On Smooth Tests of Goodness-of-Fit for Vector ARMA Time Series Models

• Activity Number: 601
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Joseph Francois Tagne Tatsinkou*+ and Pierre Duchesne and Pierre Lafaye de Micheaux
• Companies: Universite de Montreal and Universite de Montreal and Universite de Montreal
• Keywords: Goodness-of-fit test ; Smooth test ; VARMA process ; white noise ; residuals ; normality test

Abstract

Neyman (1937) derived a goodness-of-fit test for univariate standard uniform distribution. The test consists of projecting the density in a space defined by a family of orthogonal functions and then to use the Rao score test for the parametric testing problem. This test has been generalized to any distribution by Rayner and Best (1989). Ducharme and Lafaye de Micheaux (2004) combined this approach to the Ledwina (1994) data driven principle to find out a goodness-of-fit test for the errors of an ARMA process with known mean. After extending the work of Ducharme and Lafaye de Micheaux to the unknown mean case, we generalize here, the results to a vector ARMA process (VARMA) with unknown mean. For this purpose, we have built a multivariate orthogonal family and then used the residuals properties of VARMA processes to obtain the asymptotic null distribution of our test statistic. Simulation study and an application to real data are provided.