Nonparametric Block Bootstrap Kolmogorov-Smirnov Goodness-of-Fit Test

Abstract: The Kolmogorov--Smirnov (KS) test is a widely used statistical test that assesses the conformity of a sample to a specified distribution. Its efficacy, however, diminishes with serially dependent data and when parameters within the hypothesized distribution are unknown. For independent data, parametric and nonparametric bootstrap procedures are available to adjust for estimated parameters. For serially dependent stationary data, parametric bootstrap has been developed with a working serial dependence structure. A counterpart for the nonparametric bootstrap approach, which needs a bias correction, has not been studied. Addressing this gap, our study introduces a bias correction method employing a nonparametric block bootstrap, which approximates the distribution of the KS statistic in assessing the goodness-of-fit of the marginal distribution of a stationary series, accounting for unspecified serial dependence and unspecified parameters. We assess its effectiveness through simulations, scrutinizing both its size and power. The practicality of our method is further illustrated with an examination of stock returns from the S&P 500 index, showcasing its utility in real-world applications.