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INAR模型的多变点探测
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Abstract:
本文考虑了分段平稳的整数值自回归模型的多变点问题。借助最小描述长度函数得到似然比扫描方法，并将似然比扫描方法运用到分段平稳的整数值自回归模型中。此外，还研究了当模型系数之和趋于1时的情况，此时针对似然比扫描方法中的最小描述长度函数进行了调整，以提高变点探测的准确性。然后通过大量的数值模拟，验证了似然比扫描方法在不同的模型参数设置下的有效性，最后并将其运用于一组精神分裂症患者在知觉速度测试中的日常观察得分数据的实证分析之中。
This paper considers the multiple change-points problem in piecewise stationary integer-valued autoregressive model. Using the Minimum Description Length function, the likelihood ratio scanning method is obtained and applied to the piecewise stationary integer-value autoregressive model. In addition, when the sum of the model coefficients tends to 1, the Minimum Description Length function in the likelihood ratio scanning method is adjusted to improve the accuracy of the change point detection. Then, through many numerical simulations, the effectiveness of the likelihood ratio scanning method in different model parameter settings was verified. Finally, it was applied to the empirical analysis of the daily observations of the score achieved by a schizophrenic patient on a test of perceptual speed.
| [1] | Page, E.S. (1955) A Test for a Change in a Parameter Occurring at an Unknown Point. Biometrika, 42, 523-527. https://doi.org/10.1093/biomet/42.3-4.523 |
| [2] | Bauwens, L., Backer B. and Dufays, A. (2014) A Bayesian Method of Change-Point Estimation with Recurrent Regimes: Application to GARCH Models. Journal of Empirical Finance, 29, 207-229. https://doi.org/10.1016/j.jempfin.2014.06.008 |
| [3] | Barry, D. and Hartigan, J.A. (1993) A Bayesian Analysis for Change Point Problems. Journal of the American Statistical Association, 88, 309-319. https://doi.org/10.1080/01621459.1993.10594323 |
| [4] | Cs？rg？, M. and Horváth L. (1988) 20 Nonparametric Methods for Changepoint Problems. Handbook of Statistics, 7, 403-425. https://doi.org/10.1016/S0169-7161(88)07022-1 |
| [5] | Wilcox, R.R. (2005) Introduction to Robust Estimation and Hypothesis Testing. Technometrics, 40, 77-78. https://doi.org/10.1080/00401706.1998.10485491 |
| [6] | Schmid, F. and Trede, M. (1998) A Kolmogorov-Type Test for Second-Order Stochastic Dominance. Statistics & Probability Letters, 37, 183-193. https://doi.org/10.1016/S0167-7152(97)00116-8 |
| [7] | Kim, S., Cho, S. and Lee, S. (2000) On the Cusum Test for Parameter Changes in Garch (1,1) Models. Communication in Statistics-Theory and Methods, 29, 445-462. https://doi.org/10.1080/03610920008832494 |
| [8] | Lee, S., Tokutsu, Y. and Maekawa, K. (2004) The Cusum Test for Parameter Change in Regression Models with ARCH Error. Journal of the Japanese Statistical Society, 34, 173-188. https://doi.org/10.14490/jjss.34.173 |
| [9] | Vostrikova, L.Y. (1981) Detecting “Disorder” in Multidimensional Random Processes. Soviet Mathematics Doklady, 24, 55-59. |
| [10] | Bai, J. (1997) Estimating Multiple Breaks One at a Time. Econometric Theory, 13, 315-352. https://doi.org/10.1017/S0266466600005831 |
| [11] | Inclan, C. and Tiao, G.C. (1994) Use of Cumulative Sums of Squares for Retrospective Detection of Change of Variance. Journal of the American Statistical Association, 89, 913-923. https://doi.org/10.1080/01621459.1994.10476824 |
| [12] | Berkes, J., Gombay, E. and Horvath, L. (2009) Testing for Changes in the Covariance Structure of Linear Processes. Journal of Statistical Planning and Inference, 139, 2044-2063. https://doi.org/10.1016/j.jspi.2008.09.004 |
| [13] | Fryzlewicz, P. (2014) Wild Binary Segmentation for Multiple Change-Point Detection. The Annals of Statistics, 42, 2243-2281. https://doi.org/10.1214/14-AOS1245 |
