Neyman smooth goodness-of-fit tests for the marginal distribution of dependent data

Abstract

We establish a data-driven version of Neyman's smooth goodness-of-fit test for the marginal distribution of observations generated by an alpha-mixing discrete time stochastic process (X-t)(t is an element of Z). This is a simple extension of the test for independent data introduced by Ledwina (J Am Stat Assoc 89:1000-1005, 1994). Our method only requires additional estimation of the cumulative autocovariance. Consistency of the test will be shown at essentially any alternative. A brief simulation study shows that the test performs reasonable especially for the case of positive dependence. Finally, we illustrate our approach by analyzing the validity of a forecasting method ("historical simulation") for the implied volatilities of traded options.