Multivariable time series prediction method based on adaptive lifting wavelet transform

Abstract

The invention discloses a multivariable time sequence prediction method based on adaptive lifting wavelet transform, which comprises the following steps: constructing an adaptive update function and an adaptive prediction function, and realizing adaptive lifting wavelet decomposition; obtaining a low-frequency approximation coefficient and a high-frequency detail coefficient by adaptively lifting wavelet decomposition time sequence data; the low-frequency approximation coefficient obtained through decomposition and hierarchical reconstruction is predicted through an OIF Elman nerve, and a nonlinear prediction result of the time sequence is obtained; capturing linear features of the time sequence by using an SARIMA model to obtain a linear prediction result of the time sequence; and carrying out weighted fusion on the nonlinear prediction result and the linear result to obtain a final prediction result. According to the method, effective decomposition of the time sequence can be realized, time domain and frequency domain information of the time sequence is fully utilized, and nonlinear and linear characteristics of the time sequence are captured, so that the prediction precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of time series prediction, and in particular to a multivariate time series prediction method based on adaptive lifting wavelet transform. Background Art

[0002] Time series forecasting technology aims to extract the trend, seasonality and periodicity of data by analyzing the complex time information of historical data, so as to predict the long-term trend in the future. Time series analysis methods are mainly divided into time domain methods and frequency domain methods. The time domain method regards time series data as ordered data points arranged in chronological order and analyzes the correlation between these data. However, if the time series is analyzed only from the time domain perspective, the frequency domain information will be ignored, thus limiting the model's acquisition of comprehensive information about the time series. The frequency domain method uses a series of transformation algorithms to convert the time series from the time domain to the frequency domain, and then captures the frequency domain characteristics of the time series by analyzing the subsequences of different frequencies after the transformation. However, the existing frequency domain analysis methods have the problem of incomplete decomposition of the original time series, which makes it difficult to fully utilize the high and low frequency information after decomposition, thus affecting the prediction accuracy.

[0003] Early time series prediction mainly used statistical methods to predict time series by fitting models, but these methods have low scalability and are mostly linear models, which makes it difficult to capture the complex nonlinear relationships of time series. Classical machine learning methods can only model and predict based on the features of the current moment, resulting in the neglect of the time correlation in time series data. In recent years, with the development of deep learning in various fields, deep neural networks have shown powerful nonlinear feature extraction and expression capabilities, and have therefore been widely used in time series prediction tasks. However, most of these models only analyze time series from a time domain perspective, ignoring frequency domain information, and a small number of frequency domain-based methods are difficult to effectively decompose time series, resulting in incomplete information utilization, thereby limiting the model's acquisition of comprehensive information about time series. In summary, designing an effective time series decomposition method and making full use of the time-frequency information of time series is the focus of this paper. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art and propose a multivariate time series prediction method based on adaptive lifting wavelet transform, which can adaptively complete the update and prediction process, realize the effective decomposition of the time series, make full use of the time domain and frequency domain information of the time series, and improve the prediction accuracy by adopting the hierarchical reconstruction prediction method.

[0005] To achieve the above object, the technical solution provided by the present invention is: a multivariate time series prediction method based on adaptive lifting wavelet transform, comprising the following steps:

[0006] 1) Obtain time series data and preprocess it to obtain time series data within a specified range;

[0007] 2) Using the SARIMA model to extract linear features from the preprocessed time series data, we obtain the linear prediction results of the time series; performing adaptive lifting wavelet decomposition on the preprocessed time series data to decompose low-frequency approximate coefficients and high-frequency detail coefficients;

[0008] 3) Preliminary prediction of the low-frequency approximate coefficients obtained in step 2) is performed through the OIF Elman neural network to obtain the low-frequency approximate coefficients after preliminary prediction;

[0009] 4) The high-frequency detail coefficients obtained in step 2) and the low-frequency approximate coefficients initially predicted in step 3) are reconstructed by adaptive lifting wavelet hierarchical reconstruction, and the low-frequency approximate coefficients after each layer of reconstruction are predicted again until they are completely reconstructed, thereby obtaining the nonlinear prediction result of the time series;

[0010] 5) Perform weighted fusion on the nonlinear prediction result obtained in step 4) and the linear prediction result obtained in step 2) to obtain the final prediction result.

