Date & Time: Thursday, December 18, 2014, 15:30-16:30.
Venue: Ramanujan Hall

Title: Goodness-of-fit tests for long memory moving-average marginal density

Speaker: Hira L. Koul, Michigan State University

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 estimatedby 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. This talk is based on joint work with Nao Mimoto and Donatas Surgailis.