×

zbMATH — the first resource for mathematics

Piecewise autoregression for general integer-valued time series. (English) Zbl 1455.62170
Summary: This paper proposes a piecewise autoregression for general integer-valued time series. The conditional mean of the process depends on a parameter which is piecewise constant over time. We derive an inference procedure based on a penalized contrast that is constructed from the Poisson quasi-maximum likelihood of the model. The consistency of the proposed estimator is established. From practical applications, we derive a data-driven procedure based on the slope heuristic to calibrate the penalty term of the contrast; and the implementation is carried out through the dynamic programming algorithm, which leads to a procedure of \(\mathcal{O} (n^2)\) time complexity. Some simulation results are provided, as well as the applications to the US recession data and the number of trades in the stock of Technofirst.
MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
62P20 Applications of statistics to economics
Software:
CAPUSHE; basta; wbs
PDF BibTeX Cite
Full Text: DOI
References:
[1] Ahmad, A.; Francq, C., Poisson QMLE of count time series models, J. Time Series Anal., 37, 291-314 (2016) · Zbl 1381.62244
[2] Arlot, S.; Celisse, A.; Celisse, Z., A kernel multiple change-point algorithm via model selection (2016)
[3] Arlot, S.; Massart, P., Data-driven calibration of penalties for least-squares regression, J. Mach. Learn. Res., 10, 245-279 (2009)
[4] Bai, J., Estimating multiple breaks one at a time, Econometric Theory, 13, 3, 315-352 (1997)
[5] Bai, J.; Perron, P., Estimating and testing linear models with multiple structural changes, Econometrica, 66, 47-78 (1998) · Zbl 1056.62523
[6] Bardet, J. M.; Kengne, K.; Wintenberger, O., Multiple breaks detection in general causal time series using penalized quasi-likelihood, Electron. J. Stat., 6, 435-477 (2012) · Zbl 1337.62210
[7] Baudry, J. P.; Maugis, C.; Michel, B., Slope Heuristics: Overview and Implementation RR-INRIA \(n^o7223 (2010)\)
[8] Cleynen, A.; Lebarbier, E., Segmentation of the Poisson and negative binomial rate models: a penalized estimator, ESAIM Probab. Stat., 18, 750-769 (2014) · Zbl 1310.62041
[9] Cleynen, A.; Lebarbier, E., Model selection for the segmentation of multiparameter exponential family distributions, Electron. J. Stat., 11, 800-842 (2017) · Zbl 1362.62068
[10] Davis, R. A.; Hancock, S. A.; Yao, Y.-C., On consistency of minimum description length model selection for piecewise autoregressions, J. Econometrics, 194, 360-368 (2016) · Zbl 1443.62250
[11] Davis, R. A.; Lee, T. C.M.; Rodriguez-Yam, G. A., Break detection for a class of nonlinear time series models, J. Time Series Anal., 29, 5, 834-867 (2008) · Zbl 1199.62006
[12] Davis, R. A.; Liu, H., Theory and inference for a class of observation-driven models with application to time series of counts, Statist. Sinica, 26, 1673-1707 (2016) · Zbl 1356.62137
[13] Davis, R. A.; Yau, C. Y., Consistency of minimum description length model selection for piecewise stationary time series models, Electron. J. Stat., 7, 381-411 (2013) · Zbl 1337.62254
[14] Diop, M. L.; Kengne, W., Testing parameter change in general integer-valued time series, J. Time Series Anal., 38, 880-894 (2017) · Zbl 1386.60132
[15] Douc, R.; Fokianos, K.; Moulines, E., Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models, Electron. J. Stat., 11, 2707-2740 (2017) · Zbl 1366.62173
[16] Doukhan, P.; Fokianos, K.; Tjøstheim, D., On weak dependence conditions for Poisson autoregressions, Statist. Probab. Lett., 82, 942-948 (2012) · Zbl 1241.62109
[17] Doukhan, P.; Fokianos, K.; Tjøstheim, D., Correction to on weak dependence conditions for Poisson autoregressions, Statist. Probab. Lett., 83, 1926-1927 (2013), [Statist. Probab. Lett. 82 (2012) 942-948] · Zbl 1412.62100
[18] Doukhan, P.; Kengne, W., Inference and testing for structural change in general Poisson autoregressive models, Electron. J. Stat., 9, 1267-1314 (2015) · Zbl 1349.62397
[19] Fokianos, K.; Rahbek, A.; Tjøstheim, D., Poisson autoregression, J. Amer. Statist. Assoc., 104, 1430-1439 (2009) · Zbl 1205.62130
[20] Fokianos, K.; Tjøstheim, D., Log-linear Poisson autoregression, J. Multivariate Anal., 102, 563-578 (2011) · Zbl 1207.62165
[21] Fokianos, K.; Tjøstheim, D., Nonlinear Poisson autoregression, Ann. Inst. Statist. Math., 64, 1205-1225 (2012) · Zbl 1253.62058
[22] Franke, J.; Kirch, C.; Tadjuidje Kamgaing, J., Changepoints in times series of counts, J. Time Series Anal., 33, 757-770 (2012) · Zbl 1281.62181
[23] Fryzlewicz, P., Wild binary segmentation for multiple change-point detection, Ann. Statist., 42, 6, 2243-2281 (2014) · Zbl 1302.62075
[24] Fryzlewicz, P.; Subba Rao, S., Multiple-change-point detection for auto-regressive conditional heteroscedastic processes, J. R. Stat. Soc. Ser. B Stat. Methodol., 76, 5, 903-924 (2014) · Zbl 1411.62248
[25] Harchaoui, Z.; Lévy-Leduc, C., Multiple change-point estimation with a total variation penalty, J. Amer. Statist. Assoc., 105, 1480-1493 (2010) · Zbl 1388.62211
[26] Hudecová, Š., Structural changes in autoregressive models for binary time series, J. Statist. Plann. Inference, 143, 1744-1752 (2013) · Zbl 1279.62186
[27] Inclán, C.; Tiao, G. C., Use of cumulative sums of squares for retrospective detection of changes of variance, J. Amer. Statist. Assoc., 89, 427, 913-923 (1994) · Zbl 0825.62678
[28] Kang, J.; Lee, S., Parameter change test for Poisson autoregressive models, Scand. J. Stat., 41, 4, 1136-1152 (2014) · Zbl 1305.62313
[29] Kashikar, A. S.; Rohan, N.; Ramanathan, T. V., Integer autoregressive models with structural breaks, J. Appl. Stat., 40, 12, 2653-2669 (2013) · Zbl 07265967
[30] Lebarbier, E., Detecting multiple change-points in the mean of Gaussian process by model selection, Signal Process., 85, 717-736 (2005) · Zbl 1148.94403
[31] Lerasle, M., Optimal model selection for density estimation of stationary data under various mixing conditions, Ann. Statist., 39, 4, 1852-1877 (2011) · Zbl 1227.62018
[32] Leung, S. H.; Ng, W. L.; Yau, C. Y., Sequential change-point detection in time series models based on pairwise likelihood, Statist. Sinica, 27, 2, 575-605 (2017) · Zbl 1369.62231
[33] Ma, T. F.; Yau, C. Y., A pairwise likelihood-based approach for changepoint detection in multivariate time series models, Biometrika, 103, 2, 409-421 (2016) · Zbl 07072120
[34] Yau, C. Y.; Zhao, Z., Inference for multiple change points in time series via likelihood ratio scan statistics, J. R. Stat. Soc. Ser. B Stat. Methodol., 78, 895-916 (2016) · Zbl 1414.62386
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.