[0011] Further, in step 2), the pre-processed time series data is subjected to adaptive lifting wavelet decomposition to decompose low-frequency approximate coefficients and high-frequency detail coefficients. The specific operation steps are as follows:

[0012] For the preprocessed time series data, the splitting process of adaptive lifting wavelet decomposition is firstly carried out. Based on the correlation between adjacent time points of the time series, the time series data is decomposed by lazy wavelet transform to obtain even sequence and odd sequence. The splitting process is expressed as:

[0013] Split[X(t)]=[X e (t),X o (t)]

[0014] X e (t) = X(2t)

[0015] X o (t) = X (2t + 1)

[0016] In the formula, Split means splitting, t means the current time value, X(t) means the preprocessed time series data, and X e (t) represents the decomposed even sequence, X(2t) represents the time series with time 2t, and X o (t) represents the odd sequence after decomposition, X(2t+1) represents the time series with time 2t+1;

[0017] In the update phase, the choice of the update operator depends on the locally available information in the even and odd sequences, and a decision map is defined based on this information:

[0018]

[0019] In the formula, D(X o ,X e )(t) is the decision function; |v(t)|+|w(t)| represents the sum of the absolute values ​​of the differences between the even sequence and the two adjacent odd sequences at time t, and represents the judgment condition of the decision function; v(t)=X e (t)-X o (t-1), represents the difference between the even sequence after decomposition at time t and the odd sequence after decomposition at time t-1; w(t) = X e (t)-X o (t) represents the difference between the even sequence and the odd sequence after decomposition at time t; T is the preset threshold;

[0020] After defining the decision function, different update operators will be selected according to the different judgment results: o ,X e When )(t) = 0, it indicates that the gap between the even sequence and the two adjacent odd sequences is small. In order to eliminate the influence of noise and show the trend of the time series, the mean of the even sequence and the two adjacent odd sequences is used as the update improvement; when D(X o ,X e When )(t) = 1, it indicates that the gap between the even sequence and the two adjacent odd sequences is large. In order to retain the mutation part, the value of the odd sequence at time t is used as the update improvement; the update operator is defined as:

[0021]

[0022] Where U d is the adaptive update function, X o (t-1) represents the odd sequence after decomposition at time t-1;

[0023] After the update is completed, the approximate coefficient is obtained, which describes the global trend of the original time series and is expressed as:

[0024]

[0025] Where X′(t) is the updated even sequence, which represents the low-frequency approximation coefficient. is the addition operator, using the average of the even sequence after decomposition at time t and the odd sequence after update at time t, defined as:

[0026]

[0027] In the prediction stage, according to the characteristics of time series correlation, the updated even sequence value is used to predict the odd sequence, and the difference between the odd sequence and the predicted value is calculated to obtain the detail coefficient, which reflects the similarity between the two. The high-frequency detail coefficient corresponding to the original time series is:

[0028] d(t) = X o (t)-P(X′(t))

[0029] Where d(t) is the high-frequency detail coefficient, P(X′(t)) represents the adaptive prediction function, and a single-layer linear neural network suitable for the length of the time series is used.

[0030] Further, in step 4), the high-frequency detail coefficients obtained by adaptive lifting wavelet decomposition and the low-frequency approximate coefficients initially predicted by the OIF Elman neural network are subjected to adaptive lifting wavelet hierarchical reconstruction. The reconstruction process is shown as follows:

[0031] X o (t) = d(t) + P[X′(t)]

[0032] X e (t) = X′(t) − U d (X o (t))

[0033] X m (t) = Merge[X e (t),X o (t)]

[0034] In the formula, Merge means the fusion of even-odd sequences, X m (t) represents the sequence after the even-odd sequence is fused.

[0035] Furthermore, in step 5), the nonlinear prediction result obtained by adaptive lifting wavelet hierarchical reconstruction prediction and the linear prediction result obtained by SARIMA model prediction are weighted summed to obtain the final prediction result:

[0036] y out (t) = αy nl (t)+βy l (t)

[0037] In the formula, out represents output, y out (t) represents the final prediction result output at time t, nl represents nonlinearity, and y nl (t) represents the nonlinear prediction result of OIF Elman neural network prediction, l represents linear prediction, y l(t) represents the linear prediction result of the SARIMA model, α and β represent weighted values, and α+β=1, which is used to adjust the weights of the nonlinear part and the linear part.

