Prediction and classification of non-stationary categorical time series
type: Item
instance of: scholarly article
title: Prediction and classification of non-stationary categorical time series
zbMATH Open document ID: 0919.62105
author: Konstantinos Fokianos
author: Benjamin Kedem-Kimelfeld
published in: Journal of Multivariate Analysis
publication date: 1999-08-16T00:00:00Z
full work available at URL: http://hdl.handle.net/1903/5768
review text: 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.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 62J12
zbMATH DE Number: 1241225
zbMATH Keywords: covariates
zbMATH Keywords: partial likelihood
zbMATH Keywords: goodness of fit
zbMATH Keywords: asymptotic theory
reviewed by: Georgi N. Boshnakov
describes a project that uses: Fahrmeir
MaRDI profile type: Publication
OpenAlex ID: W2063890903
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DOI: 10.1006/JMVA.1998.1765
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description: scientific article; zbMATH DE number 1241225