in other various forms, and the details in the present specification can be adjusted or changed accordingly based on different perspectives and application scenarios without deviating from the core concept of the present application. The following embodiments and their included features can be combined with each other without conflict. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present disclosure.

[0074] As shown in the figure, the embodiments of the present application provide a GARCH-MIDAS-BiGRU Bitcoin volatility prediction method based on nonlinear dimensionality reduction, comprising the following steps:

[0075] S1: Collecting original data of Bitcoin and macroeconomic variables;

[0076] Macroeconomic indicators history data from 2015 to 2023, including Economic Policy Uncertainty Index (EPU), Geopolitical Risk Index (GPR), Market Volatility Index (VIX), Economic Uncertainty Index (EUI), and Global Economic Policy Uncertainty Index (GEPU) are obtained from http: / / www.policyuncertainty.com, and daily closing price history data of Bitcoin from 2015 to 2023 are obtained from Bitfinex API.

[0077] S2: Preprocess the original data;

[0078] S21: Perform log return conversion on the Bitcoin price data;

[0079] To calculate the daily return of Bitcoin, we use the closing price to calculate the log return. The specific formula is:

[0080]

[0081] where r i,t represents the return of Bitcoin on the i-th day in the t-th month, P i,t represents the closing price of Bitcoin on the t-th day, P i,t-1 represents the closing price of Bitcoin on the previous trading day.

[0082] S22: Use tSNE feature extraction;

[0083] t-SNE algorithm is used to reduce the dimensionality of the original high-dimensional data. In this study, it is chosen to be mapped to two-dimensional space, which can convert the complex features of the original data into visualized form and retain the key information. The t-SNE algorithm consists of two steps: first, calculate the similarity between data points in high-dimensional space and convert these similarities into probability distribution; then, define another probability distribution in low-dimensional space and use optimization methods such as gradient descent to minimize the KL divergence between the two probability distributions, thereby mapping high-dimensional data to low-dimensional space. The formula of tSNE algorithm is as follows:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] where σ i is the high-dimensional space with xi (x j ) is the standard deviation of the Gaussian distribution centered at x max , and n is the total number of data points.

[0090] S23: Data normalization;

[0091] The value range between different features is unified to eliminate the influence of dimensional difference and numerical difference between different features on model training. The macroeconomic data and Bitcoin yield data after tSNE dimension reduction are processed using the max-min normalization method, which linearly maps the data between the specified minimum and maximum values, and the formula is:

[0092]

[0093] where x' is the normalized data, x is the value of the original data, x max and x min are the maximum and minimum values of the original data, respectively.

[0094] After the experimental prediction, the reverse normalization operation should be performed, and the reverse normalization formula is as follows:

[0095] x=x′·(x max -x min )+x min

[0096] Taking Bitcoin yield as the high-frequency independent variable and macroeconomic variables as the low-frequency dependent variable, a multi-factor GARCH-MIDAS model with five different weight functions is constructed, including the following steps:

[0097] S31: Constructing GARCH-MIDAS model;

[0098] GARCH-MIDAS model captures short-term and long-term fluctuations of financial data, effectively combining high-frequency market fluctuations with low-frequency macroeconomics. The structure of the model is as follows:

[0099]

[0100] h i,t =τ t g i,t

[0101] where N t is the number of trading days in month t, and the total number of observation days is The total number of observation months is T, and ε i,t obeys the conditional standard normal distribution, i.e. ε i,t |ψ i-1,t ~N(0,1), indicating the information set available on the i-1 day of month t. The volatility is composed of two components: the long-term component τ tand short-term component g i,t g i,t Subject to GARCH(1,1) process:

[0102] g i,t =(1-α-β)+α(r i-1,t -μ) 2 / τ t +βg i-1,t

[0103] where α>0,β>0,α+β<1, and E t-1 (g i,t ) is assumed to equal its unconditional expectation, i.e., E t-1 (g i,t )=1. Following the MIDAS regression approach, long-term volatility τ t is expressed as:

[0104]

[0105] where m is a constant, θ is the slope coefficient, is a reflection of the MIDAS structure, K is the maximum lag order of the low-frequency variable, and RV t-k is the realized volatility, φ k (ω1,ω2) is defined as the weight equation of MIDAS.

