Ordinal Time Series Models with Application to Forest Damage Data

Abstract

The present paper proposes a time series model for an ordered categorical criterion variable Y_t, which takes into acount the dependence of Y_t on the (internal) history Y_t−1, Y_t−2, … and on the (external) covariates Z_t which are allowed to form a stochastic process. The covariates enter the model in form of the usual regression term; the influence of the history of the process is modelled by a linear combination of two probability vectors: a vector summarizing all past observations and a Markovian vector depending on the last observation only.

The familiar likelihood approach to statistical inference is presented.

The methods proposed are applied to panel data on forest damages. Damage categories together with various covariates were recorded from several sites of a forest district in the Spessart (Bavaria) over the last 9 years. The different submodels and the individual covariates are tested.