Score Statistics for Testing Serial Dependence in Count Data

15 Pages Posted: 26 Apr 2013

See all articles by Jiajing Sun

Jiajing Sun

University of Liverpool

Brendan P.M. McCabe

University of Liverpool - Management School (ULMS)

Date Written: May 2013

Abstract

In this study, we extend earlier work of Freeland (1998) and Jung and Tremayne (2003), and develop a general formula for a score statistic to test for dependence in an integer autoregressive process with an arbitrary arrivals distribution. We give two statistics that cater for arrivals processes that may be under‐, equi‐ or overdispersed. The first is based on the Katz family which includes Poisson, binomial and negative binomial distributions as special cases. The second uses the generalized Poisson which includes the Poisson distribution as a special case and can also cater for under‐ and over‐dispersion. The null distribution of the tests is provided and consistency is discussed. Size and power properties are investigated under different model assumptions by Monte Carlo simulations. The autocorrelation coefficient is also investigated as a benchmark for comparison.

Keywords: Time series of counts, INAR model, Poisson autoregressive models, score test, Monte‐Carlo, size and power properties, random coefficient thinning, binomial thinning, beta‐binomial thinning, hypergeometric thinning

Suggested Citation

Sun, Jiajing and McCabe, Brendan P.M., Score Statistics for Testing Serial Dependence in Count Data (May 2013). Journal of Time Series Analysis, Vol. 34, Issue 3, pp. 315-329, 2013, Available at SSRN: https://ssrn.com/abstract=2256845 or http://dx.doi.org/10.1111/jtsa.12014

Jiajing Sun (Contact Author)

University of Liverpool

Chatham Street
Liverpool, L69 7ZA
United Kingdom

Brendan P.M. McCabe

University of Liverpool - Management School (ULMS) ( email )

Chatham Street
Liverpool, L69 7ZH
United Kingdom

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