Estimation and testing for the integer-valued threshold autoregressive models based on negative binomial thinning

Abstract To better describe the characteristics of time series of counts such as overdispersion or structural change, in this paper, we redefines the integer-valued threshold autoregressive models based on negative binomial thinning (NBTINAR(1)) under a weaker condition that the expectation of the innovations is finite. Parameters’ point estimation and interval estimation problems are considered. A method to test the nonlinearity of the data is provided. As an illustration, we conduct a simulation study and empirical analysis of Pittsburgh crime data sets.

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