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Forecasting of Categorical Time Series Using a Regression Model

Author

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  • Pruscha Helmut

    (Mathematical Institute, University of Munich, Theresienstr. 39, D-80333 Munich, Germany. pruscha@mathematik.uni-muenchen.de)

  • Göttlein Axel

    (Forest Nutrition and Water Resources, Technical University of Munich, Am Hochanger 13, D-85354 Freising, Germany. goettlein@forst.tu-muenchen.de)

Abstract

This paper deals with time series of categorical or ordinal variables, which are combined with time varying covariates. The conditional expectations (probabilities) are modelled as a regression model in a GLM-type manner, its parameters are estimated using a (partial) likelihood-approach. Special attention is given to the multivariate and the cumulative logistic regression model, with a regression term defined by a recursive scheme. The main concern is directed at forecasts for such time series. Using an approximation formula for conditional expectations l-step predictors are developed. Bias and mean square errors are estimated by using expansion formulas and by employing Box-Jenkins as well as nonparametric methods. The procedures proposed are numerically applied to a data set of yearly forest health inventories.

Suggested Citation

  • Pruscha Helmut & Göttlein Axel, 2003. "Forecasting of Categorical Time Series Using a Regression Model," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 223-240, January.
    • Handle: RePEc:bpj:ecqcon:v:18:y:2003:i:2:p:223-240:n:5
    DOI: 10.1515/EQC.2003.223
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    References listed on IDEAS

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    1. Fokianos, Konstantinos & Kedem, Benjamin, 1998. "Prediction and Classification of Non-stationary Categorical Time Series," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 277-296, November.
    2. Ludwig Fahrmeir & Heinz Kaufmann, 1987. "Regression Models For Non‐Stationary Categorical Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 147-160, March.
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