References
- Bai, J. 1994. Least squares estimation of a shift in linear processes. Journal of Time Series Analysis 15 (5):453–72. doi:https://doi.org/10.1111/j.1467-9892.1994.tb00204.x.
- Basrak, B., R. A. Davis, and T. Mikosch. 2002a. A characterization of regular variation. The Annals of Applied Probability 12:908–20. doi:https://doi.org/10.1214/aoap/1031863174.
- Basrak, B., R. A. Davis, and T. Mikosch. 2002b. Regular variation of GARCH processes. Stochastic Processes and Their Applications 99 (1):95–115. doi:https://doi.org/10.1016/S0304-4149(01)00156-9.
- Chen, Z., Z. Jin, Z. Tian, and P. Qi. 2012. Bootstrap testing multiple changes in persistence for a heavy-tailed sequence. Computational Statistics & Data Analysis 56 (7):2303–16. doi:https://doi.org/10.1016/j.csda.2012.01.011.
- Davis, R. A., and T. Hsing. 1995. Point process and partial sum convergence for weakly dependent random variables. The Annals of Probability 23 (2):879–917. doi:https://doi.org/10.1214/aop/1176988294.
- Hawkins, M. D. 1977. Testing a sequence of observations for a shift in location. Journal of the American Statistical Association 72 (357):180–6. doi:https://doi.org/10.2307/2286934.
- Horváth, L., Z. Horváth, and M. Hušková. 2008. Ratio tests for change point detection. Institute of Mathematical Statistics 1:293–304.
- Jin, H., J. Zhang, S. Zhang, and C. Yu. 2013. The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks. Computational Statistics & Data Analysis 67:25–40. doi:https://doi.org/10.1016/j.csda.2013.04.011.
- Jin, H., Z. Tian, and R. Qin. 2009. Bootstrap tests for structural change with infinite variance observations. Statistics & Probability Letters 79 (19):1985–95. doi:https://doi.org/10.1016/j.spl.2009.06.008.
- Kokoszka, P., and M. Wolf. 2004. Subsampling the mean of heavy-tailed dependent observations. Journal of Time Series Analysis 25 (2):217–34. doi:https://doi.org/10.1046/j.0143-9782.2003.00346.x.
- McElroy, T., and D. N. Politis. 2002. Robust inference for the mean in the presence of serial correlation and heavy-tailed distributions. Econometric Theory 18 (5):1019–39. doi:https://doi.org/10.1017/S026646660218501X.
- Paparoditis, E., and D. N. Politis. 2003. Residual-based block bootstrap for unit root testing. Econometrica 71 (3):813–55. doi:https://doi.org/10.1111/1468-0262.00427.
- Pena, V., T. Lai, and Q. Shao. 2009. Self-normalized Processes-Limit Theory and Statistical Applications. Berlin: Springer.
- Phillips, P. C. 1990. Time series regression with a unit root and infinite-variance errors. Econometric Theory 6 (1):44–62. doi:https://doi.org/10.1017/S0266466600004904.
- Qin, R., and W. Liu. 2019. Ratio detection for mean change in α mixing observations. Communications in Statistics - Theory and Methods 48 (7):1693–708. doi:https://doi.org/10.1080/03610926.2018.1438623.
- Sen, A., and M. S. Srivastava. 1975. On tests for detecting change in mean when the variance is unknown. Annals of the Institute of Statistical Mathematics 27 (1):479–86. doi:https://doi.org/10.1007/BF02504665.
- Wang, D., P. Guo, and Z. Xia. 2017. Detection and estimation of structural change in heavy-tailed sequences. Communications in Statistics-Theory and Methods 46 (2):815–27.
- Xia, Z., and P. Qiu. 2015. Jump information criterion for statistical inference in estimating discontinuous curves. Biometrika 102 (2):397–408. doi:https://doi.org/10.1093/biomet/asv018.
- Xia, Z., P. Guo, and W. Zhao. 2009. Monitoring structural changes in generalized linear models. Communications in Statistics - Theory and Methods 38 (11):1927–47. doi:https://doi.org/10.1080/03610920802549910.
- Yao, Y. 1987. Approximating the distribution of the maximum likelihood estimate of the change-point in a sequence of independent random variables. The Annals of Statistics 15 (3):1321–8. doi:https://doi.org/10.1214/aos/1176350509.
- Zhao, W., and H. Lv. 2016. Ratio test for change point in the mean of heavy-tailed dependent sequence. Journal of ShanXi University 39 (3):410–4.
- Zhao, W., Z. Xia, and Z. Tian. 2011. Ratio test to detect change in the variance of linear process. Statistics 45 (2):189–98. doi:https://doi.org/10.1080/02331880903461326.