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Parameter change test for zero-inflated generalized Poisson autoregressive models
Authors:Sangyeol Lee  Youngmi Lee  Cathy WS Chen
Institution:1. Department of Statistics, Seoul National University, Seoul, Korea;2. Department of Statistics, Feng Chia University, Taichung, Taiwan
Abstract:In this paper, we consider the problem of testing for parameter change in zero-inflated generalized Poisson (ZIGP) autoregressive models. We verify that the ZIGP process is stationary and ergodic and that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal. Based on these results, we construct CMLE- and residual-based cumulative sum tests and show that their limiting null distributions are a function of independent Brownian bridges. The simulation results are provided for illustration. A real data analysis is performed on some crime data of Australia.
Keywords:time series of counts  zero-inflated Poisson autoregressive model  integer-valued GARCH model  test for parameter change  CUSUM test  weak convergence to a Brownian bridge
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