1. Introduction

The Shanghai Composite Index is the oldest of the major indexes in the A-share market in China. Different from other major stock market indexes, Shanghai Composite index is a comprehensive index, that is, it considers as many securities listed on Shanghai Composite Index as possible to be included in the index scope, so the biggest feature of Shanghai Composite Index is comprehensive, the study of Shanghai Stock Index is of great significance to China's stock market.

Prediction of stock prices is a classic problem. The love affair with stock investing has never waned over time. People try to profit from the stock market by predicting share prices. If stocks can predict effectively, then people will be able to earn high returns in the capital market. In addition, from an academic point of view, the predictability of stocks contributes to the study of the efficiency of the capital market and helps scholars to realize a more realistic capital model. So, the issue of stock forecasting is very important. But the price of a stock is subject to so many uncertainties that it is difficult for investors to make effective predictions about the stock.

Previous researchers mostly used a single machine learning model to forecast the stock price, including nonlinear time series model [1,2], artificial neural network [3-5], decision tree [6,7], genetic algorithm [8,9], Markov model [10], support vector set [11-13], etc. However, previous investigations seem still limited. Thus, this paper selects the historical data of Shanghai Composite Index from 1991 to 2016 and use ARIMA and LSTM models to forecast the data of the Shanghai Composite Index.

2. Methodology

This paper mainly uses ARIMA and LSTM to forecast the closing price of Shanghai Composite Index (1991-2016). This chapter mainly introduces these two methods, which predict the closing price from 2014 to 2016 respectively. The rmse is calculated from the predicted value and the real value. Then, this paper select a model with better predictions by comparing the result of the rmse of the two models.

2.1. ARIMA

ARIMA is a statistical forecasting method and a time series forecasting method. It builds the model through the combination of white noise and ensures that the residual difference between the model and the actual data is also a normal distribution with a small mean. This method is based on the assumption that the data are stationary and time-dependent and also change linearly.

Firstly, by building an ARIMA model, time series should be made stationarily. The parameter d should also be determined. The stability of the sequence is observed by drawing the sequence or performing ADF test. And then differentiate it. Difference means subtracting the previous value from the last value. The parameter d is determined by the minimum figure of differencing needed to make the series stationary.

The parameter p of the autoregressive model indicates that predicting the current value is to use the historical value in several periods. And in an autoregressive model, if it is not a white noise sequence, it is usually considered as a q order moving average. Next, comparing autocorrelations and partial autocorrelations and determine the order of regression (p) and order of moving average (q).

Then, this paper can build the model according to p, q and d and select the model with the smallest AIC and BIC.

2.2. LSTM

LSTM is a machine learning algorithm based on deep learning. Stock data is a set of time series in which samples are correlated with each other in sequential order and predictions are made based on the correlation. LSTM improves the linearity, meets the nonlinear condition well, and can solve the problems of length dependence and gradient disappearance better than the general RNN.

The transmission form of A recurrent neural network RNN is that X serves as the input layer and generates input h and a signal after processing by neuron A. This signal will be input to A together with X as the next input, and repeat. Where, the generated signal can be the same or different from h. Think of the signals that neurons produce for the next round of input as experiences. The output of neurons depends not only on X, but also on experience. This experience is also seen as an association between sequence samples.

Long-term memory network is a kind of RNN, which is mainly composed of forgetting gate, input gate, updating neuron state gate and output gate. It is compared to a traditional recurrent neural network, where C represents the state of the node, where C and h are passed down as experience during learning (See Figure 1).

Figure 1: LSTM model.

3. Results

3.1. ARIMA

First, ADF Test result is compared to different degrees at 1%, 5%, and %10 and checking the result if it can reject the statistical value of the original hypothesis at those degrees. If the result is all less than three degrees at the same time, it means that the hypothesis can be very well rejected. In this data, the adf result is -12, which is less than the statistical value of three degrees. In the result got from the data, the P-value is 1.005e-23, which is close to 0. After first-order difference, the data series becomes a stationary white noise series, so the model can be preliminarily judged as AR (1) model.

The autocorrelation graphs and partial autocorrelation graphs after first-order difference are as follows in Figures 2 and 3:

Figure 2: Autocorrelation.

Figure 3: Partial Autocorrelation.

According to the autocorrelation graph and partial autocorrelation graph, the autocorrelation coefficient and partial autocorrelation coefficient rapidly decrease to near 0, so it is determined to be a first-order truncation, so p is equal to 1 and q is equal to 1.

Then, according to the results of the evaluation criteria, when p = 1 and q = 1, the two values are the smallest, AIC is 64325.120, BIC is 64352.068.

Model test is carried out, and all the P-values are less than 0.05 except the intercept term (indicating that there is no constant term), that is, the null hypothesis is rejected, indicating that the model diagnosis passes.

Finally, the model predicts and visualizes the closing prices from 2014 to 2016 (See Figure 4). Calculate the rmse of the predicted value and the real value. Rmse is calculated to be 1101. From the results, the prediction effect is not very good.

Figure 4: ARIMA Predicts Result.

3.2. LSTM

A two-layer LSTM model is built for prediction and the results are visualized in Figure 5.

Figure 5: LSTM Predicts Result.

3.3. Comparison

By comparing the predictions of the two models, this paper makes the conclusion that LSTM is better than ARIMA in predicting the performance of Shanghai Composite Index (See Table 1).

Table 1: Rmse Comparison Results.

4. Conclusion

This paper uses ARIMA and LSTM models to forecast the Shanghai Composite Index (1991-2016). The prediction effect of the two models is compared and analyzed. Rmse is used as the standard of prediction, and LSTM is better for the data set used in this paper. LSTM has already optimized to other advanced models, this paper only takes LSTM into consideration, adopting alternative models deserve further investigations.