Time series multistep-ahead predictability estimation and ranking

A predictability index was defined as the ratio of the variance of the optimal prediction to the variance of the original time series by Granger and Anderson, and Bhansali. A new simplified algorithm for estimating the predictability index is introduced and the new estimator is shown to be a simple and effective tool in applications of predictability ranking and as an aid in the preliminary analysis of time series. The relationship between the predictability index and the position of the poles and lag p of a time series which can be modelled as an AR(p) model are also investigated. The effectiveness of the algorithm is demonstrated using numerical examples including an application to stock prices.