Statistical analysis of dyadic stationary processes

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 {Mathematical expression} of θ, and give the asymptotic distribution of {Mathematical expression} 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.