Goodness-of-fit testing for the marginal distribution of regime-switching models

In this paper we propose a new goodness-of-fit testing scheme for the marginal distribution of regime-switching models. We consider models with an observable (like threshold autoregressions), as well as, a latent state process (like Markov regime-switching). The test is based on the Kolmogorov-Smirnov supremum-distance statistic and the concept of the weighted empirical distribution function. The motivation for this research comes from a recent stream of literature in energy economics concerning electricity spot price models. While the existence of distinct regimes in such data is generally unquestionable (due to the supply stack structure), the actual goodness-of-fit of the models requires statistical validation. We illustrate the proposed scheme by testing whether commonly used Markov regime-switching models fit deseasonalized electricity prices from the NEPOOL (U.S.) day-ahead market.