Predictive power of ARIMA models in forecasting equity returns: a sliding window method
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ORIGINAL ARTICLE
Predictive power of ARIMA models in forecasting equity returns: a sliding window method Huijian Dong1 · Xiaomin Guo2 · Han Reichgelt3 · Ruizhi Hu4 Revised: 7 July 2020 © Springer Nature Limited 2020
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. Keywords ARIMA · Forecast · Equity · Asset price · Accuracy · Algorithm
Introduction
* Huijian Dong [email protected] Xiaomin Guo [email protected] Han Reichgelt [email protected] Ruizhi Hu [email protected] 1
Associate Professor of Finance, Kate Tiedemann School of Business and Finance, University of South Florida, 140 7th Ave. S, St. Petersburg, FL 33701, USA
2
Instructor of Finance, University of South Florida, St. Petersburg, USA
3
Professor of Information Systems, University of South Florida, St. Petersburg, USA
4
Department of Law and Management, University of York, York, UK
Financial market asset price forecast is a topic that probably attracts most attention from academia and industry. The benefits of successful price forecasts are obvious. The most widely used model is the Autoregressive Integrated Moving Average (ARIMA) model. ARIMA is used to predict future equity returns based on returns of the assets in question in a time series. Despite its widespread use, three questions related to the precision of ARIMA are still under debate: (1) what the appropriate window length is to use to generate the regression parameters and therefore the forecast results; (2) whether the window should be fixed-width sliding, or
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