Categorical time semes with a recursive scheme and with covariates

Abstract

We are concerned with time series Yt, t=1, 2,… where the categorical (ordered) variable Ytis influenced by covariates Ztand by the history Yt-1, Yt-2,… of the process. We propose a time series model which combines the logistic regression model (stemming from the generalized linear model family) and the linear OM-chain (stemming from random systems with complete connections). While the influence of the history Yt-1, Yt-2… is modelled by a recursive scheme and by a Markovian term the covariates enter the model via a regression term fif [d]T 1ZrTo prove the familiar asymptotic results on maximum likelihood estimations and related test statistics Norman's ergodicity concept in distance diminishing models is used. To ensure that the time series Ytshows the desired ergodic properties, we have to stipulate similar properties for the covariate process Zt.