Predictive power of ARIMA models in forecasting equity returns: a sliding window method

Abstract

The ARIMA model is widely adopted by the financial industry as the standard statistical instrument for forecasting asset returns. Numerous studies have compared the accuracy of the ARIMA model with other competing models. However, there are no studies that cover a broad range of equities and their time series. Furthermore, there is no clear guideline on the time series window selected to fit the ARIMA model. In addition, there are no firm conclusions on whether older information in the sample should be abandoned. This makes it impossible to draw a definitive conclusion about the predictive power of the ARIMA model. This study sets out to address this gap in the literature. It summarizes more than two million ARIMA forecasts of future daily returns, using data from January 3, 1996 to May 12, 2017. The forecasts are run with different model parameter settings. We find that the five-year sliding fixed-width window fits US equity market asset prices to the highest degree, with an annual over-optimistic error of 2.6561%. However, when environments with positive and negative returns are separated, the ARIMA models generate forecasting errors of − 0.0009% and 0.011%, and both underestimate gain and loss. These errors are lower for low volatility equities. We conclude that the lack of nonlinearity of the ARIMA model is not a major concern, and that the ARIMA models do not lose their validity if the data windows are carefully selected. Our conclusions are not in conflict with the weak form market efficiency hypothesis and are robust in an environment with transaction cost.

Appendix

The first part of the Appendix presents the facts of the randomly selected companies and their stocks to conduct the ARIMA forecast accuracy measure. The purpose of this list is to demonstrate that our study covers a wide range of companies, regarding their sector, industry, market capitalization, systematic risk, and listing agents (Table 6).

Table 6 Companies studied in the data sample

The second part of the Appendix presents the detailed ARIMA forecast errors for the individual assets categorized in different volatility groups. The errors are presented in the order of growing window sample, one-year sliding window, two-year sliding window, three-year sliding window, and five-year sliding window. The error measures included are:

“Positive”, or “P”: ARIMA forecast deviation of the asset on the trading days when positive returns are realized;

“Negative”, or “N”: ARIMA forecast deviation of the asset on the trading days when negative returns are realized;

“Total”, or “T”: ARIMA forecast deviation of the asset with both positive and negative return environments;

“Skewness”, or “S”: The skewness of ARIMA forecast deviation of the asset;

“Kurtosis”, or “K”: The kurtosis of ARIMA forecast deviation of the asset (Tables 7, 8, 9);

Table 7 ARIMA errors in positive and negative return environments I: low volatility equities

Table 8 ARIMA errors in positive and negative return environments II: mid volatility equities

Table 9 ARIMA errors in positive and negative return environments III: high volatility equities