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Parameter Change Test for Time Series of Counts
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 이상열 | - |
dc.contributor.author | 이영미 | - |
dc.date.accessioned | 2017-10-27T17:14:59Z | - |
dc.date.available | 2017-10-27T17:14:59Z | - |
dc.date.issued | 2017-08 | - |
dc.identifier.other | 000000145516 | - |
dc.identifier.uri | https://hdl.handle.net/10371/137178 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 자연과학대학 통계학과, 2017. 8. 이상열. | - |
dc.description.abstract | In this thesis, we consider parameter change test for time series of counts. First 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. Then, 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. Simulation results are provided for illustration and a real data analysis is performed on data of crimes in Australia. Second we consider bivariate Poisson integer-valued GARCH(1,1) models, constructed via a trivariate reduction method of independent Poisson variables. We verify that the CMLE of the model parameters is asymptotically normal. Then, based on these results, we construct CMLE- and residual-based CUSUM tests and derive that their limiting null distributions are a function of independent Brownian bridges. A simulation study are conducted for illustration. We analyze two daily data sets of car accidents that occurred in Sungdong and Seocho counties in Seoul, Korea. Finally, we consider the problem of testing for a parameter change in general nonlinear
integer-valued time series models where the conditional distribution of current observations is assumed to follow a one-parameter exponential family. We consider score-, (standardized) residual-, and estimate-based CUSUM tests, and show that their limiting null distributions take the form of the functions of Brownian bridges. Based on the obtained results, we then conduct a comparison study of the performance of CUSUM tests, through the use of Monte Carlo simulations. Our findings demonstrate that the standardized residual-based CUSUM test largely outperforms the others. | - |
dc.description.tableofcontents | Abstract i
List of Tables viii List of Figures x 1 Introduction 1 2 Literature Review 6 2.1 CUSUM test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 The Poisson AR models . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Parameter Change Test for Zero-Inflated Generalized Poisson Autoregressive Models 9 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Zero-inflated generalized Poisson AR model . . . . . . . . . . . . . . 10 3.3 Change point test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3.1 Estimates-based CUSUM test . . . . . . . . . . . . . . . . . . 15 3.3.2 Residual-based CUSUM test . . . . . . . . . . . . . . . . . . . 18 3.4 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.5 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5.1 Number of robbery with rearms in Inner Sydney . . . . . . . 21 3.5.2 Number of assault police in Inner Sydney . . . . . . . . . . . . 22 3.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.8 Supplementary Material . . . . . . . . . . . . . . . . . . . . . . . . . 27 4 Asymptotic Normality and Parameter Change Test for Bivariate Poisson INGARCH Models 55 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2 Bivariate Poisson INGARCH model . . . . . . . . . . . . . . . . . . . 56 4.3 Change point test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3.1 Estimate-based CUSUM test . . . . . . . . . . . . . . . . . . . 59 4.3.2 Residual-based CUSUM test . . . . . . . . . . . . . . . . . . . 60 4.4 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.5 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.8 Supplementary Material . . . . . . . . . . . . . . . . . . . . . . . . . 69 5 Comparison Study on CUSUM Tests for General Nonlinear Integer-valued GARCH Models 86 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2 Models and likelihood inferences . . . . . . . . . . . . . . . . . . . . 87 5.2.1 Basic set-up and asymptotics . . . . . . . . . . . . . . . . . . 87 5.2.2 INGARCH(1,1) models . . . . . . . . . . . . . . . . . . . . . . 90 5.3 Change point test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.3.1 Score vector-based CUSUM test . . . . . . . . . . . . . . . . . 93 5.3.2 Residual-based CUSUM test . . . . . . . . . . . . . . . . . . . 93 5.4 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.4.1 Test for Poisson INGARCH(1,1) models . . . . . . . . . . . . 95 5.4.2 Test for NB-INGARCH(1,1) models . . . . . . . . . . . . . . . 96 5.4.3 Test for binomial INGARCH(1,1) models . . . . . . . . . . . . 97 5.5 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.7 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 | - |
dc.format | application/pdf | - |
dc.format.extent | 4109150 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | Time series of counts | - |
dc.subject | zero-inflated generalized Poisson autoregressive model | - |
dc.subject | integer-valued GARCH model | - |
dc.subject | test for parameter change | - |
dc.subject | CUSUM test | - |
dc.subject | weak convergence to a Brownian bridge | - |
dc.subject | bivariate Poisson INGARCH model | - |
dc.subject | exponential family | - |
dc.subject | comparison of tests | - |
dc.subject.ddc | 519.5 | - |
dc.title | Parameter Change Test for Time Series of Counts | - |
dc.type | Thesis | - |
dc.description.degree | Doctor | - |
dc.contributor.affiliation | 자연과학대학 통계학과 | - |
dc.date.awarded | 2017-08 | - |
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