Adaptive Test for Periodic ARFIMA Models
Keywords:
Local asymptotic normality property, long memory process, locally asymptotically optimal test, residual autocorrelations, periodically correlated modelsAbstract
The goal of this article is to construct an adaptive test for periodic long memory models, using the main technical tool of Le Cam (1986)’s Local Asymptotic Normality (LAN) property constructed in Amimour and Belaide (2020), and a Correlogram-Based LAN Result. We consider the problem of testing a given ARFIMA model in which the density of the generating white noise is specified
against a periodic ARFIMA model. The perspectives of this work are, first to establish a locally asymptotically most stringent parametric tests, when the density of the innovations and the longmemory parameter are unspecified. Second to define and investigate so-called residual rank tests.
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