On distinguishing between random walk and change in the mean alternatives

Econometric Theory

Volumn 25, Issue 2, 2009, Pages 411-441

  Aue, Alexander ^a   Horváth, Lajos ^b   Huškov, Marie ^c   Ling, Shiqing ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF UTAH   (United States)

^c CHARLES UNIVERSITY   (Czech Republic)

^d HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 69849115038     PISSN: 02664666     EISSN: 14694360     Source Type: Journal    
DOI: 10.1017/S0266466608090130     Document Type: Article

References (45)

1. Andreau, E. & A. Spanos (2003) Statistical adequacy and the testing of trend versus difference stationarity. Econometric Reviews 22, 217-237.
2. Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance estimation. Econometrica 59, 817-858.
3. Aue, A., I. Berkes, & L. Horváth (2006) Strong approximation for the sums of squares of augmented GARCH sequences. Bernoulli 12, 583-608.
4. Bai, J. (1994) Least squares estimation of a shift in linear processes. Journal of Time Series Analysis 15, 453-470.
5. Banerjee, A., R. Lumsdaine, & Stock, J. (1992) Recursive and sequential tests of the unit root and trend break hypothesis: Theory and international evidence. Journal of Business & Economic Statistics 10, 271-288.
6. Bartlett, M.S. (1950) Periodogram analysis of continuous spectra. Biometrika 37, 1-16.
7. Belaire-Franch, J. (2005) A proof of the power of Kim's test against stationary processes with structural breaks. Econometric Theory 21, 1172-1176.
8. Berkes, I., L. Horváth, P. Kokoszka, & Q.-M. Shao (2005) Almost sure convergence of the Bartlett estimator. Periodica Mathematica Hungarica 51, 11-25.
9. Berkes, I., L. Horváth, P. Kokoszka, & Q.-M. Shao (2006) On discriminating between long-range dependence and changes in the mean. Annals of Statistics 34, 1140-1165.
10. Berkes, I. & W. Philipp (1979) Approximation theorem for independent and weakly dependent random vectors. Annals of Probability 7, 29-54.
11. Busetti, F. & A.M.R. Taylor (2004) Tests of stationarity against a change in persistence. Journal of Econometrics 123, 33-66.
12. Breidt, F.J., N. Crato, & P. de Lima (1998) On the detection and estimation of long memory in stochastic volatility. Journal of Econometrics 83, 325-348.
13. Carrasco, M. & X. Chen (2002) Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 17-39.
14. Csörgo, M. & L. Horváth (1997) Limit Theorems in Change-Point Analysis. Wiley.
15. Csörgo, M. & P. R'ev'esz (1981) Strong Approximations in Probability and Statistics. Academic Press.
16. Den Haan,W.J. & A. Levin (1996) Inference from Parametric and Non-parametric co-Variance Matrix Estimation Procedures. National Bureau of Economic Research Technical Working Paper 2000-2011
17. Feller, W. (1951) The asymptotic distribution of the range of sums of independent random variables. Annals of Mathematical Statistics 22, 427-432.
18. Giraitis, L., P. Kokoszka, & R. Leipus (2001) Testing for long memory in the presence of a general trend. Journal of Applied Probability 10, 1002-1024.
19. Giraitis, L., P. Kokoszka, R. Leipus, & G. Teyssi'ere (2003) Rescaled variance and related tests for long memory in volatility and levels. Journal of Econometrics 112, 265-294.
20. Hall, P. & C.C. Heyde (1980) Martingale Limit Theory and Its Application. Academic Press.
21. Harvey, D.I. & T.C. Mills (2004) Tests for stationarity in a series with endogenously determined structural change. Oxford Bulletin of Economics and Statistics 66, 863-894.
22. Hurst, H. (1951) Long term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers 116, 770-799.
23. Kim, J.-Y. (2000) Detection of change in persistence of a linear time series. Journal of Economics 95, 97-116.
24. Kim, J.-Y, J. Belaire-Franch, & R. Badillo-Amador (2002) Corringendum to "Detection of change in persistence of a linear time series." Journal of Economics 109, 389-392.
25. Kuiper, N.H. (1960) Tests concerning random points on the circle. Proceedings of the Koninklijke Nederlandse Akademie Van Wettenschappen, Series A 63, 38-47.
26. Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, & Y. Shin (1992) Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics 54, 159-178.
27. Leybourne, S., T.-H. Kim, V. Smith, & P. Newbold (2003) Tests for a change in persistence against the null of difference-stationarity. Econometrics Journal 6, 291-311.
28. Lo, A. (1991) Long-term memory in stock market prices. Econometrica 59, 1279-1313.
29. Mandelbrot, B.B. & M.S. Taqqu (1979) Robust R/S analysis of long run serial correlation. In 42nd Session of the International Statistical Institute, Manila, book 2, pp. 69-99.
30. Nelson, C.R. & C.I. Plosser (1982) Trends and random walks in macroeconomics time series: Some evidence and implications. Journal of Monetary Economics 10, 139-162.
31. Nyblom, J. & T.Mäkeläinen (1983) Comparisons of tests for the presence of random walk coefficients in a simple linear model. Journal of the American Statistical Association 78, 856-864.
32. Page, E.S. (1954) Continuous inspection schemes. Biometrika 41, 100-105.
33. Perron, P. (1989) The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57, 1361-1401.
34. Perron, P. (1990) Testing for a unit root in a time series with a changing mean. Journal of Business & Economic Statistics 8, 153-162.
35. Perron, P. & T.J. Vogelsang (1992) Testing for a unit root in a time series with a changing mean: Corrections and extensions. Journal of Business & Economic Statistics 10, 467-470.
36. Philipp, W. (1986) Invariance principles for independent and weakly dependent random variables. In Dependence in Probability and Statistics, Progress in Probability and Statistics, 11, pp. 225-268 Birkhäuser.
37. Shao, Q.-M. (1993) Almost sure invariance principles for mixing sequences of random variables. Stochastic Processes and Their Applications 48, 319-334.
38. Shorack, G.R. & J.A. Wellner (1986) Empirical Processes with Applications to Statistics. Wiley.
39. Taylor, A.M.R. (2005) Fluctuation tests for change in persistance. Oxford Bulletin of Economics and Statistics 67, 207-229.
40. Teverovsky, V., M.S. Taqqu, & W. Willinger (1999). Stock market prices and long-range dependence. Finance and Stochastics 3, 1-13.
41. Vostrikova, L.J. (1981) Discovery of "discord" in multidimensional random processes. Doklady Akademii Nauk SSSR 259, 270-274.
42. Watson, G.S. (1961) Goodness-of-fit tests on a circle. Biometrika 48, 109-114.
43. Xiao, Z. (2001) Testing the null hypothesis of stationarity against an autoregressive unit root alternative. Journal of Time Series Analysis 22, 87-105.
44. Yao, Y.-C. (1988). Estimating the number of change-points via Schwartz's criterion. Statistics and Probability Letters 6, 173-177.
45. Zhang, A., R. Gabrys, & P. Kokoszka (2007) Discriminating between long memory and volatility shifts. Austrian Journal of Statistics 36, 253-275.