# zbMATH — the first resource for mathematics

Empirical likelihood for break detection in time series. (English) Zbl 1349.62383
Summary: Structural breaks have become an important research topic in time series analysis and in many fields of application, e.g. econometrics, hydrology, seismology, engineering and industry, chemometrics, and medicine. In most phenomena encountered in the real world modeling assuming no change of structure may obviously lead to inconsistent estimates and poor forecasts. Much research work has been carried out in the past decades and efforts mostly concentrated on the identification of points in time where structural breaks possibly occur and on the development of statistical tests of absence of breaks. Common procedures are the CUSUM based statistics and the F based statistics proposed by Bai and Perron in several papers and technical reports. The need of specification of a probability distribution for conducting the statistical tests has been often a drawback in practical applications. If the distribution is misspecified the test may turn to be unreliable. In this paper a distribution free procedure for identification of change points and testing for structural breaks is proposed based on the empirical likelihood and the empirical likelihood ratio statistics. A comparison with the F test and the CUSUM test is performed on both simulated and real world data. The size and power of the test is comparable with existing procedures and the identification procedure is generally accurate and effective.
##### MSC:
 62M07 Non-Markovian processes: hypothesis testing 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G10 Nonparametric hypothesis testing 62G30 Order statistics; empirical distribution functions
Full Text:
##### References:
 [1] Andrews, D. W. K. (1993). Tests for parameter instability and structural change with unknown change point. Econometrica 61 821-856. · Zbl 0795.62012 [2] Aue, A. and Horvath, L. (2013). Structural breaks in time series. J. Time Series Anal. 34 1-16. · Zbl 1274.62553 [3] Bai, J. (1999). Likelihood ratio tests for multiple structural changes. J. Econometrics 91 299-323. · Zbl 1041.62514 [4] Bai, J. and Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica 66 47-78. · Zbl 1056.62523 [5] Bai, J. and Perron, P. (2003a). Computation and analysis of multiple structural change models. J. Appl. Econometrics 18 1-22. [6] Bai, J. and Perron, P. (2003b). Critical values for multiple structural change tests. Econom. J. 6 72-78. · Zbl 1032.62064 [7] Bai, J. and Perron, P. (2006). Multiple structural change models: a simulation analysis. In Econometrics and Practice: Frontiers of Analysis and Applied Research ( D. Corbea, S. Durlauf and B. E. Hansen, eds.) 212-237. Cambridge University Press. [8] Baragona, R., Battaglia, F. and Poli, I. (2011). Evolutionary Statistical Procedures . Springer, Heidelberg. · Zbl 1378.62005 [9] Battaglia, F. and Protopapas, M. K. (2011). Time-varying multi-regime models fitting by genetic algorithms. J. Time Series Anal. 32 237-252. · Zbl 1290.62069 [10] Battaglia, F. and Protopapas, M. K. (2012). An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models. Stat. Methods Appl. 21 315-373. (with Discussion). · Zbl 1255.86008 [11] Chan, N. H. and Ling, S. (2006). Empirical likelihood for Garch models. Econom. Theory 22 403-428. · Zbl 1125.62097 [12] Chan, N. H., Peng, L. and Zhang, D. (2011). Empirical-likelihood based confidence intervals for conditional variance in heteroskedastic regression models. Econom. Theory 27 154-177. · Zbl 1401.62143 [13] Chen, J., Variyath, A. M. and Abraham, B. (2008). Adjusted empirical likelihood and its properties. J. Comput. Graph. Statist. 17 426-443. [14] Chuang, C.-S. and Chan, N. H. (2002). Empirical likelihood for autoregressive models, with applications to unstable time series. Statist. Sinica 12 387-407. · Zbl 0998.62075 [15] Csorgo, M. and Horvath, L. (1997). Limit theorems in change-point analysis . Wiley, Chichester. · Zbl 0884.62023 [16] Fan, G.-L. and Xu, H.