[0106] Five restrictive weight functions are adopted: Beta weight function, Almon weight function, exponential Almon weight function, Gompertz weight function, and Log-Cauchy weight function

[0107] S32: Constructing multi-factor GARCH-MIDAS model;

[0108] The above single-factor GARCH-MIDAS model only considers historical volatility data and fails to incorporate the influence of other exogenous low-frequency variables. The multi-factor GARCH-MIDAS model is expressed as:

[0109]

[0110] S33: Parameter estimation and model validation;

[0111] Maximum likelihood estimation (MLE) is used to estimate the model parameters, and Akaike information criterion (AIC) and Bayesian information criterion (BIC) are used to evaluate the goodness of fit of the model, and the model with the smallest AIC and BIC values is selected. The specific formula is as follows:

[0112] AIC=2k-2ln(L)

[0113] BIC = kln(n) - 2ln(L)

[0114] where k is the number of model parameters, L is the maximum value of the likelihood function, and n is the number of samples.

[0115] The prediction error of each model is calculated, including MSE, RMSE, and MAE. The model with the smallest MSE, RMSE, and MAE value is selected. After comprehensive evaluation, the model with the best comprehensive performance is selected.

[0116] S4: Construct a BiGRU neural network to further improve the accuracy of volatility prediction, including the following steps:

[0117] S41: Data preparation;

[0118] The closing price of Bitcoin in the past n days, the reduced macroeconomic variables, and the conditional volatility output by the optimal GARCH-MIDAS model are used as input features.

[0119] S42: Model construction;

[0120] The running mechanism of the GRU network can be described by the following mathematical expressions:

[0121] r t =σ(W rx x t +W rh h t-1 +b r )

[0122] z t =σ(W zx x t +W zh h t-1 +b z )

[0123] h' t =tanh(W hx x t +W hr r t h t-1 +b h )

[0124] h t =(1-z t )h t-1 +z t h' t

[0125] where r t is the output signal of the reset gate at time t; z t is the output signal of the update gate at time t; W rxWreset is the reset gate weight vector; zx Wupdate is the update gate weight vector; hx Wih is the input layer to hidden layer weight vector; rh Wih is the input layer to hidden layer weight vector; zh Wih is the input layer to hidden layer weight vector; hr b is the hidden layer state vector; r b is the hidden layer state vector; z b is the hidden layer state vector; h b is the hidden layer state vector. σ represents the sigmoid function; tanh represents the activation function.

[0126] Based on the GRU network, a bidirectional learning strategy is introduced, that is, the BiGRU network can be obtained. By processing the forward (from front to back) and reverse (from back to front) sequence information at the same time, the model can comprehensively consider the context information and improve the understanding depth of the sequence data. Specifically to the bitcoin volatility rate prediction problem, the influence factor data before and after the corresponding time point of the volatility rate data to be predicted can be used for prediction. The operation mechanism of the BiGRU network can be described by the following mathematical expressions:

[0127] h q (t)=T G (x(t),h q (t-1))

[0128] h h (t)=T G (x(t),h h (t-1))

[0129] h(t)=f(W q h q (t)+W h h h (t)+b o )

[0130] Wherein, T G represents the output of the GRU network; h q (t) and h h (t) respectively represent the forward hidden layer state and the backward hidden layer state transmitted at t time; W q and W h respectively represent the forward hidden layer weight vector and the backward hidden layer weight vector; b o represents the bias vector matrix of the hidden layer.

[0131] S43: model training and evaluation;

[0132] The number of neurons in the input layer hidden layer of the BiGRU network is set to 250, the number of network training iterations is set to 100, the mean absolute error is used as the loss function, and the Aadm optimization algorithm is used to update the weight matrix and bias matrix of the neurons, and the optimal prediction state of the network is obtained through optimization iteration. The output of the model is a sequence of 30-day bitcoin volatility prediction values, each prediction value corresponds to the volatility prediction result of the next day. By calculating the mean square error (MSE), root mean square error (RMSE) and mean absolute error (MAE) between the predicted value and the actual value, the accuracy of the model prediction is quantitatively evaluated.

