# Deep Neural Network Model Forecasting for Financial and Economic Market

Authors: Fan Chen
Journal: Journal of Mathematics
 (2022)

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## Abstract

Recently, the Internet financial market has developed rapidly both at home and abroad. Simultaneously, its study has also become the focus of academic circles. The financial markets have higher liquidity and volatility as compared to traditional financial markets. In view of the Internet financial market dynamic (volume and daily trading), it is proposed based on a deep neural network for fusion level time series prediction model. First, the proposed model processes the input of characteristic variables of multiple series (market macrodynamic series and multiseed series) and uses an attention mechanism to fuse the input variables in two dimensions of time and sequence feature. Second, the model also designs an optimization function based on the stability constraints of the prediction sequence, so that the model has better robustness. Finally, a large number of experiments are carried out on real large-scale data sets, and the results fully prove the effectiveness and robustness of the proposed model in the dynamic prediction of the Internet financial market.


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## Body

## 1. Introduction

Financial forecast is the prediction, estimation, and judgment of the financial activity process and its changing trend. The essence of financial forecasting is a special financial analysis method, which is related to the future as well as uncertainty [1]. The whole forecasting process is a scientific analysis process of financial activities. The analysis process is mainly based on the actual data and past experience, uses scientific methods and means to simulate the past financial development process, and obtains the change trend of the future development process. Preconceived judgments and inferences are made about the impact of financial activities to reduce uncertainty about the future [2]. At present, financial forecasting is highly valued in academic circles, financial circles, and people’s daily life. News and information on financial forecasts related to stocks, futures, and exchange rates can be found everywhere on the Internet, Television (TV) media, and newspapers. But financial activities are particularly complex and subject to many uncertainties, making it difficult to grasp future trends [3]. With regard to the current economic situation and the vigorous development of the market economy, the government must timely understand the actual situation of national economic development and financial market changes and grasp more accurate financial information.From the 1950s to the present, information science and technology and computer network development by leaps and bounds, big data increasingly rich. People used to predict financial market prices on the basis of economics and finance, but now, they use a variety of interdisciplinary combination models to predict financial markets, which makes financial market forecasting become a unique field of financial research [4]. The research content and purpose of this article can be described: USES certain method to maximize the extraction of financial time series contains rules and information; according to the existing financial time series, information reflected to robust hybrid forecasting model is established, and by using the model to predict financial time series trend of short-term operation, as a reference of market investors’ investment decisions [5].The prediction process of the financial time series includes the following steps: data preparation, algorithm definition, self-training and learning, prediction evaluation, and optimization. The data preparation stage is mainly data acquisition, data feature selection, data denoising, time series segmentation, clustering to provide data sets for self-learning, training, prediction, evaluation, and optimization [6]. The algorithm definition stage includes determining the prediction model and calculation method. The self-training learning stage includes selecting training learning algorithm, implementing training learning process, and adjusting training learning parameters. The prediction evaluation and optimization stage includes defining feedback indicators and optimizing the model according to the prediction results [7]. The basic framework of the financial time series forecasting process is shown in Figure 1.Figure 1
The general steps of financial forecasting.Most traditional financial time series prediction algorithms take the sequence of target variables as the main research object. Among them, representative technologies include the autoregressive model [8], vector autoregressive model [9, 10]. With deep learning technology development, recurrent neural network (RNN) is widely used in the sequence problem and shows a better learning ability than traditional linear model [11]; especially in the financial market dynamic prediction problem, deep learning model has good nonlinear mapping ability and strong generalization ability, thus better able to model the variable characteristics of financial markets, nonlinear associations, and time series dependencies. Among various deep neural network models, long short-term memory (LSTM) effectively solves the problem of long sequence dependence by introducing gate structure and retaining the long-term information that needs to be remembered in sequence features [12]. In addition, with the help of the powerful heterogeneous data processing ability of the neural network, some scholars designed fusion based on the structure of long- and short-term neural network. The prediction model is based on composite variable features [13]. Recent studies have found that the introduction of attention mechanism [14] into the sequence prediction problem can more effectively and quickly screen out the information that is more critical to the current task, thus further enhancing the prediction ability of the model. However, the traditional attention mechanism is mainly designed from the time dimension and cannot distinguish the different effects of multivariable time series.Aiming at the dynamic sequence of the Internet financial market (including daily trading volume and daily trading times), this paper designs a prediction model based on long- and short-term memory neural network structure. The dynamic macromodel of the overall market sequence integrates the dynamic sequence of each submarket and combines two attention mechanisms in terms of the time dimension and sequence characteristics. Due to the time dependence of modeling characteristics and the comprehensive influence of sequence input, the model is based on the sequence stability constraint optimization function so that the model has good robustness. The experimental results verified on the large-scale data of real Internet financial platforms fully demonstrate the effectiveness of the method designed in this paper in predicting the dynamics of the Internet financial market. In section two of this paper, we presented some of the related works to our research topic. In section three, we explained the neural networks and attention mechanism in much detail. In section four, the prediction model has been presented. In section five, we carried out experiments using the real data sets and analyzed their results to verify the working and efficiency of our method. In section six, the conclusion to the research is written.


## 2. Related Work

In financial scenarios, market information changes dynamically over time. Therefore, time series-based analysis and prediction are the focus of research in this field. This section first introduces the traditional time series prediction method, then introduces the deep learning model and attention mechanism in sequence problems related to research, and finally discusses the latest research work of sequence prediction in financial scenarios.


### 2.1. Traditional Time Series Prediction Method

According to the output results of the model, the traditional classical models are classified. The prediction models can be divided into random sequence model and deterministic sequence model. The traditional time series model generally needs strict mathematical principles. As the support of the model, it needs to be subject to more stringent constraints in order to use the extrapolation principle to predict future changes.Deterministic model: In many practical application problems, the change of time series is obtained by the superposition or coupling of many factors, such as seasonal change, trend factor, periodic change, and irregularity. In order to eliminate the influence of irregular factors on time series prediction, scholars have carried out relevant research. In this kind of prediction model, the decomposition method [15], moving average method [16], and seasonal coefficient method [16] are often used to construct the time series analysis model.Random model: Scholars in the field of statistics study time series by using random theory and find that irregular changes in time series caused by the joint action of many random factors are not completely chaotic but have certain regularity. Inspired by this phenomenon, the design of prediction models based on stochastic theory has attracted the attention of many scholars. Such models are generally based on the following procedures: First, the distribution of time series data to determine some reasonable conditions is observed and then used deductive reasoning to get a theoretical model describing the time series. If the theoretical model meets the characteristics of actual data, the actual model will be established and then used for time series analysis and prediction. Representative models of this kind include auto-regressive–moving average (ARMA) [17], auto-regressive integrated moving average (ARIMA) [18], auto-regressive conditional heteroskedasticity (ARCH) [19].


