Analysis and Forecasting the Price of the S&P 500 Index Using the Arima Model

Abstract

The results of the research allowed to determine that the chosen S&P 500 index can serve as a reflection of the state and forecasts of economic development of the United States. A successful forecast of the index can serve not only as a key point in building an individual investment strategy, but also as an indicator of the general state of the economy. The mathematical model for predicting the dynamics of the index was built. Through exploratory data analysis, a better understanding of the time series and its characteristics was obtained. The application of various statistical methods, such as moving statistics and stationarity tests, made it possible to identify trends and seasonality in the data. Seasonal decomposition and logarithmic transformation helped to better understand the contribution of each component to the overall index dynamics, and special attention was paid to the stationary ADF test, where was considered not only the code but also the significant formulas. The optimal selection of parameters was done automatically. ARIMA model showed good results – the evaluation of the model accuracy included the comparison of the predicted values with the actual values of the SP500 index, both visually and using several metrics – MAE, MSE, RMSE, MAPE. The result of the work is a model for predicting the dynamics of the S & P 500 index, implemented using the Python programming language with a MAPE of about 1.9%, the accuracy of the model is 98.1%. and such good results indicate the possibility of using this tool by market participants in real conditions.