Abstract
In this paper we consider the detection problem of variance change point in linear process with long memory. We propose the ratio test to detect the variance change point. The limiting distribution for test statistics under H 0 is derived and the consistency of the test is also established. In comparison with the existing CUSUM of squares (SCUSUM) test, the ratio test does not need to estimate the long memory parameter in practical situation and therefore it can be used more conveniently.
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References
Abraham B, Wei WWS (1984) Inferences about the parameters of a time series model with changing variance. Metrika 31: 183–194
Avram F, Taqqu M (1987) Noncentral limit theorems and appell polynomials. Ann Probab 15: 767–775
Gombay E, Horváth L, Hus̈ková M (1996) Estimators and tests for change in variances. Stat Decis 14: 145–159
Ho H, Hsing T (1997) Limit theorems for functionals of moving averages. Ann Probab 25: 1636–1669
Horváth L, Horváth Z, Hus̈ková M (2008) Ratio tests for change point detection. Inst Math Stat 1: 293–304
Hsu DA, Miller RB, Wichern DW (1974) On the stable paretian behavior of stock market prices. J Am Stat Assoc 69: 108–113
Inclàn C, Tiao GC (1994) Use of cumulative of sums squares for retrospective detection of changes of variance. J Am Stat Assoc 89: 913–923
Kim JY (2000) Detection of change in persistence of a linear time series. J Econom 95: 97–116
Kim JY, Belaire-Franch J, Amador R (2002) Corrigendum to “Detection of change in persistence of a linear time series”. J Econom 109: 389–392
Lee S, Park S (2001) The cusum of squares test for scale changes in infinite order moving average process. Scand J Statist 28: 625–644
Mandelbrot PR, Van Ness JW (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev 10: 422–437
Wang L, Wang J (2006) Change of variance problem for linear processes with long memory. Stat Papers 47: 279–298
Wichern DW, Miller RB, Hsu DA (1976) Changes of variance in first-order autoregressive time series models-with an application. Appl Statist 25: 248–256
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Zhao, W., Tian, Z. & Xia, Z. Ratio test for variance change point in linear process with long memory. Stat Papers 51, 397–407 (2010). https://doi.org/10.1007/s00362-009-0202-3
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DOI: https://doi.org/10.1007/s00362-009-0202-3