### 2.2. Time Series Prediction Method Based on Deep Learning

Deep neural network can obtain better representation capability than traditional methods through nonlinear variation of high-dimensional features. In time series prediction, the most widely used deep learning model is a cyclic neural network (RNN) [11] and long- and short-term memory neural network [12]. Cyclic neural network deals with the before and after dependence in time series data by introducing a cyclic mechanism. On the basis of RNN, LSTM introduces a “gate” structure to screen the antecedent information and selectively forget the unimportant information, so as to solve the difficulty of gradient disappearing in long sequence problems of RNN and further strengthen the dependence of long-distance information in learning time series.


### 2.3. Time Series Prediction Method Based on Attention Mechanism

Attention mechanism is an optimization method based on deep learning framework [20]. At present, attention mechanism has been well applied in natural language processing, computer vision, speech recognition, and other fields. Because the accuracy index of the attention model has increased significantly, many researchers have been exploring how to apply it to scenes that need more optimization details. The attention model refers to the mechanism of human visual attention. That is, when human beings obtain information, they will give priority to important information or some information they need at present.


## 2.1. Traditional Time Series Prediction Method

According to the output results of the model, the traditional classical models are classified. The prediction models can be divided into random sequence model and deterministic sequence model. The traditional time series model generally needs strict mathematical principles. As the support of the model, it needs to be subject to more stringent constraints in order to use the extrapolation principle to predict future changes.Deterministic model: In many practical application problems, the change of time series is obtained by the superposition or coupling of many factors, such as seasonal change, trend factor, periodic change, and irregularity. In order to eliminate the influence of irregular factors on time series prediction, scholars have carried out relevant research. In this kind of prediction model, the decomposition method [15], moving average method [16], and seasonal coefficient method [16] are often used to construct the time series analysis model.Random model: Scholars in the field of statistics study time series by using random theory and find that irregular changes in time series caused by the joint action of many random factors are not completely chaotic but have certain regularity. Inspired by this phenomenon, the design of prediction models based on stochastic theory has attracted the attention of many scholars. Such models are generally based on the following procedures: First, the distribution of time series data to determine some reasonable conditions is observed and then used deductive reasoning to get a theoretical model describing the time series. If the theoretical model meets the characteristics of actual data, the actual model will be established and then used for time series analysis and prediction. Representative models of this kind include auto-regressive–moving average (ARMA) [17], auto-regressive integrated moving average (ARIMA) [18], auto-regressive conditional heteroskedasticity (ARCH) [19].


## 2.2. Time Series Prediction Method Based on Deep Learning

Deep neural network can obtain better representation capability than traditional methods through nonlinear variation of high-dimensional features. In time series prediction, the most widely used deep learning model is a cyclic neural network (RNN) [11] and long- and short-term memory neural network [12]. Cyclic neural network deals with the before and after dependence in time series data by introducing a cyclic mechanism. On the basis of RNN, LSTM introduces a “gate” structure to screen the antecedent information and selectively forget the unimportant information, so as to solve the difficulty of gradient disappearing in long sequence problems of RNN and further strengthen the dependence of long-distance information in learning time series.


## 2.3. Time Series Prediction Method Based on Attention Mechanism

Attention mechanism is an optimization method based on deep learning framework [20]. At present, attention mechanism has been well applied in natural language processing, computer vision, speech recognition, and other fields. Because the accuracy index of the attention model has increased significantly, many researchers have been exploring how to apply it to scenes that need more optimization details. The attention model refers to the mechanism of human visual attention. That is, when human beings obtain information, they will give priority to important information or some information they need at present.


## 3. Neural Network and Attention Mechanism

This section first introduces the structure and principle of long- and short-term memory neural network model and then analyzes the design and construction of attention mechanism in sequence prediction for the extraction of important information in time series.


### 3.1. LSTM Neural Network

Based on the classical recurrent neural network RNN, the LSTM network can selectively forget nonimportant information and strengthen the prior important information by adding a nonlinear “gate” structure inside network neurons. Therefore, LSTM avoids the inevitable gradient disappearance problem when RNN trains on long sequences. Specifically, the gate structure of LSTM is defined as follows:(1)it=δWixt+Whiht−1+Wcict−1+b^i,ft=δWfxt+Whfht−1+Wcfct−1+b^f,ct=ftct−1+ittanhWcxt+Whcht−1+b^c,ot=δWoxt+Whoht−1+Wcoct+b^o,ht=ottanhct,where it, ft, ct, ot, and ht represent the hidden state of input gate, forgetting gate, memory module, output gate, and neuron, respectively. The forgetting gate and input gate structure of LSTM effectively propagates gradients by selectively preserving historical information, avoiding the problem of gradient disappearance caused by long-time sequence information. LSTM solves the problem that RNN cannot effectively learn the long-distance information dependency in time series, so it has been well applied in many time series modeling problems. The network structure of LSTM is shown in Figure 2.Figure 2
The network structure of LSTM.


### 3.2. Attentional Mechanism

The attention mechanism in the timing problem is mostly based on the encoder-decoder process of the deep loop network. The learning model is divided into two modules. The first is an encoder composed of a single or multilayer RNN, and the input sequence is input into the encoder according to the time relationship, which is used to learn the before and after dependencies of known sequences and the current state representation. The hidden state at the last moment is obtained and retained, which is called vectorC, which retains the dynamic information of the input sequence and the current state of the sequence. Then, a decoder is also composed of neural network units with similar structure, and the encoding vector E is converted into timing sequence information with predicted length T′. The input of each moment j is the vector obtained by the mapping vector E with the target value sequence y1,y2,…,yj−1. The output value of moment j is the predicted value of the corresponding moment, and its mathematical expression is(2)E=Fx1,x2,…,xT,yj=GE,y1,y2,…,yj−1.In the traditional codec model, the context vectorE used at each moment of decoding is fixed, and this construction does not incorporate the different principles of information concerned at different moments into the model. Researchers have further explored this problem by introducing the attention mechanism in image recognition into the sequence problem. By combining the attention mechanism with the codec structure, a sequential attention mechanism method is proposed, which is as follows:(3)Ej=Fx1,x2,…,xT,h,hj−1',yj=GEi,y1,y2,…,yj−1,where F represents the process of combining the attention mechanism with the encoder, hj−1' is the implicit state of the previous step of the decoder, and h is the implicit state set of the encoder. Different from the traditional codec model, for each prediction moment j, the encoder gets a dynamic context vector E that pays attention to different information, so that the decoding process can pay more attention to the historical information that is more important to the prediction content of the current time.


