A new procedure for unit root to long-memory process change-point monitoring

Zhanshou Chen; Muci Peng; Li Xi; Zhanshou Chen; Muci Peng; Li Xi

doi:10.3934/math.2022360

AIMS Mathematics

2022, Volume 7, Issue 4: 6467-6477. doi: 10.3934/math.2022360

Previous Article Next Article

Research article

A new procedure for unit root to long-memory process change-point monitoring

1.
School of Mathematics and Statistics, Qinghai Normal University, Xining, China
2.
The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Xining, Qinghai, China

Received: 27 August 2021 Revised: 09 January 2022 Accepted: 17 January 2022 Published: 20 January 2022
MSC : 62F03, 62L10

In this paper, we propose a Dickey-Fuller difference statistic to sequentially detect the change-point that shift from an unit root process to a long-memory process. The limiting distribution of monitoring statistic under the unit root process null hypothesis as well as its consistency under the alternative hypothesis are proved. Simulations indicate that the new method can control the empirical size well even for the heavy-tailed unit root process when using the sieve bootstrap method computing its critical values. In particular, it performs significantly better than the available method in the literature under the alternative hypothesis. Finally, we illustrate the new monitoring procedure by a set of foreign exchange rate data.
- change-point monitoring,
- Dickey-Fuller statistic,
- long-memory process,
- unit root process
Citation: Zhanshou Chen, Muci Peng, Li Xi. A new procedure for unit root to long-memory process change-point monitoring[J]. AIMS Mathematics, 2022, 7(4): 6467-6477. doi: 10.3934/math.2022360

Related Papers:

Abstract

In this paper, we propose a Dickey-Fuller difference statistic to sequentially detect the change-point that shift from an unit root process to a long-memory process. The limiting distribution of monitoring statistic under the unit root process null hypothesis as well as its consistency under the alternative hypothesis are proved. Simulations indicate that the new method can control the empirical size well even for the heavy-tailed unit root process when using the sieve bootstrap method computing its critical values. In particular, it performs significantly better than the available method in the literature under the alternative hypothesis. Finally, we illustrate the new monitoring procedure by a set of foreign exchange rate data.