[0133] The present application effectively handles the high-dimensional characteristics of macroeconomic variables by introducing the nonlinear dimensionality reduction technique t-SNE. Traditional methods can usually only capture linear relationships, while the present application can deeply explore the complex nonlinear relationships between variables, while reducing data redundancy through dimensionality reduction, improving the training efficiency and prediction performance of the model. This capture and dimensionality reduction optimization of nonlinear features significantly enhances the model's ability to adapt to complex economic environments; the present application innovatively combines the multi-factor GARCH-MIDAS model, which simultaneously processes data of different frequencies. This mixed frequency data modeling method not only makes full use of the information of various types of data, but also effectively solves the time mismatch problem of different frequency data through MIDAS regression technology, improving the model's explanatory power and prediction accuracy; the present application further introduces the BiGRU neural network, combining deep learning technology with traditional econometric models. BiGRU can effectively handle the complex dynamic characteristics of time series data and capture long-term dependencies in the data. This fusion not only retains the interpretability of traditional models, but also enhances the model's predictive ability through deep learning technology, significantly improving the accuracy and robustness of bitcoin volatility prediction.

[0134] The above has made a detailed explanation to the embodiments of the present application. For those skilled in the art, after mastering the basic principles of the present application, various modifications, equivalent replacements and improvements can be made to the present application without deviating from the concept of the present application, which should be included in the protection scope of the present application.

Claims

1. A GARCH-MIDAS-BiGRU Bitcoin volatility forecasting method based on nonlinear dimensionality reduction, characterized in that, It comprises the following steps: S1: Collecting bitcoin and macroeconomic variable raw data; S2: Preprocessing the raw data; S3: Building a multi-factor GARCH-MIDAS model with five different weight functions, using bitcoin yield as the high-frequency independent variable and macroeconomic variables as the low-frequency dependent variable. S4: Building a BiGRU neural network to further improve the accuracy of volatility prediction.

2. The nonlinear dimensionality reduction based GARCH-MIDAS-BiGRU Bitcoin volatility forecasting method according to claim 1, characterized in that, In step S1, the historical data of macroeconomic indicators from 2015 to 2023 is obtained from http: / / www.policyuncertainty.com, including economic policy uncertainty index (EPU), geopolitical risk index (GPR), market volatility index (VIX), economic uncertainty index (EUI), and global economic policy uncertainty index (GEPU). The historical data of daily closing price of bitcoin from 2015 to 2023 is obtained from Bitfinex API.

3. The nonlinear dimensionality reduction based GARCH-MIDAS-BiGRU Bitcoin volatility forecasting method according to claim 1, characterized in that, The data preprocessing in step S2 includes: S21: Log return conversion of bitcoin price data. To calculate the daily yield of bitcoin, we use the closing price to calculate the log yield. The specific formula is: where r i,t represents the return rate of Bitcoin on the ith day within t months, P i,t represents the closing price of Bitcoin on the tth day, P i,t-1 represents the closing price of Bitcoin on the previous trading day. S22: Using tSNE feature extraction; The t-SNE algorithm is used to reduce the dimensionality of the original high-dimensional data. In this study, we choose to map it to a two-dimensional space, which can convert the complex features of the original data into a visual form while retaining the key information. The t-SNE algorithm consists of two steps: first, calculate the similarity between data points in high-dimensional space and convert these similarities into probability distributions; then, define another probability distribution in low-dimensional space and use optimization methods such as gradient descent to minimize the KL divergence between the two probability distributions, thereby mapping high-dimensional data to low-dimensional space. The formula of tSNE algorithm is as follows: where σ i is the standard deviation of the Gaussian distribution centered at x i in the high-dimensional space, and n is the total number of data points. j ) as the center. S23: Data normalization; The value range of different features is unified to eliminate the influence of dimension difference and numerical difference between different features on model training. The maximum-minimum normalization method is used to process the macroeconomic data and bitcoin yield data after tSNE dimensionality reduction, which linearly maps the data between the specified minimum and maximum values. The formula is: where x' is the normalized data, x is the value of the original data, and x max and x min are the maximum and minimum values of the original data, respectively. The reverse normalization operation should be performed after the experimental prediction, and the reverse normalization formula is as follows: x = x' • (x max - x min + x min 。 4. The nonlinear dimensionality reduction based GARCH-MIDAS-BiGRU Bitcoin volatility forecasting method of claim 1, wherein, The step S3 specifically includes the following: S31: Building a GARCH-MIDAS model; The GARCH-MIDAS model captures the short-term and long-term volatility of financial data, effectively combining high-frequency market volatility with low-frequency macroeconomics. The structure of this model is as follows: h i,t = τ t g i,t where N t is the number of trading days in month t, and the total number of observed days in month t is The total number of observed months is T, and ε i,t is the standard normal distribution, i.e. ε i,t |ψ i-1,t ~ N(0, 1) represents the information set available at day i - 1 in month t. The volatility is composed of two components: a long-term component τ t and a short-term component g i,t . g i,t is subject to a GARCH(1,1) process: g i,t = (1 - a - b) + a(r i-1,t - m) 2 / t t + b gi-1,t where a > 0, β > 0, a + β < 1, and E t-1 (g i,t ) equals its unconditional expectation, i.e. E t-1 (g i,t ) = 1. With reference to the MIDAS regression approach, the long-term volatility τ t is expressed as: where m is a constant, θ is a slope coefficient, is a reflection of the MIDAS structure, K is the maximum lag order of the low-frequency variable, RV t-k is the realized volatility, φ k (ω1,ω2) is defined as the weight equation of the MIDAS. Five restrictive weight functions are adopted: Beta weight function, Almon weight function, exponential Almon weight function, Gompertz weight function, and Log-Cauchy weight function S32: Building a multi-factor GARCH-MIDAS model; The above single-factor GARCH-MIDAS model only considers historical volatility data and fails to incorporate the influence of other exogenous low-frequency variables. The multi-factor GARCH-MIDAS model is represented as: S33: Parameter estimation and model validation; The maximum likelihood estimation (MLE) is used to estimate the model parameters, and the Akaike information criterion (AIC) and Bayesian information criterion (BIC) are used to evaluate the goodness of fit of the model. The specific formula is as follows: AIC = 2k - 2ln(L) BIC = kln(n) - 2ln(L) Where k is the number of model parameters, L is the maximum value of the likelihood function, and n is the sample size. Calculate the prediction error of each model, including MSE, RMSE, and MAE. Select the model with the smallest MSE, RMSE, and MAE value. Comprehensive evaluation, select the model with the best comprehensive performance.