## 3.1. LSTM Neural Network

Based on the classical recurrent neural network RNN, the LSTM network can selectively forget nonimportant information and strengthen the prior important information by adding a nonlinear “gate” structure inside network neurons. Therefore, LSTM avoids the inevitable gradient disappearance problem when RNN trains on long sequences. Specifically, the gate structure of LSTM is defined as follows:(1)it=δWixt+Whiht−1+Wcict−1+b^i,ft=δWfxt+Whfht−1+Wcfct−1+b^f,ct=ftct−1+ittanhWcxt+Whcht−1+b^c,ot=δWoxt+Whoht−1+Wcoct+b^o,ht=ottanhct,where it, ft, ct, ot, and ht represent the hidden state of input gate, forgetting gate, memory module, output gate, and neuron, respectively. The forgetting gate and input gate structure of LSTM effectively propagates gradients by selectively preserving historical information, avoiding the problem of gradient disappearance caused by long-time sequence information. LSTM solves the problem that RNN cannot effectively learn the long-distance information dependency in time series, so it has been well applied in many time series modeling problems. The network structure of LSTM is shown in Figure 2.Figure 2
The network structure of LSTM.


## 3.2. Attentional Mechanism

The attention mechanism in the timing problem is mostly based on the encoder-decoder process of the deep loop network. The learning model is divided into two modules. The first is an encoder composed of a single or multilayer RNN, and the input sequence is input into the encoder according to the time relationship, which is used to learn the before and after dependencies of known sequences and the current state representation. The hidden state at the last moment is obtained and retained, which is called vectorC, which retains the dynamic information of the input sequence and the current state of the sequence. Then, a decoder is also composed of neural network units with similar structure, and the encoding vector E is converted into timing sequence information with predicted length T′. The input of each moment j is the vector obtained by the mapping vector E with the target value sequence y1,y2,…,yj−1. The output value of moment j is the predicted value of the corresponding moment, and its mathematical expression is(2)E=Fx1,x2,…,xT,yj=GE,y1,y2,…,yj−1.In the traditional codec model, the context vectorE used at each moment of decoding is fixed, and this construction does not incorporate the different principles of information concerned at different moments into the model. Researchers have further explored this problem by introducing the attention mechanism in image recognition into the sequence problem. By combining the attention mechanism with the codec structure, a sequential attention mechanism method is proposed, which is as follows:(3)Ej=Fx1,x2,…,xT,h,hj−1',yj=GEi,y1,y2,…,yj−1,where F represents the process of combining the attention mechanism with the encoder, hj−1' is the implicit state of the previous step of the decoder, and h is the implicit state set of the encoder. Different from the traditional codec model, for each prediction moment j, the encoder gets a dynamic context vector E that pays attention to different information, so that the decoding process can pay more attention to the historical information that is more important to the prediction content of the current time.


## 4. Prediction Model

On the basis of the above introduction of long- and short-term memory neural network and attention mechanism, this section presents the specific content of the integrated multitime series market dynamic prediction model proposed in this paper in detail. Let’s start with the model. The framework is then introduced in detail from three aspects: multisequence input, attention mechanism design, and optimization function.


### 4.1. Model Framework

In this section, an attention network model based on multiple time series (MALSTM) is designed and implemented by analyzing the dynamic characteristics of the financial market. The arrows in Figure3 represent the corresponding vectors of input and output in each module. Structures such as LSTM and full-connection layer are represented by marked rectangular boxes, and the state matrix of the hidden layer is represented by rounded rectangles. Specifically, the model first proposes an input module based on multiple time series and then designs the attention mechanism from two dimensions of time and feature. Finally, an optimization function based on the stability constraint of the prediction sequence is designed to make the prediction results more robust.Figure 3
Structure diagram of multitime series attention network model.


### 4.2. Multisequence Input

The traditional time series prediction method only considers the change of the target variable time series and does not consider the interaction of other feature sequences at the same time. However, in the dynamic analysis of the Internet financial market, its market dynamics will be affected by a number of different subcategories of market dynamics. Therefore, this paper modeled the overall macrodynamics of the market and the subsequences of multiple market categories at the same time and established multiple time series inputs.(4)xt=xt1,xt2,…,xtn,where xt represents the overall input of the model at time t, and xtc represents the input data of the c−th subclass sequence at the current time. For example, xt1 represents the observed trading volume of the platform at time t. xti represents the volume of transactions in a particular category (such as technology or robust items). Next, the model uses a single-layer LSTM to model the dynamic evolution process of multi-input time series. Specifically, for each time step, there are(5)ht,ct=LSTMht−1,ct−1,where ht and ct, respectively, represent the market hidden state and memory state of the current moment t. Therefore, the dynamic representation ht of the current multisequence can be obtained through LSTM.


