Monitoring Mean Shift in INAR(1)s Processes based on CLSE-CUSUM Procedure
Keywords:
Average run length, INAR(1)s process, CLSE-based CUSUM test, CUSUM chart, small to moderate shiftAbstract
In this paper, we consider a new control procedure for monitoring mean shift using the conditional least squares estimator (CLSE)-based cumulative sum (CUSUM) test for the first-order seasonal integer-valued autoregressive (INAR(1)s) processes. Numerical experiments show that the proposed CLSE-CUSUM procedure outperforms conventional CUSUM charts for small to moderate up-shifts in mean of innovation processes, in terms of average run length (ARL), standard deviation (SD) and median.
References
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Billingsley P. Probability and measure. New York: John Wiley & Sons; 1979.
Bourguignon M, Vasconcellos KL, Reisen VA, Ispány MA. Poisson INAR(1) process with a seasonal structure. J Stat Comput Simul. 2016; 86(2): 373-387.
Chen J, Gupta AK. Parametric statistical change point analysis: with applications to genetics, medicine, and finance. New York: Springer Science & Business Media; 2011.
Huh J, Kim H, Lee S. Monitoring parameter shift with Poisson integer-valued GARCH models. J Stat Comput Simul. 2017; 87(9): 1754-1766.
Kang J, Lee S. Parameter change test for random coefficient integer-valued autoregressive processes with application to polio data analysis. J Time Ser Anal. 2009; 30(2): 239-258.
Kim H, Lee S. On first-order integer-valued autoregressive process with Katz family innovations. J Stat Comput Simul. 2017; 87(3): 546-562.
Klimko LA, Nelson PI On conditional least squares estimation for stochastic processes. Ann Stat. 1978; 6(3): 629-642.
Lee S, Ha J, Na O, Na S. The CUSUM test for parameter change in time series models. Scand Stat. 2003; 30(4): 781-796.
Lee S, Na O. Test for parameter change in stochastic processes based on conditional least-squares estimator. J Multivar Anal. 2005; 93(2): 375-393.
Montgomery DC. Statistical Quality Control: A Modern Introduction. 7th edition. New York: John Wiley & Sons; 2012.
Page ES. Continuous inspection schemes. Biometrika. 1954; 41(1-2): 100-115.
Page ES. A test for a change in a parameter occurring at an unknown point. Biometrika. 1955; 42(3/4): 523-527.
Scotto MG, Weiß CH, Gouveia S. Thinning-based models in the analysis of integer-valued time series: a review. Stat Model. 2015; 15(6): 590-618.
Steutel FW, van Harn K. Discrete analogues of self-decomposability and stability. Ann Prob. 1979; 7(5): 893-899.
Weiß CH. Thinning operations for modeling time series of counts-a survey. AStA Adv Stat Anal. 2008; 92(3): 319-341.
Weiß CH. Process capability analysis for serially dependent processes of Poisson counts. J Stat Comput Simul. 2012; 82(3): 383-404.
Weiss CH, Testik MC. CUSUM monitoring of first-order integer-valued autoregressive processes of Poisson counts. J Qual Technol. 2009; 41(4): 389-400.
Yontay P, Weiß CH, Testik MC. and Pelin Bayindir, Z. A two-sided cumulative sum chart for first-order integer-valued autoregressive processes of Poisson counts. Qual Reliab Eng Int. 2013; 29(1): 33-42.
Billingsley P. Probability and measure. New York: John Wiley & Sons; 1979.
Bourguignon M, Vasconcellos KL, Reisen VA, Ispány MA. Poisson INAR(1) process with a seasonal structure. J Stat Comput Simul. 2016; 86(2): 373-387.
Chen J, Gupta AK. Parametric statistical change point analysis: with applications to genetics, medicine, and finance. New York: Springer Science & Business Media; 2011.
Huh J, Kim H, Lee S. Monitoring parameter shift with Poisson integer-valued GARCH models. J Stat Comput Simul. 2017; 87(9): 1754-1766.
Kang J, Lee S. Parameter change test for random coefficient integer-valued autoregressive processes with application to polio data analysis. J Time Ser Anal. 2009; 30(2): 239-258.
Kim H, Lee S. On first-order integer-valued autoregressive process with Katz family innovations. J Stat Comput Simul. 2017; 87(3): 546-562.
Klimko LA, Nelson PI On conditional least squares estimation for stochastic processes. Ann Stat. 1978; 6(3): 629-642.
Lee S, Ha J, Na O, Na S. The CUSUM test for parameter change in time series models. Scand Stat. 2003; 30(4): 781-796.
Lee S, Na O. Test for parameter change in stochastic processes based on conditional least-squares estimator. J Multivar Anal. 2005; 93(2): 375-393.
Montgomery DC. Statistical Quality Control: A Modern Introduction. 7th edition. New York: John Wiley & Sons; 2012.
Page ES. Continuous inspection schemes. Biometrika. 1954; 41(1-2): 100-115.
Page ES. A test for a change in a parameter occurring at an unknown point. Biometrika. 1955; 42(3/4): 523-527.
Scotto MG, Weiß CH, Gouveia S. Thinning-based models in the analysis of integer-valued time series: a review. Stat Model. 2015; 15(6): 590-618.
Steutel FW, van Harn K. Discrete analogues of self-decomposability and stability. Ann Prob. 1979; 7(5): 893-899.
Weiß CH. Thinning operations for modeling time series of counts-a survey. AStA Adv Stat Anal. 2008; 92(3): 319-341.
Weiß CH. Process capability analysis for serially dependent processes of Poisson counts. J Stat Comput Simul. 2012; 82(3): 383-404.
Weiss CH, Testik MC. CUSUM monitoring of first-order integer-valued autoregressive processes of Poisson counts. J Qual Technol. 2009; 41(4): 389-400.
Yontay P, Weiß CH, Testik MC. and Pelin Bayindir, Z. A two-sided cumulative sum chart for first-order integer-valued autoregressive processes of Poisson counts. Qual Reliab Eng Int. 2013; 29(1): 33-42.
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Published
2018-07-19
How to Cite
Kim, H., & Lee, S. (2018). Monitoring Mean Shift in INAR(1)s Processes based on CLSE-CUSUM Procedure. Thailand Statistician, 16(2), 173–189. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/135561
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