Tests for Duration Clustering and Diagnostic Checking of ACD Models Using Kernel-based Spectral Density Estimators

• Activity Number: 308
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economics Statistics Section
• Author(s): Maria Pacurar*+ and Pierre Duchesne
• Companies: HEC Montréal and Université de Montréal
• Keywords: duration clustering ; model adequacy ; kernel-based spectral density ; time series

Abstract

Engle and Russell's autoregressive conditional duration (ACD) models have been widely used to model financial data that arrive at irregular intervals. In the modeling of such data, testing for duration clustering and evaluation procedures of a particular model are important steps. We propose two classes of tests for ACD effects and one class for the adequacy, using kernel-based spectral density estimators. The tests of ACD effects of the first class are obtained by comparing a kernel-based normalized spectral density estimator and the normalized spectral density under the null hypothesis of no ACD effects, using a norm. The second class exploits the one-sided nature of the alternative hypothesis. Tests for the adequacy are obtained by comparing a kernel-based spectral density estimator of the standardized residuals and the null hypothesis of adequacy using a norm. Asymptotic distributions of the test statistics are obtained, which are normal. We present a simulation study illustrating the merits of the proposed procedures and an application with financial data is conducted.