| [14] | Davis, R.A., Lee, T.C.M. and Rodriguez-Yam, G.A. (2005) Structural Breaks Estimation for Non-Stationary Time Series Signals. EEE/SP 13th Workshop on Statistical Signal Processing, Bordeaux, 17-20 July 2005, 233-238. https://doi.org/10.1109/SSP.2005.1628598 |
| [15] | Killick, R., Fearnhead, P. and Eckley, I.A. (2012) Optimal Detection of Change Points with a Linear Computational Cost. Journal of the American Statistical Association, 107, 1590-1598. https://doi.org/10.1080/01621459.2012.737745 |
| [16] | Yau, C.Y. and Zhao, Z. (2016) Inference for Multiple Change Points in Time Series via Likelihood Ratio Scan Statistics. Journal of the Royal Statistical Society Series B: Statistical Methodology, 78, 895-916. https://doi.org/10.1111/rssb.12139 |
| [17] | McKenzie, E. (1985) Some Simple Models for Discrete Variate Time Series1. JAWRA Journal of the American Water Resources Association, 21, 645-650. https://doi.org/10.1111/j.1752-1688.1985.tb05379.x |
| [18] | Al-Osh, M.A. and Alzaid, A.A. (1987) First Order Integer Valued Autoregressive (INAR(1)) Process. Journal of Time Series Analysis, 8, 261-275. https://doi.org/10.1111/j.1467-9892.1987.tb00438.x |
| [19] | Alzaid, A.A. and Al-Osh, M.A. (1990) An Integer-Valued pth-Order Autoregressive Structure (INAR(p)) Process. Journal of Applied Probability, 27, 314-324. https://doi.org/10.2307/3214650 |
| [20] | Jin-Guan, D. and Yuan, L. (1991) The Integer-Valued Autoregressive (INAR(p)) Model. Journal of Time Series Analysis, 12,129-142. https://doi.org/10.1111/j.1467-9892.1991.tb00073.x |
| [21] | Cui, Y. and Wu, R. (2020) Test of Parameter Changes in a Class of Observation-Driven Models for Count Time Series. Communications in Statistics-Theory and Methods, 49, 1933-1959. https://doi.org/10.1080/03610926.2019.1565843 |
| [22] | Zhang, C., Wang, D., et al. (2022) Generalized Poisson Integer-Valued Autoregressive Processes with Structural Changes. Journal of Applied Statistics, 49, 2717-2739. https://doi.org/10.1080/02664763.2021.1915255 |
| [23] | Yu, K., Wang, H. and Wei？, C.H. (2022) An Empirical-Likelihood-Based Structural-Change Test for INAR Processes. Journal of Statistical Computation and Simulation, 93, 442-458. https://doi.org/10.1080/00949655.2022.2109635 |
| [24] | Steutel, F.W. and Harn, K. (1979) Discrete Analogues of Self-Decomposability and Stability. The Annals of Probability, 7, 893-899. https://doi.org/10.1214/aop/1176994950 |
| [25] | Davis, R.A., Lee, T.C.M. and Rodriguez-Yam, G.A. (2006) Structural Break Estimation for Non-Stationary Time Series Models. Journal of the American Statistical Association, 101, 223-239. https://doi.org/10.1198/016214505000000745 |
| [26] | Ling, S. (2016) Estimation of Change-Points in Linear and Nonlinear Time Series Models. Econometric Theory, 32, 402-430. https://doi.org/10.1017/S0266466614000863 |
| [27] | Rissanen, J. (1988) Stochastic Complexity in Statistical Inquiry. World Scientific, Singapore. |
| [28] | McCleary, R. and Hay, R.A., et al. (1980) Applied Time Series Analysis for the Social Sciences. Sage Publications, Beverly Hills. |
| [29] | Neal, P. and Subba R.T. (2007) MCMC for Integer-Valued ARMA Processes. Journal of Time Series Analysis, 28, 92-110. https://doi.org/10.1111/j.1467-9892.2006.00500.x |
| [30] | Kashikar, A.S., Rohan, N. and Ramanathan, T.V. (2013) Integer Autoregressive Models with Structural Breaks. Journal of Applied Statistics, 40, 2653-2669. https://doi.org/10.1080/02664763.2013.823920 |
