Specification tests for autoregressive conditional duration (ACD) models

Abstract

In this dissertation, we propose specification tests for the innovation distribution in autoregressive conditional duration (ACD) models, with specific emphasis on ACD(1,1) models with exponential and Lomax innovations. Literature on ACD models with Lomax innovations is relatively scarce, in particular specification tests for these models. As a result, we introduce a newly developed test for Lomax innovations, which is based on a characterisation of the Lomax law using Stein’s method. For the hypothesis of exponential innovations, we compare the powers of classical tests as well as some modern tests using a simulation study. The classical tests include the Kolmogorov-Smirnov, Cram´ er-von Mises and Anderson Darling tests. Testing for Lomax distributed innovations, we compare the new test with classical tests, to analyse its finite sample performance. The numerical comparisons presented are conducted for various sample sizes and for a number of alternative distributions. Testing for exponential innovations, the results of the simulation study showed that the tests with the best overall performance are the score test by Cox and Oakes, as well as the Anderson-Darling test. The results for Lomax innovations showed that the new test outperformed all the classical tests. We illustrate some of the tests using a real-data example.