[0038] Furthermore, the OIF Elman neural network is composed of an input layer, a hidden layer, a hidden-input feedback layer, an output-input feedback layer and an output layer, wherein the time length of the input layer is determined by the lookback window, the hidden layer takes the input of the previous moment and the output of the input layer at the current moment as input to improve the network's ability to process dynamic information, the hidden-input feedback layer stores the output value of the hidden layer at the previous moment and is self-connected to the hidden layer, having a memory and storage function, the output-input feedback layer enhances the utilization of feedback information of each layer, and the output layer outputs the result according to the prediction length; the representation forms of the above hidden layer, hidden-input feedback layer, output-input feedback layer and output layer are as follows:

[0039] x(t)=f(w 1 u(t-1)+w 2 x c (t)+w 4 y c (t))

[0040] x c (t) = νx c (t-1)+x(t-1)

[0041] y c (t) = γy c (t-1)+y(t-1)

[0042] y nl (t) = g(w 3 x(t)

[0043] In the formula, u(t-1) represents the input vector, x(t), x c (t), y c (t) and y nl (t) represents the output of the hidden layer, hidden-input feedback layer, output-input feedback layer and output layer at the current moment, x(t-1), y(t-1), x c (t-1) and y c (t-1) represents the output of the hidden layer, output layer, hidden-input feedback layer, and output-input feedback layer at the previous moment, respectively. 1 、w 2 、w 3 and w 4are the connection weights from the input layer to the hidden layer, from the hidden-input feedback layer to the hidden layer, from the hidden layer to the output layer, and from the output-input feedback layer to the hidden layer, respectively. ν and γ are the self-connection feedback gain factors. g(·) is the transfer function of the output layer, using the purelin function. f(·) is the transfer function of the hidden layer, using the sigmoid function.

[0044] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0045] 1. The present invention utilizes adaptive lifting wavelet transform to decompose time series data. By adopting adaptive update function and adaptive prediction function, the time domain and frequency domain information of the time series can be fully utilized to achieve effective decomposition of the time series.

[0046] 2. The present invention uses a hierarchical reconstruction prediction method to capture the nonlinear characteristics of the time series, thereby improving the prediction accuracy of the time series.

[0047] 3. The present invention uses a parallel approach to capture the characteristics of the time series, wherein the OIF Elman neural network is used to capture the nonlinear characteristics of the time series, and the SARIMA model is used to capture the linear characteristics of the time series.

[0048] In summary, the present invention can effectively decompose the time series into low-frequency approximate coefficients and high-frequency detail coefficients through adaptive lifting wavelet decomposition, and improve the prediction accuracy through hierarchical reconstruction prediction. At the same time, it adopts a parallel approach to capture the nonlinear and linear characteristics of the time series, thereby improving the prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of the method of the present invention.

[0050] Figure 2 Decomposition diagram of adaptive lifting wavelet transform.

[0051] Figure 3 Diagram of the adaptive update process.

[0052] Figure 4 This is the structural diagram of the OIF Elman neural network. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0054] like Figure 1As shown, this embodiment discloses a multivariate time series prediction method based on adaptive lifting wavelet transform. The method first decomposes the original time series X(t) into low-frequency approximation coefficient A3 and high-frequency detail coefficients D3, D2 and D1 through adaptive lifting wavelet decomposition, and then performs initial prediction of the low-frequency approximation coefficient through OIF Elman neural network. Then, the high-frequency detail coefficients obtained by decomposition and the low-frequency approximation coefficients predicted by OIF Elman neural network are hierarchically reconstructed to obtain A2, A1 and X. m (t), and re-forecast until it is fully reconstructed, thereby capturing the nonlinear characteristics of the time series. At the same time, the SARIMA model is used to extract the linear characteristics of the original time series. It includes the following steps:

