Prediction of S&P500 Stock Index Using ARIM and Linear Regression

Abstract

This paper mainly establishes a linear model suitable for the volatility of the S&P 500 index and forecasts the S&P 500 index. Firstly, the data set is divided into the training set and test set. After testing a series of data attributes such as the smoothness of the original data series and log series, the original data series and log series of the S&P 500 index weekly data series are modeled based on the ARIMA model. The next step is to check the fit of the model and use ACF and PACF to determine the parameters of two different models to fit the original data series and the log data series, respectively. Based on two different models, the rationality of the model is confirmed by the residual white noise test and various natural maps. By establishing the model and analyzing the residual error of the model, finding out unreasonable fluctuation of the residual error of the model fitting and giving the corresponding explanation combined with the history. Finally, a fitted model to make rough forecasts for the S&P 500 from January 2020 to December 2020. Although this forecasting model cannot predict detailed fluctuations daily, it can still correctly determine whether a stock is going up or down. To sum up, the ARIMA model does not perform well in stock forecasting and it may need to be improved using other methods.