Effects of Overdispersion on Testing for Serial Dependence in the Time Series of Counts Data

Abstract

To test for the serial dependence in time series of counts data, (2003) evaluated the size and power of several tests under the class of INARMA models based on binomial thinning operations for Poisson marginal distributions. The overdispersion phenomenon(i.e., a variance greater than the expectation) is common in the real world. Overdispersed count data can be modeled by using alternative thinning operations such as random coefficient thinning,iterated thinning, and quasi-binomial thinning. Such thinning operations can lead to time series models of counts with negative binomial or generalized Poisson marginal distributions. This paper examines whether the test statistics used by (2003) on serial dependence in time series of counts data are affected by overdispersion.