[0055] 1) Obtain time series data and perform preprocessing, including missing data filling and data standardization, to obtain time series data within the specified range;

[0056] 2) The SARIMA model is used to extract linear features from the preprocessed time series data to obtain the linear prediction results of the time series; the preprocessed time series data X(t) is subjected to adaptive lifting wavelet decomposition to decompose the low-frequency approximate coefficient X′(t) and the high-frequency detail coefficient d(t), as shown in Figure 2 The specific steps are as follows:

[0057] For the preprocessed time series data, the splitting process of adaptive lifting wavelet decomposition is firstly carried out. Based on the correlation between adjacent time points of the time series, the time series data is decomposed by lazy wavelet transform to obtain even sequence and odd sequence. The splitting process is expressed as:

[0058] Split[X(t)]=[X e (t),X o (t)]

[0059] X e (t) = X(2t)

[0060] X o (t) = X(2t+1)

[0061] In the formula, Split means splitting, t means the current time value, X(t) means the preprocessed time series data, and X e (t) represents the decomposed even sequence, X(2t) represents the time series with time 2t, and X o (t) represents the odd sequence after decomposition, X(2t+1) represents the time series with time 2t+1;

[0062] During the update phase, Figure 3 As shown, the odd sequence X o (t) and even sequence Xe (t), firstly through the decision function D(X o ,X e )(t) Make a decision. After the decision is made, update the operator U d Implement adaptive update and finally use the addition operator The updated X′(t) is obtained. The choice of the update operator depends on the locally available information in the even and odd sequences, and the decision mapping is defined based on this information:

[0063]

[0064] In the formula, D(X o ,X e )(t) is the decision function; |v(t)|+|w(t)| represents the sum of the absolute values ​​of the differences between the even sequence and the two adjacent odd sequences at time t, and represents the judgment condition of the decision function; v(t)=X e (t)-X o (t-1), represents the difference between the even sequence after decomposition at time t and the odd sequence after decomposition at time t-1; w(t) = X e (t)-X o (t) represents the difference between the even sequence and the odd sequence after decomposition at time t. By comparing the prediction accuracy of different thresholds T multiple times, T is selected as 0.2;

[0065] After defining the decision function, different update operators will be selected according to the different judgment results: o ,X e When )(t) = 0, it indicates that the gap between the even sequence and the two adjacent odd sequences is small. In order to eliminate the influence of noise and show the trend of the time series, the mean of the even sequence and the two adjacent odd sequences is used as the update improvement; when D(X o ,X e When )(t) = 1, it indicates that the gap between the even sequence and the two adjacent odd sequences is large. In order to retain the mutation part, the value of the odd sequence at time t is used as the update improvement. The update operator is defined as:

[0066]

[0067] Where U d is the adaptive update function, X o (t-1) represents the odd sequence after decomposition at time t-1;

[0068] After the update is completed, the approximate coefficient is obtained, which describes the global trend of the original time series and corresponds to the low-frequency approximate coefficient, expressed as:

[0069]

[0070] Where X′(t) is the updated even sequence, which represents the low-frequency approximation coefficient. is the addition operator, using the average of the even sequence after decomposition at time t and the odd sequence after update at time t, defined as:

[0071]

[0072] In the prediction stage, according to the characteristics of time series correlation, the updated even sequence value is used to predict the odd sequence, and the difference between the odd sequence and the predicted value is calculated to obtain the detail coefficient. The detail coefficient reflects the similarity between the two, and the high-frequency detail coefficient corresponding to the original time series is:

[0073] d(t) = X o (t)-P(X′(t))

[0074] Where d(t) is the detail coefficient, which represents the high-frequency detail coefficient obtained after decomposition, and P(X′(t)) represents the adaptive prediction function, which adopts a single-layer linear neural network suitable for the length of the time series.