### 4.3. Attention Mechanism Design

After multisequence LSTM input modeling, the dynamic stateht of the market at every moment and the memory state ct of multisequence input can be obtained. Considering that the macrodynamic modeling of the financial market requires important information in the sequential time series, the model needs to learn the key role of information at a different time for long-term change prediction. At the same time, considering the composition of the macromarket, the model should be able to automatically mine the subclass sequence that has the greatest influence on the overall macroseries prediction and further enhance the ability to forecast the market dynamics. Therefore, this paper designs two attention mechanisms from time dimension and multisequence feature dimension, respectively, to model the important influencing factors of market dynamics.First, the attention mechanism based on the historical state of the market is constructed in the time dimension by referring to the design idea of the traditional codec model; that is, the attention degree of the hidden state at different moments is different. According to the processing process of the LSTM input module in Section4.1, the output matrix h=h1,h1,…,hT model composed of hidden layer state at each moment can be obtained, and h is further taken as the output of the encoder. Each column vector h in matrix ht represents the market state at moment t, and it is taken as the input of the attention mechanism. Then, through formula (6), the importance of the current moment state to the prediction state yj is calculated as follows:(6)etj=Va⊤tanhWahj−1′+Uaht,atj=softmaxetj,hj−1' is decoder on one phase of the hidden states, and ht is market status at encoder time t. Wa, Ua, and Va⊤ state of the encoder and decoder are hidden states attention mechanism parameter matrix, and etj represents the market state of the encoder in time t for the influence degree of the current state output prediction time j finally by softmax function, normalization of etj operation, so as to obtain the weight factor of market state at each historical moment to the current forecast, that is, the attention value in the time dimension.In addition, considering that the macromarket dynamics are affected by the temporal changes of multiple subclasses, this paper proposes another attention mechanism based on multisequence feature dimensions. Different from the time dimension, the multisequence dimension attention mechanism needs to consider the influence of the historical coding state of each sequence on the complete macrodynamics of the market. By calculating the influence of the current sequence state on the macromarket dynamics according to all states of each sequence in the encoder sequence, the specific process is as follows:(7)ek′=VβTtanhUβhkT,βk=softmaxek′,where hkT represents the historical hidden state of the k-th subsequence, Uβ and VβT are the parameter matrices of the attention mechanism, and βk is the weight factor of the influence of the current sequence on the macromarket. Considering that the decoder needs to integrate the attention mechanism of time and feature dimension at the same time, a linear joint method of attention weight is designed in this paper to obtain the total weight factor Ej of the market prediction of time j by historical sequence.(8)Ej=∑t=1Tatj∑k=1nβkht.Finally, LSTM combined with attention factorEj can be used to form the decoder part of the model, so that the predicted value yj at time j can be gradually obtained as follows:(9)yj′=LSTMEi,hj−1′,cj−1′.Whenj=1, y1′=LSTME1,hf′,cT′. Where hf′,cT′ is the coded output of the historical sequence, and hf′ is the macromarket, hidden state cT′ represents the last memory state of a historical sequence.


### 4.4. Optimization Function Design

From the macrolevel, compared with specific financial products, the dynamic change of the financial market tends to be gentle due to the relative balance between total demand and total supply [21]. Therefore, the representation of macromarket should also tend to be stable and gentle change. In this study, a linear evolution constraint process is proposed for the representation of the output of the macromarket of the model; that is, the conditional distribution of equation (10) is adopted to satisfy the linear stationary constraint in the macrodynamic coding process of the model.(10)ht|ht−1∼NMht−1,Σ,where M is the state transition matrix, whose value is optimized during model training, and Σ is the covariance matrix. It can be seen that the hidden state of the macromarket is no longer directly generated by LSTM but evolved from the final state of the market. The evolution mode is as follows:(11)hf=MhT,where hf represents the hidden state of macromarket, and hT represents the last time step state of historical information. In order to further satisfy the stable characteristics of the macromarket dynamics, we design an optimization objective based on the linear evolution process of historical hidden states, which is used to constrain the representation of the macromarket to satisfy the linear stable characteristics in the learning process of the model. The specific optimization objective is to minimize L, and its mathematical expression is(12)Lp=∑t=1T−1ht+1−Mht22+hp−MhT22.The ultimate purpose of the model is to predict the future market state atT time by learning the historical sequence information. Therefore, accuracy is the most important optimization objective. The model selects root mean square error (RMSE), which is the most common in time series prediction at present, as shown in formula (13).(13)Ln=1T′∑j=1T′yj′−yj2.In order to prevent over-fitting caused by model training, the optimization objective of the equilibrium model with adjustable parameterλ in terms of its smoothness and accuracy is introduced. The final optimization function is(14)L=min∑i=1NLn+λLp.Specifically, the model uses the RMSPROP algorithm [22] with an initial learning rate of 0.0001 to optimize model parameters until the model converges. This section proposes a decoding time model and designs a new attention structure starting with the feature dimensions to be considered and the importance of different features. Then, the model is analyzed from the macro level. Specifically, the dynamic change of the financial market is restricted by the relative balance of high total demand and total supply because the prediction process constraint is realized by driving the needle slip linear constraint function. These two improvements are the most important innovations of this model.


## 4.1. Model Framework

In this section, an attention network model based on multiple time series (MALSTM) is designed and implemented by analyzing the dynamic characteristics of the financial market. The arrows in Figure3 represent the corresponding vectors of input and output in each module. Structures such as LSTM and full-connection layer are represented by marked rectangular boxes, and the state matrix of the hidden layer is represented by rounded rectangles. Specifically, the model first proposes an input module based on multiple time series and then designs the attention mechanism from two dimensions of time and feature. Finally, an optimization function based on the stability constraint of the prediction sequence is designed to make the prediction results more robust.Figure 3
Structure diagram of multitime series attention network model.


## 4.2. Multisequence Input

The traditional time series prediction method only considers the change of the target variable time series and does not consider the interaction of other feature sequences at the same time. However, in the dynamic analysis of the Internet financial market, its market dynamics will be affected by a number of different subcategories of market dynamics. Therefore, this paper modeled the overall macrodynamics of the market and the subsequences of multiple market categories at the same time and established multiple time series inputs.(4)xt=xt1,xt2,…,xtn,where xt represents the overall input of the model at time t, and xtc represents the input data of the c−th subclass sequence at the current time. For example, xt1 represents the observed trading volume of the platform at time t. xti represents the volume of transactions in a particular category (such as technology or robust items). Next, the model uses a single-layer LSTM to model the dynamic evolution process of multi-input time series. Specifically, for each time step, there are(5)ht,ct=LSTMht−1,ct−1,where ht and ct, respectively, represent the market hidden state and memory state of the current moment t. Therefore, the dynamic representation ht of the current multisequence can be obtained through LSTM.


