| 摘要(英) |
Change point detection is an important part of time series analysis because the existence of change points indicates that there is a sudden and significant change in the process of data generation. Detecting change points can help us with pre-warning and post analysis. It is widely used in many fields, such as industrial quality control, financial market analysis, network traffic analysis, and so on. In the literature review, the maximum likelihood estimator can be used to estimate the change point under the assumption that the observations are independent. However, in many practical applications, the observations usually have dependent structure, so the
maximum likelihood estimator method with independent hypothesis is usually inefficient. In this paper, we extend the maximum likelihood estimator method to the case of dependent observations. We propose a new change point model, which the serial correlation follows the copulabased Markov chain model, and the marginal distribution follows the normal distribution and
then obtain its corresponding likelihood function. The Newton Raphson method is applied to solve the maximum likelihood estimators. In the empirical study, we analyze the stock return data for illustration. |
| 參考文獻 |
References
[1] Dette, H. and Wied, D. (2016). Detecting relevant changes in time series models Journal
of the Royal Statistical Society: Series B: Statistical Methodology :371-394.
[2] Emura, T. and Ho, Y. T. (2016). A decision theoretic approach to change point estimation
for binomial CUSUM control charts. Sequential Analysis 35(2):238-253.
[3] Genest, C. and MacKay, R. J. (1986). Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données. Canadian Journal of Statistics 14(2):145-159.
[4] Hollander, M., Wolfe, D. A. and Chicken, E. (1973). Nonparametric Statistical Methods.
New York: John Wiley.
[5] Knight, K. (2000). Mathematical Statistics. New York: Chapman & Hall.
[6] Kurt, E. M. and Becerikli, Y. (2018). Network intrusion detection on apache spark with
machine learning algorithms. International Conference on Engineering Applications of
Neural Networks :130-141.
[7] Lavielle, M. and Teyssiere, G. (2007). Adaptive detection of multiple change-points in
asset price volatility. Long memory in economics :129-156.
[8] Lehmann, E. L. (1975). Nonparametric: Statistical Methods Based on Ranks. San Francisco: Holden-Day.
[9] Long, T. H. and Emura, T. (2014). A control chart using copula-based Markov chain models. Journal of the Chinese Statistical Association 52(4):466–496.
[10] Nelsen, R. B. (2006). An introduction to copulas. New York: Springer.
[11] Page, E. S. (1954). Continuous inspection schemes. Biometrika 41:100-114.
[12] Perry, M. B. and Pignatiello, J. J. (2005). Estimation of the change point of the process
fraction nonconforming in SPC applications. International Journal of Reliability, Quality
and Safety Engineering 12(02):95-110.
[13] Perry, M. B. and Pignatiello, J. J. (2008). A change point model for the location parameter
of exponential family densities. IIE Transactions 40(10):947-956.
[14] Pignatiello J. J. and Samuel, T. R. (2000). Identifying the time of a step-change in the
process fraction nonconforming. Quality Engineering 13(3):357-365.
[15] Sun, L. H., Huang, X. W., Alqawba, M. S., Kim, J. M. and Emura, T. (2020). CopulaBased Markov Models for Time Series: Parametric Inference and Process Control. New
York: Springer.
[16] Taylor, S. J. and Letham, B. (2018). The American Statistician 72(1):37-45. |
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