Abstract
There are more and more applications involve the big data analytics. The research method of big data is particularly important in the study of time-varying volatilities. In the article, we analysis the tests for a constant mean possibly subjected to change under strong mixing dependence based on big data method. The change point methods provided here rely on ratio type test statistics based on the functional of the partial sums of residuals. The main advantage of proposed approach is that the model allows strong mixing and time-varying variance in error terms. Based on the fundamental results suggested by Cavaliere (2004, Econometric Reviews, 23, 259− 292), the limiting distribution under the original hypothesis is derived and the consistency under the alternatives is also proved.
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References
Page, M.E.: Continuous inspection schemes. Biometrika 42, 100–114 (1954)
Perron, P.: Dealing with structural breaks. Palgrave Handb. Econometrics 1, 278–352 (2006)
Chen, J., Gupta, A.K.: Parametric Statistical Change Point Analysis: With Applications to Genetics, and Finance. Springer Science and Business Media, Berlin (2011)
Brodsky, E., Darkhovsky, B.S.: Nonparametric Methods in the Problems of Change Points. Springer Science & Business Media, Berlin (2013)
Bai, J.: Least squares estimation of a shift in linear processes. J. Time Ser. Anal. 15, 453–472 (1994)
Shao, X.F.: A simple test of changes in mean in the possible presence of long-range dependence. J. Time Ser. Anal. 32, 598–606 (2010)
Aue, A., Horváth, L.: Structural breaks in time series. J. Time Ser. Anal. 34, 1–16 (2013)
Zhao, W.Z., Xia, Z.M., Tian, Z.: Ratio test for variance change point in linear process with long memory. Stat. Pap. 51, 397–407 (2010)
Horváth, L., Horváth, Z., Husková, M.: Ratio tests for change point detection. Inst. Math. Stat. 1, 293–304 (2008)
Jandhyala, V., Fotopoulos, S., MacNeill, I., Liu, P.: Inference for single and multiple change-points in time series. J. Time Ser. Anal. 34, 423–446 (2013)
Pagan, A.R., Schwert, G.W.: Testing for covariance stationarity in stock market data. Econ. Lett. 33, 165–170 (1990)
Waston, M.W.: Explaining the increased variability in long-term intest rates. Fed. Reserve Bank Richmond Econ. Quart. 85, 71–96 (1999)
van Dijk, D., Osborn, D.R., Sensier, M.: Change in variability of the business cycle in the G7 countries. Econometric Institute Report (2002)
Kim, T.H., Leybourne, S., Newbold, P.: Unit root tests with a break in innovation variance. J. Econometrics 109, 365–387 (2002)
Cavaliere, G.: Unit root tests under time-varying variances. Econometric Rev. 23, 259–292 (2004)
Cavaliere, G., Taylor, A.M.R.: Testing for unit roots in time series models with non-stationary volatility. J. Econometrics 140, 919–947 (2007)
Zhang, E., Wu, J.: Testing for structural changes in linear regressions with time-varying variance. Communications in Statistics - Theory and Methods, pp. 1–30 (2019)
Acknowledgments
This work is supported by National Natural Science Foundation of China under Grant No. 71473194; Science and Technology Foundation of Shaanxi Province of China under Grant No. 2020JM513.
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Li, C., Jin, H., Bai, H. (2021). Ratio Test for Time-Varying Variance of Mean Change Point Based on Big Data Analysis. In: Xu, Z., Parizi, R.M., Loyola-González, O., Zhang, X. (eds) Cyber Security Intelligence and Analytics. CSIA 2021. Advances in Intelligent Systems and Computing, vol 1342. Springer, Cham. https://doi.org/10.1007/978-3-030-70042-3_53
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