## 4.3. Attention Mechanism Design

After multisequence LSTM input modeling, the dynamic stateht of the market at every moment and the memory state ct of multisequence input can be obtained. Considering that the macrodynamic modeling of the financial market requires important information in the sequential time series, the model needs to learn the key role of information at a different time for long-term change prediction. At the same time, considering the composition of the macromarket, the model should be able to automatically mine the subclass sequence that has the greatest influence on the overall macroseries prediction and further enhance the ability to forecast the market dynamics. Therefore, this paper designs two attention mechanisms from time dimension and multisequence feature dimension, respectively, to model the important influencing factors of market dynamics.First, the attention mechanism based on the historical state of the market is constructed in the time dimension by referring to the design idea of the traditional codec model; that is, the attention degree of the hidden state at different moments is different. According to the processing process of the LSTM input module in Section4.1, the output matrix h=h1,h1,…,hT model composed of hidden layer state at each moment can be obtained, and h is further taken as the output of the encoder. Each column vector h in matrix ht represents the market state at moment t, and it is taken as the input of the attention mechanism. Then, through formula (6), the importance of the current moment state to the prediction state yj is calculated as follows:(6)etj=Va⊤tanhWahj−1′+Uaht,atj=softmaxetj,hj−1' is decoder on one phase of the hidden states, and ht is market status at encoder time t. Wa, Ua, and Va⊤ state of the encoder and decoder are hidden states attention mechanism parameter matrix, and etj represents the market state of the encoder in time t for the influence degree of the current state output prediction time j finally by softmax function, normalization of etj operation, so as to obtain the weight factor of market state at each historical moment to the current forecast, that is, the attention value in the time dimension.In addition, considering that the macromarket dynamics are affected by the temporal changes of multiple subclasses, this paper proposes another attention mechanism based on multisequence feature dimensions. Different from the time dimension, the multisequence dimension attention mechanism needs to consider the influence of the historical coding state of each sequence on the complete macrodynamics of the market. By calculating the influence of the current sequence state on the macromarket dynamics according to all states of each sequence in the encoder sequence, the specific process is as follows:(7)ek′=VβTtanhUβhkT,βk=softmaxek′,where hkT represents the historical hidden state of the k-th subsequence, Uβ and VβT are the parameter matrices of the attention mechanism, and βk is the weight factor of the influence of the current sequence on the macromarket. Considering that the decoder needs to integrate the attention mechanism of time and feature dimension at the same time, a linear joint method of attention weight is designed in this paper to obtain the total weight factor Ej of the market prediction of time j by historical sequence.(8)Ej=∑t=1Tatj∑k=1nβkht.Finally, LSTM combined with attention factorEj can be used to form the decoder part of the model, so that the predicted value yj at time j can be gradually obtained as follows:(9)yj′=LSTMEi,hj−1′,cj−1′.Whenj=1, y1′=LSTME1,hf′,cT′. Where hf′,cT′ is the coded output of the historical sequence, and hf′ is the macromarket, hidden state cT′ represents the last memory state of a historical sequence.


## 4.4. Optimization Function Design

From the macrolevel, compared with specific financial products, the dynamic change of the financial market tends to be gentle due to the relative balance between total demand and total supply [21]. Therefore, the representation of macromarket should also tend to be stable and gentle change. In this study, a linear evolution constraint process is proposed for the representation of the output of the macromarket of the model; that is, the conditional distribution of equation (10) is adopted to satisfy the linear stationary constraint in the macrodynamic coding process of the model.(10)ht|ht−1∼NMht−1,Σ,where M is the state transition matrix, whose value is optimized during model training, and Σ is the covariance matrix. It can be seen that the hidden state of the macromarket is no longer directly generated by LSTM but evolved from the final state of the market. The evolution mode is as follows:(11)hf=MhT,where hf represents the hidden state of macromarket, and hT represents the last time step state of historical information. In order to further satisfy the stable characteristics of the macromarket dynamics, we design an optimization objective based on the linear evolution process of historical hidden states, which is used to constrain the representation of the macromarket to satisfy the linear stable characteristics in the learning process of the model. The specific optimization objective is to minimize L, and its mathematical expression is(12)Lp=∑t=1T−1ht+1−Mht22+hp−MhT22.The ultimate purpose of the model is to predict the future market state atT time by learning the historical sequence information. Therefore, accuracy is the most important optimization objective. The model selects root mean square error (RMSE), which is the most common in time series prediction at present, as shown in formula (13).(13)Ln=1T′∑j=1T′yj′−yj2.In order to prevent over-fitting caused by model training, the optimization objective of the equilibrium model with adjustable parameterλ in terms of its smoothness and accuracy is introduced. The final optimization function is(14)L=min∑i=1NLn+λLp.Specifically, the model uses the RMSPROP algorithm [22] with an initial learning rate of 0.0001 to optimize model parameters until the model converges. This section proposes a decoding time model and designs a new attention structure starting with the feature dimensions to be considered and the importance of different features. Then, the model is analyzed from the macro level. Specifically, the dynamic change of the financial market is restricted by the relative balance of high total demand and total supply because the prediction process constraint is realized by driving the needle slip linear constraint function. These two improvements are the most important innovations of this model.


## 5. Experiments and Results

This section verifies the effectiveness of the designed model in macrodynamic prediction of the Internet financial market by constructing experiments on real data sets.


### 5.1. The Experimental Data

The experimental data in this paper are all from the Prosper platform, which is the second-largest Internet P2P lending platform in the world. The experiment collected a total of 1622 days of investment records of the lender recorded on the platform from April 1, 2006, to May 25, 2011. In the experiment, all data samples were divided into training sets and test sets according to the ratio of 4:1; that is, 1297 days’ transaction data were used for model training, and 325 days’ transaction data were used for testing. Specifically, the daily trading volume and the number of transactions are mainly used as the research objects in the experiment. The six (risk order from high to low is “HR,” “E,” “D,” “C,” “B,” and “A”) dynamic sequences of the projects with different risk ratings are extracted, and the subclass sequence of the macromarket is used as the input of the model, and the historical sequence and target sequence of each sample are constructed according to the sliding window method.In view of the incompleteness and inconsistency of the platform for collecting real data, this paper introduces the preprocessing of training set and test set, which are as follows: (1) firstly, the linear interpolation method is used to deal with the shortcomings of data set values. Linear interpolation is adopted because a missing value cannot be simply deleted in the time series problem, which will lead to the fracture of the time series index; (2) after the standardization of the original time series data, the values of time series variables with different credit ratings vary greatly. The influence of numerical series on model training and prediction results will have great interference, and direct input to the model will lead to the weight deviation of model experiment. Therefore, the data normalization method is used to map all time series variables to the [0,1] interval:(15)X∗=X−XminXmax−Xmin,where X is the original data of the sequence variable, Xmax and Xmin are the maximum and minimum values of the original sequence variable respectively, and X∗ is the value normalized by the data, whose value range is [0, 1].


