For an ARCH model, we propose a multistage weighted least squares (WLS) estimate which consists of repeated WLS procedures until the corresponding asymptotic variance equals that of the quasi-maximum likelihood estimate (QMLE). At every stage, the current estimate is of a WLS type weighted by...

In many problems, a specific function like h(⋅) is considered as the covariance function. Based on the asymptotic distribution of the periodogram and Euler characteristic, three methods are introduced to test the equality of the covariance function with h(⋅). Our analyses prove the accuracy...

We consider generalized linear models for regression modeling of count time series. We give easily verifiable conditions for obtaining weak dependence for such models. These results enable the development of maximum likelihood inference under minimal conditions. Some examples which are useful to...

This paper considers a new so-called autoregressive process with ARCH(1) errors driven by a hidden Markov chain, Xt+1=α(Δt+1)Xt+ηt+1β(Δt+1)+λ(Δt+1)Xt2,t∈N, where (ηt) is a sequence of independent and identically distributed standard normal random variables, and (Δt) is a Markov chain...