Applied Modeling Techniques and Data Analysis 2

15Forecast Uncertainty of the Weighted TAR Predictor

In this chapter, we investigate the forecast uncertainty of a new predictor proposed for the Self-Exciting Threshold AutoRegressive (SETAR) model. We consider a weighted mean predictor whose weights are obtained from the minimization of the Mean Square Forecast Errors (MSFE). Even though the “point accuracy” of this predictor has been investigated, the study of its distribution and, in particular, the construction of the prediction intervals have not been studied. Starting from the evaluation that the predictor follows a nonstandard distribution, in this chapter, we focus the attention on the generation of prediction intervals for the weighted SETAR predictor, using different bootstrap methods for dependent data. The coverage and the length of the prediction intervals are evaluated and compared through a Monte Carlo study.

15.1. Introduction

In time series analysis, the forecast generation is often confined to the point forecasts that undoubtedly have high relevance from the empirical point of view, but do not give any information on the uncertainty of the predictor. In fact, the point forecasts are usually evaluated considering indices that give evidence of how the predicted value is “far” from the observed data or, in other cases, how the predictor makes it possible to obtain forecasts that are more (or less) accurate than those obtained from other predictors, but no information is given on their likely accuracy¹.

In this ...