### 5.2. The Experimental Setup

In the experiment, the MALSTM model and all comparison methods proposed in this paper are implemented based on Python 3.5 and Tensorflow1.2.1. In all models involving LSTM structure, the number of neurons is set to 200, the dropout is 0.5, and batch size is set to 8. All the methods and programs in this paper run in the Linux environment with two 2.20GH2 Intel Xeon E5-2650 V4 CPU and four Tesla K80 GPU.In order to compare and verify the effect of the model proposed in this paper, four methods are selected and designed as the comparative experiment, which are as follows:(1)
ARIMA is a classical traditional time series prediction model. The input is a single time series, which only includes the total amount of the platform or the total number of loans.(2)
LSTM model of single sequence infusion. In the cyclic network model, LSTM is used to construct encoders and decoders, and the input of each time step only includes the total amount of platform or total number of transactions per day.(3)
LSTM model with multisequence input (denoted as LSTM-M), which uses LSTM to construct encoders and decoders. Referring to the multisequence input mechanism in this paper, the input of each time step includes not only the total amount or total transaction volume of the current platform every day but also the total amount or total transaction volume of projects with different risk levels every day. The input of each time step includes not only the total amount of money or total transactions of the current platform every day but also the total amount of money or total transactions of projects with different risk levels every day.(4)
Multisequence attention mechanism model (MALSTM-T). On the basis of LSTM-M model, the attention mechanism in time latitude is added.(5)
Multisequence attention mechanism model (MALSTM), namely, the attention model based on multisequence input proposed in this paper. MALSTM uses only RMSE as an optimization goal in training.(6)
The model of stationary optimization objective (MALSTM-L) is added. The linear stationary constraint proposed in this paper to the MALSTM model to optimize the model is added, and the complete optimization function designed in this paper is used.


### 5.3. Experimental Results and Analysis

In this paper, the total loan amount and total loan number of the platform are forecasted and compared. When the number of fixed historical days is 10, the prediction is made. The test days were adjusted from 1 to 10 to observe the performance of different models, as shown in Tables1 and 2.Table 1
The RMSE results of the market amount prediction in the next 10 days.
MethodDays12345678910ARIMA0.0640.0630.0640.0640.0650.0650.0660.0670.0680.070LSTM0.0620.0630.0640.0640.0650.0660.0670.0680.0700.072MLSTM0.0620.0630.0630.0630.0640.0640.0650.0650.0660.067MLSTM-t0.0590.0590.0600.0610.0610.0620.0620.0630.0630.064MALSTM0.0590.0590.0600.0600.0610.0610.0620.0610.0620.062MALSTM-L0.0580.0580.0590.0590.0590.0600.0580.0600.0600.061Table 2
The MAE results of the market amount prediction in the next ten days.
MethodDays12345678910ARIMA0.0450.0460.0460.0470.0490.0490.0500.0500.0520.054LSTM0.0440.0450.0460.0460.0480.0490.0500.0510.0530.055MLSTM0.0440.0440.0450.0450.0450.0460.0470.0480.0490.050MLSTM-t0.0410.0420.0430.0430.0440.0440.0450.0450.0450.046MALSTM0.0410.0420.0420.0430.0430.0440.0450.0440.0450.046MALSTM-L0.0400.0410.0410.0420.0430.0430.0430.0430.0440.044Tables1 and 2, respectively, show the RMSE and MAE values of the total transaction amount of the platform predicted by the four algorithms in the prediction days from 1 to 10 days. It can be clearly observed from the table that the model proposed in this paper (MALSTM and MALSTM-L) is significantly superior to other comparison models. Among them, in terms of RMSE index, MALSTM and MALSTM-L proposed in this paper have achieved a maximum improvement of 2.04% and 4.18%, respectively, compared with the classical attention architecture MALSTM-T and have achieved an improvement of 4.45%–6.72% and 6.04%–8.67% compared with other models without the use of attention mechanism.Meanwhile, in MAE index, compared with the classical attention architecture MALSTM-T, MALSTM and MALSTM-1 achieved a maximum improvement of 1.78% and 4.33%, respectively. Compared with other models without attention mechanism, MALSTM and MALSTM-1 achieved an improvement of 4.26%–8.96% and 5.82%–11.06%, respectively. These results illustrate the multi-input proposed in this paper. These results demonstrate the effectiveness and advancement of the multi-input attention deep network model proposed in this paper. At the same time, by comparing the two models proposed in this paper, it can be found that compared with MALSTM, the RMSE index, and Mae index of MALSTM-1 increase by 2.02% and 2.52%, which shows the rationality and effectiveness of the stability constraints based on the model and proves that the dynamic changes of the market tend to be stable.Furthermore, through the horizontal analysis of the prediction results according to the time dimension, it can be found that the prediction effect of the traditional LSTM and MLSTM models decreases significantly as the prediction time goes by. For example, the accuracy of the prediction results of the two models on the 10th day decreases 14.51% and 7.21%, respectively, under the RMSE index compared with the first day. It can be seen that the multisequence input model is significantly better than the model that directly inputs the target single sequence, which proves that the relationship between multiple sequences can effectively assist the macrodynamic modeling of the market, improves the accuracy of the model for long-term forecasting results. At the same time, for MALSTM and MALSTM-L models, the long-term prediction results are only reduced by 5.41% and 4.80% under the RMSE index, which indicates that the model proposed in this paper can well model the long-term fluctuations of the macrodynamics of the financial market and also indicates the effectiveness of the stability constraint in the macroprediction of the market, which further proves the robustness of the proposed model in financial macromarket forecasting. Figures4 and 5 show the RMSE and MAE values of the total number of transactions on the platform predicted by the four algorithms in the period from 1 to 10 days.Figure 4
Experimental results of RMSE.Figure 5
Experimental results of MAE.From Figures 4 and 5, it is clear that the MALSTM-L proposed in this paper has the largest stationarity constraint. The results further demonstrate the importance of the multisequence proposed in this paper for the prediction of macromarket dynamics and also prove the effectiveness of the multisequence attentional mechanism and the advance of the model designed in this paper. The results in Tables3 and 4 show the RMSE and MAE results of the market counts prediction in the next ten days.Table 3
The RMSE results of the market counts prediction in the next ten days.
MethodDays12345678910ARIMA0.0820.0810.0800.0790.0770.0780.0780.0790.0810.083LSTM0.0810.0800.0790.0770.0760.0760.0770.0790.0810.083MLSTM0.0800.0790.0770.0750.0750.0750.0770.0810.0780.085MLSTM-t0.0800.0780.0770.0750.0740.0750.0760.0760.0770.077MALSTM0.0790.0770.0760.0740.0740.0750.0760.0750.0760.076MALSTM-L0.0770.0770.0750.0740.0730.0730.0740.0750.0750.076Table 4
The MAE results of the market counts prediction in the next ten days.
MethodDays12345678910ARIMA0.0580.0570.0560.0550.0540.0550.0550.0570.0570.058LSTM0.0580.0560.0560.0540.0530.0550.0540.0570.0560.057MLSTM0.0570.0550.0560.0540.0520.0550.0530.0570.0550.057MLSTM-t0.0560.0550.0550.0540.0510.0550.0530.0560.0550.056MALSTM0.0560.0540.0550.0530.0510.0540.0530.0560.0540.056MALSTM-L0.0550.0540.0540.0520.0510.0530.0530.0550.0530.054The results show that the accuracy of the sequence prediction model increases first and then decreases with the passage of prediction time. Moreover, by comparing the variation trend of the prediction errors of the four methods, it can be found that the error of the MALSTM-L model has the smallest variation range over time, which further verifies the robustness of the model proposed in this paper in macromarket prediction and demonstrates the effectiveness of the introduced market stability constraint. In addition, in comparison, because the sequence of transaction number is less stable than that of the transaction amount, MAISTML has some cases weaker than MALSTM in the results of Tables3 and 4. And the graphs of the results are shown in Figures 6 and 7.Figure 6
Experimental results of RMSE.Figure 7
Experimental results of MAE.