[0075] 3) Preliminary prediction of the low-frequency approximate coefficients obtained in step 2) is performed through the OIF Elman neural network to obtain the low-frequency approximate coefficients after preliminary prediction;

[0076] like Figure 4 As shown in the figure, the OIF Elman neural network consists of an input layer, a hidden layer, a hidden-input feedback layer, an output-input feedback layer, and an output layer. Among them, the time length of the input layer is determined by the lookback window. The hidden layer will take the input of the previous moment and the output of the input layer at the current moment as input to improve the network's ability to process dynamic information. The hidden-input feedback layer stores the output value of the hidden layer at the previous moment and is self-connected to the hidden layer. It has a memory and storage function. The output-input feedback layer enhances the utilization of feedback information from each layer, and the output layer outputs the result according to the prediction length. The representations of the hidden layer, hidden-input feedback layer, output-input feedback layer, and output layer of the OIF Elman neural network are as follows:

[0077] x(t)=f(w 1 u(t-1)+w 2 x c (t)+w 4 y c (t))

[0078] x c (t) = vx c (t-1)+x(t-1)

[0079] y c (t) = γy c (t-1)+y(t-1)

[0080] y nl (t) = g(w 3 x(t)

[0081] Among them, u(t-1) represents the input vector, x(t), x c (t), y c (t) and y nl (t) represents the output of the hidden layer, hidden-input feedback layer, output-input feedback layer and output layer at the current moment, x(t-1), y(t-1), x c (t-1) and y c (t-1) represents the output of the hidden layer, output layer, hidden-input feedback layer, and output-input feedback layer at the previous moment, respectively. 1 、w 2 、w 3 and w 4 are the connection weights from the input layer to the hidden layer, from the hidden-input feedback layer to the hidden layer, from the hidden layer to the output layer, and from the output-input feedback layer to the hidden layer, respectively. ν and γ are the self-connection feedback gain factors, and y nl (t) represents the output result of the nonlinear part, g(·) is the transfer function of the output layer, which adopts the purelin function, and f(·) is the transfer function of the hidden layer, which adopts the sigmoid function.

[0082] 4) The high-frequency detail coefficients obtained in step 2) and the low-frequency approximate coefficients obtained in step 3) are reconstructed by adaptive lifting wavelet hierarchical reconstruction, and the low-frequency approximate coefficients after each layer of reconstruction are predicted again until they are completely reconstructed to obtain the nonlinear prediction results of the time series. The reconstruction process is shown as follows:

[0083] X o (t) = d(t) + P[X′(t)]

[0084] X e (t) = X′(t) − U d (X o (t))

[0085] X m (t) = Merge[X e (t),X o (t)]

[0086] In the formula, Merge means the fusion of even-odd sequences, X m (t) represents the sequence after the even-odd sequence is fused.

[0087] 5) Perform weighted fusion on the nonlinear prediction result obtained in step 4) and the linear prediction result obtained in step 2) to obtain the final prediction result.

[0088] y out (t) = αy nl (t)+βy l (t)

[0089] In the formula, out represents output, y out (t) represents the final prediction result output at time t, nl represents nonlinearity, and y nl (t) represents the nonlinear prediction result of OIF Elman neural network prediction, l represents linear prediction, y l (t) represents the linear prediction result of the SARIMA model, α and β represent weighted values, and α+β=1, which is used to adjust the weights of the nonlinear part and the linear part.

[0090] The ETTm2 dataset contains power transformer data recorded every 15 minutes from July 2016 to July 2018. The Traffic dataset contains traffic data collected every 1 hour on San Francisco Bay Area highways from July 2016 to July 2018. The Weather dataset is climate data collected every 10 minutes at the MaxPlanck Institute for Biogeochemistry weather station in 2020. The ILI dataset is patient data recorded weekly by the Centers for Disease Control and Prevention from 2002 to 2021. In order to maintain the seasonality and trend inherent in time series data, in the experiment, for the ETTm2 dataset, it is divided into training set (60%), validation set (20%), and test set (10%) in chronological order. For the other datasets, they are divided into training set (70%), validation set (10%), and test set (20%) in chronological order. The basic information of the five datasets is shown in Table 1.

[0091] Table 1 Basic information of the dataset

[0092]

[0093]

[0094] Mean Absolute Error (MAE) and Mean Squared Error (MSE) are two commonly used time series prediction evaluation indicators. The smaller the value, the closer the predicted value is to the true value, and the better the performance of the model. The specific calculation formula is as follows:

[0095]

[0096] In the formula, i is the specific time step of the time series, n represents the total time step of the time series, and y i and Represent the actual value and predicted value in time series forecasting respectively.

