Detecting Duration Clustering and Adequacy of Autoregressive Conditional Duration Models Using Wavelets

• Activity Number: 310
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Pierre Duchesne*+ and Yongmiao Hong
• Affiliation(s): HEC-Montreal and Cornell University
• Keywords: Autoregressive conditional duration ; Duration clustering ; High frequency financial time series ; Model adequacy ; spectral density ; wavelet

Abstract

The Autoregressive Conditional Duration (ACD) of Engle and Russell have been used to model duration clustering for financial data, such as the arrival times of trades. However, few evaluation procedures for adequacy of ACD models are available. A commonly used diagnostic test is the Ljung-Box statistic adapted to the estimated standardized duration residuals, but its asymptotic distribution is unknown and perhaps has to be adjusted. Here, we propose a test for duration clustering and a diagnostic test for ACD models using a wavelet spectral density estimator of the duration. The first test exploits the one-sided nature of duration clustering. As a joint time-frequency decomposition method, wavelets can effectively capture spectral peaks and, thus, are expected to be powerful. Our second test checks the adequacy of an ACD model by using a wavelet spectral density of the standardized estimated duration residuals. The asymptotic distribution of each test is given under the null hypothesis. We propose and justify data-driven methods to choose the finest scale---the smoothing parameter in wavelet estimation. A simulation study is presented, illustrating the merits of the procedures.