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On Fisher’s dispersion test for integer-valued autoregressive Poisson models with applications
Authors:Sangyeol Lee  Siyun Park
Institution:1. Department of Statistics, Seoul National University, Seoul, Korea;2. Korea University Business School, Seoul, Korea
Abstract:The integer-valued autoregressive (INAR) model has been widely used in diverse fields. Since the task of identifying the underlying distribution of time-series models is a crucial step for further inferences, we consider the goodness-of-fit test for the Poisson assumption on first-order INAR models. For a test, we employ Fisher’s dispersion test due to its simplicity and then derive its null limiting distribution. As an illustration, a simulation study and real data analysis are conducted for the counts of coal mining disasters, the monthly crime data set from New South Wales, and the annual numbers of worldwide earthquakes.
Keywords:Coal mining disasters in the United Kingdom  Fisher’s dispersion test  goodness of fit test  Poisson with a break  time series of counts
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