[0097] To verify the effectiveness of the method of the present invention, MAE and MSE are used as evaluation criteria, and a comparative analysis is carried out with InParformer, FEDformer-w, CLformer and Autoformer methods on four commonly used data sets ETTm2, Traffic, Weather and ILI. The method of the present invention maintains the same lookback window and prediction length as the above-mentioned comparison models. When the data set is ILI, the lookback window is 36, and the prediction lengths are {24, 36, 48, 60} respectively. For the other data sets, the lookback window is 96, and the prediction lengths are {96, 192, 336, 720} respectively.

[0098] Experimental conclusion: It is difficult for existing models to utilize the time domain and frequency domain information of time series to achieve effective decomposition of time series. Experimental evaluation on four public time series data sets ETTm2, Traffic, Weather and ILI shows that the use of the method of the present invention has a certain improvement in prediction accuracy, which is better than the existing methods. In the next study, we will focus on designing the lifting wavelet prediction and update function considering the period to further improve the decomposition ability of the lifting wavelet.

[0099] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A multivariate time series prediction method based on adaptive lifting wavelet transform, characterized in that: The following steps are involved: 1) Obtain time series data and preprocess it to obtain time series data within a specified range; 2) Use the SARIMA model to extract linear features from the preprocessed time series data to obtain the linear prediction results of the time series; The preprocessed time series data is subjected to adaptive lifting wavelet decomposition to decompose low-frequency approximate coefficients and high-frequency detail coefficients; 3) Preliminary prediction of the low-frequency approximate coefficients obtained in step 2) is performed through the OIF Elman neural network to obtain the low-frequency approximate coefficients after preliminary prediction; 4) The high-frequency detail coefficients obtained in step 2) and the low-frequency approximate coefficients initially predicted in step 3) are reconstructed by adaptive lifting wavelet hierarchical reconstruction, and the low-frequency approximate coefficients after each layer of reconstruction are predicted again until they are completely reconstructed, thereby obtaining the nonlinear prediction result of the time series; 5) Perform weighted fusion on the nonlinear prediction result obtained in step 4) and the linear prediction result obtained in step 2) to obtain the final prediction result.

2. The multivariate time series prediction method based on adaptive lifting wavelet transform according to claim 1 is characterized in that: In step 2), the preprocessed time series data is subjected to adaptive lifting wavelet decomposition to decompose low-frequency approximate coefficients and high-frequency detail coefficients. The specific operation steps are as follows: For the preprocessed time series data, the splitting process of adaptive lifting wavelet decomposition is firstly carried out. Based on the correlation between adjacent time points of the time series, the time series data is decomposed by lazy wavelet transform to obtain even sequence and odd sequence. The splitting process is expressed as: Split[X(t)]=[X e (t),X o (t)] X e (t)=X(2t) X o (t)=X(2t+1) In the formula, Split means splitting, t means the current time value, X(t) means the preprocessed time series data, and X e (t) represents the decomposed even sequence, X(2t) represents the time series with time 2t, and X o (t) represents the odd sequence after decomposition, X(2t+1) represents the time series with time 2t+1; In the update phase, the choice of the update operator depends on the locally available information in the even and odd sequences, and a decision map is defined based on this information: In the formula, D(X o ,X e )(t) is the decision function; |v(t)|+|w(t)| represents the sum of the absolute values ​​of the differences between the even sequence and the two adjacent odd sequences at time t, and represents the judgment condition of the decision function; v(t)=X e (t)-X o (t-1), represents the difference between the even sequence after decomposition at time t and the odd sequence after decomposition at time t-1; w(t) = X e (t)-X o (t) represents the difference between the even sequence and the odd sequence after decomposition at time t; T is the preset threshold; After defining the decision function, different update operators will be selected according to the different judgment results: o ,X e When )(t) = 0, it indicates that the gap between the even sequence and the two adjacent odd sequences is small. In order to eliminate the influence of noise and show the trend of the time series, the mean of the even sequence and the two adjacent odd sequences is used as the update improvement; when D(X o ,X e When )(t) = 1, it indicates that the gap between the even sequence and the two adjacent odd sequences is large. In order to retain the mutation part, the value of the odd sequence at time t is used as the update improvement; the update operator is defined as: Where U d is the adaptive update function, X o (t-1) represents the odd sequence after decomposition at time t-1; After the update is completed, the approximate coefficient is obtained, which describes the global trend of the original time series and is expressed as: Where X′(t) is the updated even sequence, which represents the low-frequency approximation coefficient. is the addition operator, using the average of the even sequence after decomposition at time t and the odd sequence after update at time t, defined as: In the prediction stage, according to the characteristics of time series correlation, the updated even sequence value is used to predict the odd sequence, and the difference between the odd sequence and the predicted value is calculated to obtain the detail coefficient, which reflects the similarity between the two. The high-frequency detail coefficient corresponding to the original time series is: d(t)=X o (t)-P(X′(t)) Where d(t) is the high-frequency detail coefficient, P(X′(t)) represents the adaptive prediction function, and a single-layer linear neural network suitable for the length of the time series is used.

