Comparing predictive accuracy of multiple forecasts.

In this dissertation, we consider different statistical tests of equal predictive accuracy (EPA). In the first chapter, a background of key time series models and results are presented that are foundational to the existing tests for EPA, as well as the new methods proposed within. In Chapter two, we extended the approach of Hering and Genton (2012) from comparing two forecasts of univariate to comparing more than two competing forecasts for vector time series. In Chapter three, we provide a bias modification to a nonparametric estimator of the asymptotic variance of the loss differential series, and use that in a modified test statistics. The bias correction resulted in a different null distribution, the Hotelling T2 distribution for finding critical values and p-values. We also consider a bootstrap approach for estimating p-values. Finally, in Chapter four we consider a parametric approach. In particular, the loss differential series is modeled using a stationary linear process. The estimated coefficients are used for computing a parametric estimate of the variance of the loss differential series, and that estimator is then applied to the test statistics. Because of the relatively good performance of the methods in Chapter four to the methods of the previous chapter, the tests in Chapter four were applied to a series of residuals from predicting the paths of satellites orbiting the earth. The data were provided by NASA. For each of the newly proposed methods in Chapters two through four, extensive Monte Carlo simulations are conducted for investigating the probabilistic properties of the tests, and each simulation study is accompanied by a discussion. Of all methods considered in the dissertation, the methods of Chapter four were better overall in terms of empirical size being close to nominal and having higher power in most of the cases.