Prediction and classification of non-stationary categorical time series
The authors study time series with non-numeric values (nominal or ordinal). They extend the generalised linear models to non-stationary categorical time series with covariates. The model is specified by a link function which links the probabilities of the categories to the covariates. Examples of popular link functions are multinomial logits and cumulative odds. The estimation method is based on maximization of the partial likelihood (PL), defined in the following way. Let \({F}_t\), \(t=0,1,\ldots\) be an increasing sequence of sigma fields and let \(X_t\) be a sequence of random variables adapted to \({F}_t\). Let \(f_t(x_t;\beta)\) be the conditional density of \(X_t\) given \({F}_{t-1}\), where \(\beta\) is a vector parameter. Then the PL for a set of data \(X_1\), \(X_2\), \(\ldots\), \(X_n\) is given by \[ PL(\beta;X_1,\ldots,X_n)=\prod_{t=1}^{n}f_t(x_t;\beta) . \] PL is similar to the conditional likelihood in the sense that it is obtained by omitting some factors in the complete likelihood. However the PL does not require complete knowledge of the joint distribution of the covariates. The authors develop large sample theory for the proposed estimators and provide goodness of fit test statistics.
scientific article; zbMATH DE number 1241225
scientific article