Forecasting Ability of a Periodic Component Extracted from Large‐Cap Index Time Series

We develop a method to extract periodic variations in a time series that are hidden in large non‐periodic and stochastic variations. This method relies on folding the time series many times and allows direct visualization of a hidden periodic component without resorting to any fitting procedure. Applying this method to several large‐cap stock time series in Europe, Japan and the USA yields a component with periodicity of 1 year. Out‐of‐sample tests on these large‐cap time series indicate that this periodic component is able to forecast long‐term (decade) behavior for large‐cap time series. Copyright © 2016 John Wiley & Sons, Ltd.