This study provides new methods of assessing the adequacy of the Poisson autoregressive time-series model for count data. New expressions are given for the score function and the information matrix and these lead to the construction of new types of residuals for this model. However, these residuals often need to be supplemented by formal statistical procedures and an overall test of the model adequacy is given via the information matrix equality that holds for correctly specified models. The techniques are applied to a monthly count data set of claimants for wage loss benefit, in order to estimate the the expected duration of claimants in the system.
We construct an integer-valued stationary symmetric AR(1) process which can have either a positive or a negative lag-one autocorrelation. Nearly all integervalued time series models are designed for observations which are non-negative integers or counts. They have innovations which are distributed on the non-negative integers and therefore obviously non-symmetric. We build our model using innovations that come from the difference of two independent identically distributed Poisson random variables. These innovations have a symmetric distribution, which has many advantages; in particular, they will allow us to model negative correlations. For our AR(1) process, we examine its basic properties and consider estimation via conditional least squares.
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