Tests of forecast accuracy and forecast encompassing
\(\newcommand{\mub}{{\boldsymbol{\mu}}}
\newcommand{\eb}{{\boldsymbol{e}}}
\newcommand{\betab}{\boldsymbol{\beta}}\)Applied time-series researchers often want to compare the accuracy of a pair of competing forecasts. A popular statistic for forecast comparison is the mean squared forecast error (MSFE), a smaller value of which implies a better forecast. However, a formal test, such as Diebold and Mariano (1995), distinguishes whether the superiority of one forecast is statistically significant or is simply due to sampling variability.
A related test is the forecast encompassing test. This test is used to determine whether one of the forecasts encompasses all the relevant information from the other. The resulting test statistic may lead a researcher to either combine the two forecasts or drop the forecast that contains no additional information.
In this post, Read more…