Time series analysis of categorical data using auto-odds ratio function. (English) Zbl 1458.62204

Maiti, Raju; Biswas, Atanu

Statistics 52, No. 2, 426-444 (2018).

Summary: In this paper, we consider the auto-odds ratio function (AORF) as a measure of serial association for a stationary time series process of categorical data at two different time points. Numerical measures such as the autocorrelation function (ACF) have no meaningful interpretation, unless the time series data are numerical. Instead, we use the AORF as a measure of association to study the serial dependency of the categorical time series for both ordinal and nominal categories. A. Biswas and P. X. K. Song [Stat. Probab. Lett. 79, No. 17, 1884–1889 (2009; Zbl 1169.62073)] provided some results on this measure for Pegram’s operator-based AR(1) process with binary responses. Here, we extend this measure to more general set-ups, i.e. for AR\((p)\) and MA\((q)\) processes and for a general number of categories. We discuss how this method can effectively be used in parameter estimation and model selection. Following C. H. Weiß [J. Stat. Comput. Simulation 81, No. 4, 411–429 (2011; Zbl 1221.62129)], we derive the large sample distribution of the estimator of the AORF under independent and identically distributed (iid) set-up. Some simulation results and two categorical data examples (one is ordinal and other nominal) are presented to illustrate the proposed method.

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12	Estimation in multivariate analysis
62-08	Computational methods for problems pertaining to statistics
62P10	Applications of statistics to biology and medical sciences; meta analysis

Keywords:

Pegram’s operator; auto-odds ratio function; autocorrelation function; categorical time series

Citations:

Zbl 1169.62073; Zbl 1221.62129

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