K-depth tests for testing simultaneously independence and other model assumptions in time series

Abstract

We consider the recently developed K-depth tests for testing simultaneously independence and other model assumptions for univariate time series with a potentially related d-dimensional process of explanatory variables. Since these tests are based only on signs of residuals, they are easy to comprehend. They can be used in a full version and in a simplified version. While former investigations already showed that the full version is appropriate for testing model assumptions, we concentrate here on either testing the independence assumption on its own or on simultaneously testing independence- and model assumptions with both types of tests. In an extensive simulation study, we compare these tests with several known independence test such as the runs test, the Durbin-Watson test, and the Von-Neumann-Rank-Ratio test. Finally, we demonstrate how the K-depth tests can be used for improved modelling of crack width time series depending on temperature measurements in a bridge monitoring.