Testing For INARCH Effects

First-order integer-valued autoregressive conditional heteroscedasticity(I-NARCH(1))process has been applied to model the counts of events for a long time.In this thesis,we focus on the Poisson INARCH(1)process,we mainly test the independence of the serial when the null hypothesis is that the pa-rameter a in INARCH(1)process is zero,where a is the parameter in process Xt|Ft-1?P(?+aXt-1).We present the definition and some properties such as the mean,variance and moments of the process.Based on INARCH(1)pro-cess,we propose two different explicit approximations of the likelihood ratio statistic,we also derive the limiting distributions of our statistics under the null hypothesis.Finally,in a simulation study,we compare the test statistics we constructed with the score test statistic in size and power,the size is de-rived via asymptotic critical values or response surface regressions of critical values.The simulation study shows that our statistics are superior to score in terms of power and work just as well in terms of size,another finding is that the powers of our approximate likelihood ratio tests perform are very similar.