Rolling Analysis of Time Series

Abstract

A rolling analysis of a time series model is often used to assess the model's stability over time. When analyzing financial time series data using a statistical model, a key assumption is that the parameters of the model are constant over time. However, the economic environment often changes considerably , and it may not be reasonable to assume that a model's parameters are constant. A common technique to assess the constancy of a model's parameters is to compute parameter estimates over a rolling window of a fixed size through the sample. If the parameters are truly constant over the entire sample, then the estimates over the rolling windows should not be too dierent. If the parameters change at some point during the sample, then the rolling estimates should capture this instability. Rolling analysis is commonly used to backtest a statistical model on historical data to evaluate stability and predictive accuracy. Backtesting generally works in the following way. The historical data is initially split into an estimation sample and a prediction sample. The model is then fit using the estimation sample and-step ahead predictions are made for the prediction sample. Since the data for which the predictions are made are observed-step ahead prediction errors can be formed. The estimation sample is then rolled ahead a given increment and the estimation and prediction exercise is repeated until it is not possible to make any more-step predictions. The statistical properties of the collection of-step ahead pre