References

[1]	F. Busetti, A. M. R. Taylor, Tests of stationarity against a change in persistence, J. Econom., 123 (2004), 33–66. https://doi.org/10.1016/j.jeconom.2003.10.028 doi: 10.1016/j.jeconom.2003.10.028
[2]	M. Caporin, R. Gupta, Time-varying persistence in US inflation, Empir. Econ., 53 (2017), 423–439. https://doi.org/10.1007/s00181-016-1144-y doi: 10.1007/s00181-016-1144-y
[3]	Z. S. Chen, Z. Jin, Z. Tian, P. Y. Qi, Bootstrap testing multiple changes in persistence for a heavy-tailed sequence, Comput. Stat. Data Anal., 56 (2012), 2303–2316. https://doi.org/10.1016/j.csda.2012.01.011 doi: 10.1016/j.csda.2012.01.011
[4]	Z. Chen, Z. Tian, Y. Xing, Sieve bootstrap monitoring persistence change in long memory process, Stat. Interface, 9 (2016), 37–45. https://doi.org/10.4310/SII.2016.v9.n1.a4 doi: 10.4310/SII.2016.v9.n1.a4
[5]	Z. Chen, Y. Xing, Z. A. Chen, Y. H. Xing, F. X. Li, Sieve bootstrap monitoring for change from short to long memory, Econ. Lett., 140 (2016), 53–56. https://doi.org/10.1016/j.econlet.2015.12.023 doi: 10.1016/j.econlet.2015.12.023
[6]	Z. S. Chen, F. X. Li, L. Zhu, Y. H. Xing, Monitoring mean and variance change-points in long-memory time series, J. Syst. Sci. Complex., 2021. https://doi.org/10.1007/s11424-021-0222-1 doi: 10.1007/s11424-021-0222-1
[7]	Z. S. Chen, Y. T. Xiao, F. X. Li, Monitoring memory parameter change-points in long-memory time series, Empir. Econ., 60 (2021), 2365–2389. https://doi.org/10.1007/s00181-020-01840-4 doi: 10.1007/s00181-020-01840-4
[8]	H. Dette, J. Gösmann, A likelihood ratio approach to sequential change point detection for a general class of parameters, J. Am. Stat. Assoc., 115 (2019), 1361–1377. https://doi.org/10.1080/01621459.2019.1630562 doi: 10.1080/01621459.2019.1630562
[9]	J. Gösmann, T. Kley, H. Dette, A new approach for open-end sequential change point monitoring, J. Time Ser. Anal., 42 (2021), 63–84. https://doi.org/10.1111/jtsa.12555 doi: 10.1111/jtsa.12555
[10]	D. I. Harvey, S. J. Leybourne, A. M. R. Taylor, Modified tests for a change in persistence, J. Econom., 134 (2006), 441–469. https://doi.org/10.1016/j.jeconom.2005.07.002 doi: 10.1016/j.jeconom.2005.07.002
[11]	U. Hassler, J. Scheithauer, Detecting changes from short to long memory, Stat. Papers, 52 (2011), 847–870. https://doi.org/10.1007/s00362-009-0292-y doi: 10.1007/s00362-009-0292-y
[12]	U. Hassler, B. Meller, Detecting multiple breaks in long memory the case of U.S. inflation, Empir. Econ., 46 (2014), 653–680. https://doi.org/10.1007/s00181-013-0691-8 doi: 10.1007/s00181-013-0691-8
[13]	F. Iacone, Š. Lazarová, Semiparametric detection of changes in long range dependence, J. Time Ser. Anal., 40 (2019), 693–706. https://doi.org/10.1111/jtsa.12448 doi: 10.1111/jtsa.12448
[14]	M. Kejriwal, P. Perron, J. Zhou, Wald tests for detecting multiple structural changes in persistence, Economet. Theor., 29 (2013), 289–323. https://doi.org/10.1017/S0266466612000357 doi: 10.1017/S0266466612000357
[15]	J. Y. Kim, Detection of change in persistence of a linear time series, J. Econ., 95 (2000), 97–116. https://doi.org/10.1016/S0304-4076(99)00031-7 doi: 10.1016/S0304-4076(99)00031-7
[16]	C. Kirch, S. Weber, Modified sequential change point procedures based on estimating functions, Electron. J. Stat., 12 (2018), 1579–1613. https://doi.org/10.1214/18-EJS1431 doi: 10.1214/18-EJS1431
[17]	F. Lavancier, R. Leipus, A. Philippe, D. Surgailis, Detection of nonconstant long memory parameter, Economet. Theor., 29 (2013), 1009–1056. https://doi.org/10.1017/S0266466613000303 doi: 10.1017/S0266466613000303
[18]	S. Leybourne, R. Taylor, T. H. Kim, CUSUM of squares-based tests for a change in persistence, J. Time Ser. Anal., 28 (2007), 408–433. https://doi.org/10.1111/j.1467-9892.2006.00517.x doi: 10.1111/j.1467-9892.2006.00517.x
[19]	F. X. Li, Z. S. Chen, Y. T. Xiao, Sequential change-point detection in a multinomial logistic regression model, Open Math., 18 (2020), 807–819. https://doi.org/10.1515/math-2020-0037 doi: 10.1515/math-2020-0037
[20]	R. B. Qin, Y. Liu, Block bootstrap testing for changes in persistence with heavy-tailed innovations, Commun. Stat.-Theor. M., 47 (2018), 1104–1116. https://doi.org/10.1080/03610926.2017.1316398 doi: 10.1080/03610926.2017.1316398
[21]	P. Sibbertsen, R. Kruse, Testing for a break in persistence under long-range dependences, J. Time Ser. Anal., 30 (2009), 263–285. https://doi.org/10.1111/j.1467-9892.2009.00611.x doi: 10.1111/j.1467-9892.2009.00611.x
[22]	M. S. Taqqu, Weak convergence to fractional Brownian motion and to the Rosenblatt process, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 31 (1975), 287–302. https://doi.org/10.1007/BF00532868 doi: 10.1007/BF00532868
[23]	W. Z. Zhao, Y. X. Xue, X. Liu, Monitoring parameter change in linear regression model based on the efficient score vector, Physica A, 527 (2019), 121135. https://doi.org/10.1016/j.physa.2019.121135 doi: 10.1016/j.physa.2019.121135

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)