Reassessing Rolling Window effects in the Era of Machine Learning: Evidence from ARIMA and LSTM Models for Stock Index Forecasting

Abstract

Under the theories of the Efficient Market Hypothesis (EMH) and Adaptive Market Hypothesis (AMH), the study aims to evaluate and compare the forecasting accuracy of three competing models, viz., ARIMA (recursive), ARIMA (rolling), and LSTM, across three international stock market indices from India, the US, and China using the Diebold-Mariano (DM) test. To simulate real-world forecasting conditions and ensure a comparison between the LSTM and ARIMA models, the Rolling-Window Forecasting method is employed. The methodological innovation of rolling window forecasting not only aligns ARIMA (rolling) with LSTM in terms of level playing field but, crucially, delivers significantly superior forecasting accuracy. Although LSTM excels at capturing both the nonlinear and linear nature of data compared with ARIMA, the forecasting accuracy of ARIMA (rolling) is significantly better than that of LSTM and ARIMA (recursive) as per DM test. However, the forecasting accuracy of LSTM is significantly better than that of ARIMA (recursive) as per DM test. The three models for each of the three indices are also evaluated on the basis of five measures- MAE, MSE, RMSE, MAPE, R². On all five measures, ARIMA (rolling) has less forecasting errors than LSTM and ARIMA (recursive), and, like the extant literature, LSTM has fewer forecasting errors than ARIMA (recursive).