-X. (2012). Empirical likelihood inference for partially time-varying coefficients errors-in-variables models. Electron. J. Stat. 6 1040-1058. · Zbl 1295.62050 [17] Gong, Y., Li, Z. and Peng, L. (2010). Empirical likelihood intervals for conditional Value-at-Risk in Arch/{G}arch models. J. Time Series Anal. 31 65-75. · Zbl 1224.62055 [18] Guan, Z. (2004). A semiparametric changepoint model. Biometrika 91 849-862. · Zbl 1055.62029 [19] Hu, X., Wang, Z. and Zhao, Z. (2009). Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variable models. Statistist. Probab. Lett. 79 1044-1052. · Zbl 1158.62030 [20] Jandhyala, V., Fotopoulos, S., MacNeill, I. and Liu, P. (2013). Inference for single and multiple change-points in time series. J. Time Series Anal. 34 423-446. · Zbl 1275.62061 [21] Jing, B.-Y. (1995). Two-sample empirical likelihood method. Statist. Probab. Lett. 24 315-319. · Zbl 0837.62039 [22] Kakizawa, Y. (2013). Frequency domain generalized empirical likelihood method. J. Time Series Anal. 34 691-716. · Zbl 1296.62170 [23] Kolaczyk, E. D. (1994). Empirical likelihood for generalized linear models. Statist. Sinica 4 199-218. · Zbl 0824.62062 [24] Kolaczyk, E. D. (1995). An information criterion for empirical likelihood with general estimating equations Technical No. 417, Department of Statistics, The University of Chicago. [25] Liu, Y., Zou, C. and Zhang, R. (2008a). Empirical likelihood for the two-sample problem. Statist. Probab. Lett. 78 548-556. · Zbl 1136.62331 [26] Liu, Y., Zou, C. and Zhang, R. (2008b). Empirical likelihood ratio test for a change-point in linear regression model. Comm. Statist. Theory Methods 37 2551-2563. · Zbl 1147.62332 [27] Lundberg, S., Teräsvirta, T. and van Dijk, D. (2003). Time-varying smooth transition autoregressive models. J. Bus. Econom. Statist. 21 104-121. [28] Monti, A. C. (1997). Empirical likelihood confidence regions in time series models. Biometrika 84 395-405. · Zbl 0882.62082 [29] Mykland, P. A. (1999). Dual likelihood. Ann. Statist. 23 396-421. · Zbl 0877.62004 [30] Nordman, D. J. (2009). Tapered empirical likelihood for time series data in time and frequency domain. Biometrika 96 119-132. · Zbl 1162.62406 [31] Nordman, D. J. and Lahiri, S. N. (2006). A frequency domain empirical likelihood for short- and long-range dependence. Ann. Statist. 34 3019-3050. · Zbl 1114.62095 [32] Owen, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75 237-249. · Zbl 0641.62032 [33] Owen, A. B. (1991). Empirical likelihood for linear models. Ann. Statist. 19 1725-1747. · Zbl 0799.62048 [34] Owen, A. B. (2001). Empirical Likelihood . Chapman and Hall CRC. · Zbl 0989.62019 [35] Perron, P. (2006). Dealing with structural breaks. In Palgrave Handbook of Econometrics , ( K. Patterson and T. C. Mills, eds.) 1 278-352. Palgrave McMillan. [36] Qin, J. and Lawless, J. (1994). Empirical likelihood and general estimating equations. Ann. Statist. 22 300-325. · Zbl 0799.62049 [37] Robbins, M., Gallagher, C., Lund, R. and Aue, A. (2011). Mean shift testing in correlated data. J. Time Series Anal. 32 498-511. · Zbl 1294.62212 [38] Robbins, M. W., Lund, R. B., Gallagher, C. M. and Lu, Q. (2011). Changepoints in the north atlantic tropical cyclone record. J. Amer. Statist. Assoc. 106 89-99. · Zbl 1396.62264 [39] Shorack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics . Wiley, New York. · Zbl 1170.62365 [40] Variyath, A. M., Chen, J. and Abraham, B. (2010). Empirical likelihood based model selection. J. Statist. Plann. Inference 140 971-981. · Zbl 1179.62047 [41] Yau, C. Y. (2012). Empirical likelihood in long-memory time series models. J. Time Series Anal. 33 269-275. · Zbl 1300.62084 [42] You, J. and Zhou, Y. (2006). Empirical likelihood for semiparametric varying-coefficient partially linear regression models. Statist. Probab. Lett. 76 412-422. · Zbl 1086.62057 [43] Zhang, H., Wang, D. and Zhu, F. (2011). Empirical likelihood inference for random coefficient INAR$$(p)$$ process. J. Time Series Anal. 32 195-203. · Zbl 1290.62091 [44] Zi, X., Zou, C. and Liu, Y. (2012). Two-sample empirical likelihood method for difference between coefficients in linear regression model. Statist. Papers 53 83-93. · Zbl 1241.62038 [45] Zou, C., Liu, Y., Qin, P. and Wang, Z. (2007). Empirical likelihood ratio test for the change-point problem. Statist. Probab. Lett. 77 374-382. · Zbl 1108.62045
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.