## 5.1. The Experimental Data

The experimental data in this paper are all from the Prosper platform, which is the second-largest Internet P2P lending platform in the world. The experiment collected a total of 1622 days of investment records of the lender recorded on the platform from April 1, 2006, to May 25, 2011. In the experiment, all data samples were divided into training sets and test sets according to the ratio of 4:1; that is, 1297 days’ transaction data were used for model training, and 325 days’ transaction data were used for testing. Specifically, the daily trading volume and the number of transactions are mainly used as the research objects in the experiment. The six (risk order from high to low is “HR,” “E,” “D,” “C,” “B,” and “A”) dynamic sequences of the projects with different risk ratings are extracted, and the subclass sequence of the macromarket is used as the input of the model, and the historical sequence and target sequence of each sample are constructed according to the sliding window method.In view of the incompleteness and inconsistency of the platform for collecting real data, this paper introduces the preprocessing of training set and test set, which are as follows: (1) firstly, the linear interpolation method is used to deal with the shortcomings of data set values. Linear interpolation is adopted because a missing value cannot be simply deleted in the time series problem, which will lead to the fracture of the time series index; (2) after the standardization of the original time series data, the values of time series variables with different credit ratings vary greatly. The influence of numerical series on model training and prediction results will have great interference, and direct input to the model will lead to the weight deviation of model experiment. Therefore, the data normalization method is used to map all time series variables to the [0,1] interval:(15)X∗=X−XminXmax−Xmin,where X is the original data of the sequence variable, Xmax and Xmin are the maximum and minimum values of the original sequence variable respectively, and X∗ is the value normalized by the data, whose value range is [0, 1].


## 5.2. The Experimental Setup

In the experiment, the MALSTM model and all comparison methods proposed in this paper are implemented based on Python 3.5 and Tensorflow1.2.1. In all models involving LSTM structure, the number of neurons is set to 200, the dropout is 0.5, and batch size is set to 8. All the methods and programs in this paper run in the Linux environment with two 2.20GH2 Intel Xeon E5-2650 V4 CPU and four Tesla K80 GPU.In order to compare and verify the effect of the model proposed in this paper, four methods are selected and designed as the comparative experiment, which are as follows:(1)
ARIMA is a classical traditional time series prediction model. The input is a single time series, which only includes the total amount of the platform or the total number of loans.(2)
LSTM model of single sequence infusion. In the cyclic network model, LSTM is used to construct encoders and decoders, and the input of each time step only includes the total amount of platform or total number of transactions per day.(3)
LSTM model with multisequence input (denoted as LSTM-M), which uses LSTM to construct encoders and decoders. Referring to the multisequence input mechanism in this paper, the input of each time step includes not only the total amount or total transaction volume of the current platform every day but also the total amount or total transaction volume of projects with different risk levels every day. The input of each time step includes not only the total amount of money or total transactions of the current platform every day but also the total amount of money or total transactions of projects with different risk levels every day.(4)
Multisequence attention mechanism model (MALSTM-T). On the basis of LSTM-M model, the attention mechanism in time latitude is added.(5)
Multisequence attention mechanism model (MALSTM), namely, the attention model based on multisequence input proposed in this paper. MALSTM uses only RMSE as an optimization goal in training.(6)
The model of stationary optimization objective (MALSTM-L) is added. The linear stationary constraint proposed in this paper to the MALSTM model to optimize the model is added, and the complete optimization function designed in this paper is used.


