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Estimation of regression and dynamic dependence parameters for non-stationary multinomial time series. (Estimation of regression and dynamic dependence paremeters for non-stationary multinomial time series.) (English) Zbl 1301.62090

Summary: In a time-series regression setup, multinomial responses along with time dependent observable covariates are usually modelled by certain suitable dynamic multinomial logistic probabilities. Frequently, the time-dependent covariates are treated as a realization of an exogenous random process and one is interested in the estimation of both the regression and the dynamic dependence parameters conditional on this realization of the covariate process. There exists a partial likelihood estimation approach able to deal with the general dependence structures arising from the influence of both past covariates and past multinomial responses on the covariates at a given time by sequentially conditioning on the history of the joint process (response and covariates), but it provides standard errors for the estimators based on the observed information matrix, because such a matrix happens to be the Fisher information matrix obtained by conditioning on the whole history of the joint process. This limitation of the partial likelihood approach holds even if the covariate history is not influeced by lagged response outcomes. In this article, a general formulation of the auto-covariance structure of a multinomial time series is presented and used to derive an explicit expression for the Fisher information matrix conditional on the covariate history, providing the possibility of computing the variance of the maximum likelihood estimators given a realization of the covariate process for the multinomial-logistic model. The difference between the standard errors of the parameter estimators under these two conditioning schemes (covariates Vs. joint history) is illustrated through an intensive simulation study based on the premise of an exogenous covariate process.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M05 Markov processes: estimation; hidden Markov models
62J02 General nonlinear regression
62B10 Statistical aspects of information-theoretic topics
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References:

[1] Amemiya, Advanced Econometrics (1985)
[2] Fahrmeir, Regression models for non-stationary categorical time series, Journal of Time Series Analysis 8 pp 147– (1987) · Zbl 0616.62116
[3] Fokianos, Regression theory for categorical time series, Statistical Science 18 pp 357– (2003) · Zbl 1055.62095
[4] Fokianos, Partial likelihood inference for time series following generalized linear models, Journal of Time Series Analysis 25 pp 173– (2004) · Zbl 1051.62073
[5] Godambe, Quasi-likelihood and optimal estimation, International Statistical Review/Review Internationale de Statistique 55 pp 231– (1987) · Zbl 0671.62007
[6] Sutradhar, An overview on regression models for discrete longitudinal responses, Statistical Science 18 pp 377– (2003) · Zbl 1067.62072
[7] Sutradhar, On optimal lag 1 dependence estimation for dynamic binary models with application to asthma data, Sankhyä: The Indian Journal of Statistics 67 pp 448– (2007)
[8] Tagore, Conditional inference in linear versus nonlinear models for binary time series, Journal of Statistical Computation and Simulation 79 pp 881– (2009) · Zbl 1186.62110
[9] Tong, Nonlinear Time Series: a Dynamical System Approach (1990) · Zbl 0716.62085
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