ISSN:
1572-9052
Keywords:
Dyadic stationary process
;
information criterion
;
likelihood ratio criterion
;
quasi-maximum likelihood estimator
;
Walsh spectral density
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper we consider a multiple dyadic stationary process with the Walsh spectral density matrix fθ(λ), where θ is an unknown parameter vector. We define a quasi-maximum likelihood estimator % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiUdyaaja% aaaa!377D!\[{\rm{\hat \theta }}\] of θ, and give the asymptotic distribution of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiUdyaaja% aaaa!377D!\[{\rm{\hat \theta }}\] under appropriate conditions. Then we propose an information criterion which determines the order of the model, and show that this criterion gives a consistent order estimate. As for a finite order dyadic autoregressive model, we propose a simpler order determination criterion, and discuss its asymptotic properties in detail. This criterion gives a strong consistent order estimate. In Section 5 we discuss testing whether an unknown parameter θ satisfies a linear restriction. Then we give the asymptotic distribution of the likelihood ratio criterion under the null hypothesis.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00049392
Permalink