3. The multivariate time series prediction method based on adaptive lifting wavelet transform according to claim 2 is characterized in that: In step 4), the high-frequency detail coefficients obtained by adaptive lifting wavelet decomposition and the low-frequency approximate coefficients initially predicted by the OIF Elman neural network are subjected to adaptive lifting wavelet hierarchical reconstruction. The reconstruction process is shown as follows: X o (t)=d(t)+P[X′(t)] X e (t)=X′(t)-U d (X o (t)) X m (t)=Merge[X e (t),X o (t)] In the formula, Merge means the fusion of even-odd sequences, X m (t) represents the sequence after the even-odd sequence is fused.

4. The multivariate time series prediction method based on adaptive lifting wavelet transform according to claim 3 is characterized in that: In step 5), the nonlinear prediction results obtained by adaptive lifting wavelet hierarchical reconstruction prediction and the linear prediction results obtained by SARIMA model prediction are weighted summed to obtain the final prediction result: the out (t)=αy nl (t)+βy l (t) In the formula, out represents output, y out (t) represents the final prediction result output at time t, nl represents nonlinearity, and y nl (t) represents the nonlinear prediction result of OIF Elman neural network prediction, l represents linear prediction, y l (t) represents the linear prediction result of the SARIMA model, α and β represent weighted values, and α+β=1, which is used to adjust the weights of the nonlinear part and the linear part.

5. The multivariate time series prediction method based on adaptive lifting wavelet transform according to claim 4 is characterized in that: The OIF Elman neural network is composed of an input layer, a hidden layer, a hidden-input feedback layer, an output-input feedback layer and an output layer, wherein the time length of the input layer is determined by the lookback window, the hidden layer takes the input of the previous moment and the output of the input layer at the current moment as input, so as to improve the ability of the network to process dynamic information, the hidden-input feedback layer stores the output value of the hidden layer at the previous moment, and is self-connected to the hidden layer, having a memory and storage function, the output-input feedback layer enhances the utilization of feedback information of each layer, and the output layer outputs the result according to the prediction length; the representation forms of the above hidden layer, hidden-input feedback layer, output-input feedback layer and output layer are as follows: x(t)=f(w1u(t-1)+w2x c (t)+w4y c (t)) x c (t)=vx c (t-1)+x(t-1) y c (t)=γy c (t-1)+y(t-1) y nl (t)=g(w3x(t)) In the formula, u(t-1) represents the input vector, x(t), x c (t), y c (t) and y nl (t) represents the output of the hidden layer, hidden-input feedback layer, output-input feedback layer and output layer at the current moment, x(t-1), y(t-1), x c (t-1) and y c (t-1) represents the output of the hidden layer, output layer, hidden-input feedback layer, and output-input feedback layer at the previous moment, respectively. w1, w2, w3, and w4 are the connection weights from the input layer to the hidden layer, from the hidden-input feedback layer to the hidden layer, from the hidden layer to the output layer, and from the output-input feedback layer to the hidden layer, respectively. v and γ are the self-connection feedback gain factors. g(·) is the transfer function of the output layer, which uses the purelin function. f(·) is the transfer function of the hidden layer, which uses the sigmoid function.

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