J. Álvarez Liébana, W. González Manteiga, M. D. Ruiz Medina
This paper addresses the problem of testing the goodness-of-fit of an autoregressive Hilbertian model. The formulation of the test statistics is based on a functional version of the empirical process family considered in Koul and Stute (1991), marked by the functional values of the innovation process. Their large sample behavior under null hypotheses is derived applying tightness, and convergence of cylinder set measures on abstract Wiener spaces (Hilbert-valued martingale difference central limit theorem). Thus, the Kolmogorov–Smirnov (K–S) test based on the functional empirical process of the given asymptotic level would reject the null hypothesis when an appropriate critical value, obtained from the boundary crossing probabilities of the limit infinite-dimensional Brownian motion, is exceeded.
Keywords: Functional empirical processes, Hilbert-valued martingale difference, Infinite-dimensional Brownian motion
Scheduled
GT06 Functional Data Analysis IV. Functional Time Series
June 9, 2022 10:10 AM
Grade Hall
