Parameter change test for zero-inflated generalized Poisson autoregressive models |
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Authors: | Sangyeol Lee Youngmi Lee Cathy WS Chen |
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Institution: | 1. Department of Statistics, Seoul National University, Seoul, Korea;2. Department of Statistics, Feng Chia University, Taichung, Taiwan |
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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. |
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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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