Forecasting Time Series with Boot.EXPOS Procedure

Abstract

To forecast future values of a time series is one of the main goals in times series analysis. Many forecasting methods have been developed and its performance evaluated. In order to make a selection among an avalanche of such emerging methods they have to be compared in a kind of forecasting competition. One of these competitions is the M3 competition with its 3003 time series. The competition results in Makridakis and Hibon (2000) paper are frequently used as a benchmark in comparative studies. The Boot.EXPOS approach developed by the authors, combines the use of exponential smoothing methods with the bootstrap methodology to forecast time series. The idea is to join these two approaches (bootstrap and exponential smoothing) and to construct a computational algorithm to obtain forecasts. It works in an automatic way and can be summarized as follows: (i) choose an exponential smoothing model, among several proposed using the mean squared error, and obtain the model components; (ii) fit an AR to the residuals of the adjusted model; the order of the AR is selected by AIC criterion; (iii) center the new residuals obtained in previous step and resample; (iv) obtain a bootstrapped replica of the time series according to the AR model and exponential smoothing components found in first step; (v) forecast future values according to model in (i); (vi) compute the point forecast as the mean or as the median of the predicted values. The performance of the procedure here proposed is evaluated by comparing it with other procedures presented in the M3 competition. Some accuracy measures are used for that comparison. All computational work is done using the R2.8.1 software (R Development Core Team, 2008).

Keywords

• bootstrap
• exponential smoothing
• forecasting accuracy
• M3 competition