5. The nonlinear dimensionality reduction based GARCH-MIDAS-BiGRU Bitcoin volatility forecasting method according to claim 1, characterized in that, The step S4 specifically includes The following: S41: Data preparation; The past n-day closing price of Bitcoin, the reduced macroeconomic variables, and the conditional volatility output by the optimal GARCH-MIDAS model are used as input features. S42: Model construction; The GRU network operation mechanism can be described by the following mathematical expression: r t = σ(W rx x t + W rh h t-1 + b r ) z t = σ(W zx x t + W zh h t-1 + b z ) h′ t =tanh(W hx x t +W hr r t h t-1 +b h ) h t = (1 - z t )h t-1 + z t h′ t where r t is the output signal of the reset gate at time t; z t is the output signal of the update gate at time t; W rx is the reset gate weight vector; W zx is the update gate weight vector; W hx is the input-to-hidden vector; W rh is the hidden-to-reset gate weight vector; W zh is the hidden-to-update gate weight vector; W hr is the hidden state vector; b r , b z , b h are the respective bias vectors. σ denotes the sigmoid function; tanh denotes the activation function. Based on the GRU network, a bidirectional learning strategy is introduced, i.e. BiGRU network. By processing the forward (from front to back) and reverse (from back to front) sequence information simultaneously, the model can consider the context information comprehensively and improve the understanding depth of sequence data. Specifically to the Bitcoin volatility prediction problem, the influence factor data before and after the corresponding time point of the volatility data to be predicted can be used for prediction. The BiGRU network operation mechanism can be described by the following mathematical expression: h q (t) = T G (x(t), h q (t - 1)) h h (t) = T G (x(t), h h (t - 1)) h(t) = f(W q h q (t) + W h h h (t) + b o ) where T G represents the output of the GRU network; h q (t) and h h (t) represent the forward hidden layer state and the backward hidden layer state, respectively, passed at time t; W q and W h represent the forward hidden layer weight vector and the backward hidden layer weight vector, respectively; b o represents the bias vector matrix of the hidden layer. S43: Model training and evaluation; The number of neurons in the input layer and hidden layer of the BiGRU network is set to 250, the number of network training iterations is set to 100, the mean absolute error is used as the loss function, and the Aadm optimization algorithm is used to update the weight matrix and bias matrix of the neurons, and the optimal prediction state of the network is obtained by optimization iteration. The output of the model is a sequence of 30-day Bitcoin volatility prediction values, each prediction value corresponds to the volatility prediction result of the next day. By calculating the mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE) between the predicted value and the actual value, the accuracy of the model prediction is quantitatively evaluated.

Images