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Prediction and Classification of Non-stationary Categorical Time Series

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  • Fokianos, Konstantinos
  • Kedem, Benjamin

Abstract

Partial likelihood analysis of a general regression model for the analysis of non-stationary categorical time series is presented, taking into account stochastic time dependent covariates. The model links the probabilities of each category to a covariate process through a vector of time invariant parameters. Under mild regularity conditions, we establish good asymptotic properties of the estimator by appealing to martingale theory. Certain diagnostic tools are presented for checking the adequacy of the fit.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:277-296
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    References listed on IDEAS

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    1. 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.
    2. Richardson, Ralph M. & Adams, Celestine C. & DeVille, Katherine c. & Penn, Jacqueline E. & Stutzman, John W. & Kraenzle, Charles A., 1994. "Farmer Cooperative Statistics, 1993," Service Reports (SR) 280693, United States Department of Agriculture, Rural Development.
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    Cited by:

    1. Xu Gao & Daniel Gillen & Hernando Ombao, 2018. "Fisher information matrix of binary time series," METRON, Springer;Sapienza Università di Roma, vol. 76(3), pages 287-304, December.
    2. Dag Tjøstheim, 2012. "Rejoinder on: Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 469-476, September.
    3. Konstantinos Fokianos, 2012. "Comments on: Some recent theory for autoregressive count time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 451-454, September.
    4. Zhen, X. & Basawa, I.V., 2009. "Observation-driven generalized state space models for categorical time series," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2462-2468, December.
    5. Kurosawa T & Shimokawa A & Miyaoka E, 2017. "A Note on Transition Models for Binary 2×2 Cross-Over Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 3(5), pages 141-146, October.
    6. 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.
    7. Heikki Kauppi, 2008. "Yield-Curve Based Probit Models for Forecasting U.S. Recessions: Stability and Dynamics," Discussion Papers 31, Aboa Centre for Economics.
    8. Ginger M. Davis & Katherine B. Ensor, 2007. "Multivariate Time‐Series Analysis With Categorical and Continuous Variables in an Lstr Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 867-885, November.
    9. Xu Gao & Babak Shahbaba & Hernando Ombao, 2018. "Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 549-579, October.
    10. Konstantinos Fokianos, 2002. "Power Divergence Family of Tests for Categorical Time Series Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 543-564, September.
    11. Guilherme Pumi & Cristine Rauber & Fábio M. Bayer, 2020. "Kumaraswamy regression model with Aranda-Ordaz link function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1051-1071, December.
    12. Yuichi Goto & Masanobu Taniguchi, 2020. "Discriminant analysis based on binary time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 569-595, July.
    13. Zhen, X. & Basawa, I.V., 2009. "Categorical time series models for contingency tables," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1331-1336, May.

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