Change point detection in AR(1) series by optimal stopping technique

Reza Habibi

doi:10.14244/lajm.v3i1.28

Autores/as

Reza Habibi faculty member, iran banking institute

DOI:

https://doi.org/10.14244/lajm.v3i1.28

Palabras clave:

AR(1), Bayesian, Change point, Logit function, Snell envelopment

Resumen

The change point problem arises in various practical fields such as economics, engineering, medicine, quality control, statistical process control, and financial time series. The aim of this study is to detect location and time of change point at which the behavior of underlying statistical models changes in mean, variance or some other influential parameters. Change point detection methods are divided into two main branches: online methods, that aim to detect changes as soon as they occur in a real-time setting and offline methods that retrospectively detect changes when all samples are received. In practice, there are many parametric (including maximum likelihood and information criterion) and non-parametric methods. Bayesian change point detection introduces a modular Bayesian framework for online estimation of changes in the generative parameters of sequential data. Time series analysis has become increasingly important in diverse fields including medicine, aerospace, finance, business, meteorology, and entertainment. Time series data are sequences of measurements over time describing the behavior of systems. These behaviors can change over time due to external events and/or internal systematic changes in dynamics/distribution. In the current paper, change point analysis in AR(1) is studied using the optimal stopping technique. The logit of probability of having a change at a specific time is studied using the Bayesian and non-Bayesian methods. Snell envelopment method is applied to locate the possible change. Finally, concluding remarks are proposed.

Citas

[1] Li X, Ma J. Non-central Student-t mixture of Student-t processes for robust regression and prediction. In: Intelligent Computing Theories and Application: 17th International Conference, ICIC 2021, Shenzhen, China, August 12–15, 2021, Proceedings, Part I. Springer; DOI: https://doi.org/10.1007/978-3-030-84522-3_41

2021. p. 499-511.

[2] Shah V. Optimal stopping problems: autonomous trading over an infinite time horizon. Imperial College London, Department of Mathematics; 2020.

[3] Ma L, Grant AJ, Sofronov G. Multiple change point detection and validation in autoregressive time series data. Statistical Papers. 2020;61:1507-28. DOI: https://doi.org/10.1007/s00362-020-01198-w

[4] Cappello L, Padilla OHM, Palacios JA. Scalable Bayesian change point detection with spike and slab priors. arXiv preprint. 2021;arXiv:2106.10383.

[5] Veeravalli VV, Banerjee T. Quickest change detection. In: Academic Press Library in Signal Processing. vol. 3. Elsevier; 2014. p. 209-55. DOI: https://doi.org/10.1016/B978-0-12-411597-2.00006-0

[6] Øksendal B. Stochastic Differential Equations. 6th ed. Springer; 2003. DOI: https://doi.org/10.1007/978-3-642-14394-6

[7] Pan J, Liu Y, Shu J. Gradient-based parameter estimation for a nonlinear exponential autoregressive time-series model by using the multi-innovation. International Journal of Control, Automation and Systems. 2023;21(1):140-50. DOI: https://doi.org/10.1007/s12555-021-1018-8

[8] Entwistle HN, Lustri CJ, Sofronov GY. On asymptotics of optimal stopping times. Mathematics. 2022;10(2):194. DOI: https://doi.org/10.3390/math10020194

[9] Fathan A, Delage E. Deep reinforcement learning for optimal stopping with application in financial engineering. arXiv preprint. 2021;arXiv:2105.08877.