Goodness-of-Fit Tests for Long Memory Moving-Average Marginal Density

• Activity Number: 657
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Hira Lal Koul*+ and Nao Mimoto and Donatas Surgailis
• Companies: Michigan State University and Michigan State University and Vilnius University
• Keywords: Kernel density estimator ; chi square distribution

Abstract

In this talk we will discuss the problem of fitting a known d.f. or density to the marginal error density of a stationary long memory moving-average process when its mean is known and unknown. When the mean is unknown and estimated by the sample mean, the first-order difference between the residual empirical and null distribution functions is known to be asymptotically degenerate at zero. Hence, it cannot be used to fit a distribution up to an unknown mean. However, we shall show that by using a suitable class of estimators of the mean, this first order degeneracy does not occur. We also present some large sample properties of the tests based on an integrated squared-difference between kernel-type error density estimators and the expected value of the error density estimator based on errors. The asymptotic null distributions of suitably standardized test statistics are shown to be chi-square with one degree of freedom in both cases of known and unknown mean. This is totally unlike the i.i.d. errors set-up where suitable standardizations of these statistics are known to be asymptotically normally distributed.