## 5.3. Experimental Results and Analysis

In this paper, the total loan amount and total loan number of the platform are forecasted and compared. When the number of fixed historical days is 10, the prediction is made. The test days were adjusted from 1 to 10 to observe the performance of different models, as shown in Tables1 and 2.Table 1
The RMSE results of the market amount prediction in the next 10 days.
MethodDays12345678910ARIMA0.0640.0630.0640.0640.0650.0650.0660.0670.0680.070LSTM0.0620.0630.0640.0640.0650.0660.0670.0680.0700.072MLSTM0.0620.0630.0630.0630.0640.0640.0650.0650.0660.067MLSTM-t0.0590.0590.0600.0610.0610.0620.0620.0630.0630.064MALSTM0.0590.0590.0600.0600.0610.0610.0620.0610.0620.062MALSTM-L0.0580.0580.0590.0590.0590.0600.0580.0600.0600.061Table 2
The MAE results of the market amount prediction in the next ten days.
MethodDays12345678910ARIMA0.0450.0460.0460.0470.0490.0490.0500.0500.0520.054LSTM0.0440.0450.0460.0460.0480.0490.0500.0510.0530.055MLSTM0.0440.0440.0450.0450.0450.0460.0470.0480.0490.050MLSTM-t0.0410.0420.0430.0430.0440.0440.0450.0450.0450.046MALSTM0.0410.0420.0420.0430.0430.0440.0450.0440.0450.046MALSTM-L0.0400.0410.0410.0420.0430.0430.0430.0430.0440.044Tables1 and 2, respectively, show the RMSE and MAE values of the total transaction amount of the platform predicted by the four algorithms in the prediction days from 1 to 10 days. It can be clearly observed from the table that the model proposed in this paper (MALSTM and MALSTM-L) is significantly superior to other comparison models. Among them, in terms of RMSE index, MALSTM and MALSTM-L proposed in this paper have achieved a maximum improvement of 2.04% and 4.18%, respectively, compared with the classical attention architecture MALSTM-T and have achieved an improvement of 4.45%–6.72% and 6.04%–8.67% compared with other models without the use of attention mechanism.Meanwhile, in MAE index, compared with the classical attention architecture MALSTM-T, MALSTM and MALSTM-1 achieved a maximum improvement of 1.78% and 4.33%, respectively. Compared with other models without attention mechanism, MALSTM and MALSTM-1 achieved an improvement of 4.26%–8.96% and 5.82%–11.06%, respectively. These results illustrate the multi-input proposed in this paper. These results demonstrate the effectiveness and advancement of the multi-input attention deep network model proposed in this paper. At the same time, by comparing the two models proposed in this paper, it can be found that compared with MALSTM, the RMSE index, and Mae index of MALSTM-1 increase by 2.02% and 2.52%, which shows the rationality and effectiveness of the stability constraints based on the model and proves that the dynamic changes of the market tend to be stable.Furthermore, through the horizontal analysis of the prediction results according to the time dimension, it can be found that the prediction effect of the traditional LSTM and MLSTM models decreases significantly as the prediction time goes by. For example, the accuracy of the prediction results of the two models on the 10th day decreases 14.51% and 7.21%, respectively, under the RMSE index compared with the first day. It can be seen that the multisequence input model is significantly better than the model that directly inputs the target single sequence, which proves that the relationship between multiple sequences can effectively assist the macrodynamic modeling of the market, improves the accuracy of the model for long-term forecasting results. At the same time, for MALSTM and MALSTM-L models, the long-term prediction results are only reduced by 5.41% and 4.80% under the RMSE index, which indicates that the model proposed in this paper can well model the long-term fluctuations of the macrodynamics of the financial market and also indicates the effectiveness of the stability constraint in the macroprediction of the market, which further proves the robustness of the proposed model in financial macromarket forecasting. Figures4 and 5 show the RMSE and MAE values of the total number of transactions on the platform predicted by the four algorithms in the period from 1 to 10 days.Figure 4
Experimental results of RMSE.Figure 5
Experimental results of MAE.From Figures 4 and 5, it is clear that the MALSTM-L proposed in this paper has the largest stationarity constraint. The results further demonstrate the importance of the multisequence proposed in this paper for the prediction of macromarket dynamics and also prove the effectiveness of the multisequence attentional mechanism and the advance of the model designed in this paper. The results in Tables3 and 4 show the RMSE and MAE results of the market counts prediction in the next ten days.Table 3
The RMSE results of the market counts prediction in the next ten days.
MethodDays12345678910ARIMA0.0820.0810.0800.0790.0770.0780.0780.0790.0810.083LSTM0.0810.0800.0790.0770.0760.0760.0770.0790.0810.083MLSTM0.0800.0790.0770.0750.0750.0750.0770.0810.0780.085MLSTM-t0.0800.0780.0770.0750.0740.0750.0760.0760.0770.077MALSTM0.0790.0770.0760.0740.0740.0750.0760.0750.0760.076MALSTM-L0.0770.0770.0750.0740.0730.0730.0740.0750.0750.076Table 4
The MAE results of the market counts prediction in the next ten days.
MethodDays12345678910ARIMA0.0580.0570.0560.0550.0540.0550.0550.0570.0570.058LSTM0.0580.0560.0560.0540.0530.0550.0540.0570.0560.057MLSTM0.0570.0550.0560.0540.0520.0550.0530.0570.0550.057MLSTM-t0.0560.0550.0550.0540.0510.0550.0530.0560.0550.056MALSTM0.0560.0540.0550.0530.0510.0540.0530.0560.0540.056MALSTM-L0.0550.0540.0540.0520.0510.0530.0530.0550.0530.054The results show that the accuracy of the sequence prediction model increases first and then decreases with the passage of prediction time. Moreover, by comparing the variation trend of the prediction errors of the four methods, it can be found that the error of the MALSTM-L model has the smallest variation range over time, which further verifies the robustness of the model proposed in this paper in macromarket prediction and demonstrates the effectiveness of the introduced market stability constraint. In addition, in comparison, because the sequence of transaction number is less stable than that of the transaction amount, MAISTML has some cases weaker than MALSTM in the results of Tables3 and 4. And the graphs of the results are shown in Figures 6 and 7.Figure 6
Experimental results of RMSE.Figure 7
Experimental results of MAE.


## 6. Conclusion

Internet is the macrodynamic prediction of financial markets, and the author of this paper, first, introduces the time series of dynamic characteristics of the Internet financial markets and the prediction problem of the research background and reviews the traditional time series prediction method, based on the deep learning method and attention mechanism, and on the current temporal prediction, research has carried on the brief introduction of the financial markets. In view of the characteristics of strong liquidity and high volatility of the Internet financial market, this paper proposes a prediction model based on deep neural network fusion hierarchical multitime series learning. First, the model can process the input of multiple sequence feature variables (macrodynamic series and multiseed series) and fuse the input variables in time and sequence feature by using the attention mechanism. Second, the model designs an optimization function based on the stability constraint of the prediction sequence, which makes the model prediction have better robustness. Finally, a large number of experiments are carried out on a real large Internet financial data set. The experimental results show that the neural network time series learning prediction model based on multilevel fusion depth proposed in this paper has achieved the best prediction performance, which fully proves the effectiveness and robustness of the model in the macrodynamic prediction of the Internet financial market.In this paper, the macrodynamic prediction of the Internet financial market is explored, and the influence of multisequence input on market dynamics is modeled. Meanwhile, the stability of the market macrodynamic is utilized to improve the accuracy of time series prediction, providing a new research idea for time series prediction. Future research can be carried out from two aspects: (1) to further explore the influence of subsequences on macrodynamics and the interaction between subsequences; (2) to explore the influence of external information, such as news media texts, on the prediction of market macrodynamics.



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*Source: 8146555-2022-03-24.xml*