The increment ratio statistic

Journal of Multivariate Analysis

Volumn 99, Issue 3, 2008, Pages 510-541

  Surgailis, Donatas ^a   Teyssière, Gilles ^b,c   Vaičiulis, Marijus ^a  

^a VILNIUS UNIVERSITY   (Lithuania)

^b University Paris I Sorbonne Panthéon   (France)

^c UNIVERSITY OF GOTHENBURG   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38349140931     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2007.01.014     Document Type: Article

References (59)

1. K. Abadir, W. Distaso, L. Giraitis, Estimation and inference for trending I (d) and related processes, preprint, 2006.
2. Abry P., Flandrin P., Taqqu M., and Veitch D. Self-similarity and long-range dependence through the wavelet lens. In: Doukhan P., Oppenheim G., and Taqqu M.S. (Eds). Long-Range Dependence: Theory and Applications (2003), Birkhäuser, Boston 527-556
3. Abry P., and Veitch D. Wavelet analysis of long-range dependent traffic. IEEE Trans. Inform. Theory 44 (1998) 2-15
4. Arcones M.A. Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors. Ann. Probab. 22 (1994) 2242-2274
5. A. Aue, L. Horváth, J. Steinebach, Long memory versus stochastic trend, preprint, 2005.
6. Bardet J.-M., Lang G., Moulines E., and Soulier Ph. Wavelet estimator of long-range dependence processes. Statist. Inf. Stoch. Process 3 (2000) 85-99
7. Berkes I., Horváth L., Kokoszka P.S., and Shao Q.-M. On discriminating between long-range dependence and changes in mean. Ann. Statist. 34 (2006) 1140-1165
8. Bhattacharya R.N., Gupta V.K., and Waymire E. The Hurst effect under trends. J. Appl. Probab. 20 (1983) 649-662
9. Bollerslev T. A conditional heteroskedastic time series model for speculative prices and rates of return. Rev. Econ. Statist. 69 (1987) 542-547
10. Breuer P., and Major P. Central limit theorems for nonlinear functionals of Gaussian fields. J. Multivariate Anal. 13 (1983) 425-441
11. K. Bružaitė, D. Surgailis, D. Vaičiulis, Time-varying fractionally integrated processes with finite or infinite variance and nonstationary long memory, preprint, 2006.
12. Bružaitė K., and Vaičiulis M. Asymptotic independence of distant partial sums of linear process. Lithuanian Math. J. 45 (2005) 387-404
13. Chambers D., and Slud E. Central limit theorems for nonlinear functional of stationary Gaussian processes. Probab. Theory Related Fields 80 (1989) 323-346
14. Cox D.R. Long-range dependence: A review. In: David H.A., and David H.T. (Eds). Statistics: An Appraisal (1984), Iowa State University Press, Iowa 55-74
15. Cremers H., and Kadelka D. On weak convergence of integral functions of stochastic processes with applications to processes taking paths in L (p ; E). Stochastic Process. Appl. 21 (1986) 305-317
16. Csörgo{combining double acute accent} S., and Mielniczuk J. Distant long-range dependent sums and regression estimation. Stochastic Process. Appl. 59 (1995) 143-155
17. Dacorogna M.M., Müller U.A., Nagler R.J., Olsen R.B., and Pictet O.V. A geographical model for the daily and weekly seasonal volatility in the foreign exchange Market. J. Internat. Money Finance 12 (1993) 413-438
18. Davydov Y. The invariance principle for stationary processes. Theory Probab. Appl. 15 (1970) 487-498
19. Diebold F.X., and Inoue A. Long memory and regime switching. J. Econometrics 105 (2001) 131-159
20. J. Dolado, J. Gonzalo, L. Mayoral, What is what ? A simple time-domain test of long-memory vs. structural breaks, preprint, 2005.
21. Gil-Alaña L.A., and Robinson P.M. Testing of unit root and other nonstationary hypotheses in macroeconomic time series. J. Econometrics 80 (1997) 241-268
22. Giraitis L., Kokoszka P., and Leipus R. Testing for long memory in the presence of a general trend. J. Appl. Probab. 38 (2001) 1033-1054
23. Giraitis L., Kokoszka P., Leipus R., and Teyssière G. Rescaled variance and related tests for long memory in volatility and levels. J. Econometrics 112 (2003) 265-294
24. Giraitis L., Kokoszka P., Leipus R., and Teyssière G. On the power of R/S tests for stationarity against contiguous and semi-long memory alternatives. Acta Appl. Math. 78 (2003) 285-299
25. Giraitis L.P., Leipus R., and Philippe A. A test for stationarity versus trends and unit roots for a wide class of dependent errors. Econometric Theory 22 (2006) 989-1029
26. Giraitis L., Robinson P.M., and Surgailis D. A model for long memory conditional heteroscedasticity. Ann. Appl. Probab. 10 (2000) 1002-1024
27. Giraitis L., and Surgailis D. CLT and other limit theorems for functionals of Gaussian processes. Z. Wahrsch. verw. Geb. 70 (1985) 191-212
28. Giraitis L., and Surgailis D. ARCH-type bilinear models with double long memory. Stochastic Process. Appl. 100 (2002) 275-300
29. Gourieroux C., and Jasiak J. Memory and infrequent breaks. Economics Lett. 70 (2001) 29-41
30. Granger C.W.J., and Hyung N. Occasional structural breaks and long memory with an application to the S&P500 absolute stock returns. J. Empirical Finance 11 (2004) 399-421
31. Ho H.-C., and Hsing T. Limit theorems for functionals of moving averages. Ann. Probab. 25 (1997) 1636-1669
32. Ibragimov I.A., and Linnik Yu.V. Independent and Stationary Sequences of Random Variables (1971), Wolters-Noordholf, Groningen
33. P. Kokoszka, G. Teyssière, Change-point detection in GARCH models: asymptotic and bootstrap tests, preprint, 2002.
34. Künsch H. Discrimination between monotonic trends and long-range dependence. J. Appl. Probab. 23 (1986) 1025-1030
35. Kwiatkowski D., Phillips P.C.B., Schmidt P., and Shin Y. 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?. J. Econometrics 54 (1992) 159-178
36. Lavielle M. Detection of multiple changes in a sequence of dependent variables. Stochastic Process. Appl. 83 (1999) 79-102
37. Lavielle M., and Ludeña C. Random thresholds for linear model selection. Publ. INRIA 5572 (2005)
38. Lavielle M., and Moulines E. Least-squares estimation of an unknown number of shifts in a time series. J. Time Series Anal. 21 (2000) 33-59
39. Lavielle M., and Teyssière G. Adaptive detection of multiple change-points in asset price volatility. In: Teyssière G., and Kirman A. (Eds). Long Memory in Economics (2005), Springer, Berlin 129-156
40. Lavielle M., and Teyssière G. Detection of multiple change-points in multivariate time series. Lithuanian Math. J. 46 (2006) 287-306
41. Leipus R., and Viano M.-C. Long memory and stochastic trend. Statist. Probab. Lett. 61 (2003) 177-190
42. Lo A.W. Long-term memory in stock market prices. Econometrica 59 (1991) 1279-1313
43. Lobato I., and Robinson P.M. A nonparametric test for I (0). Rev. Econ. Studies 65 (1998) 475-495
44. Marinucci D., and Robinson P.M. Alternative forms of fractional Brownian motion. J. Statist. Plann. Inference 80 (1999) 111-122
45. Mikosch T., and Stǎricǎ C. Long-range dependence effects and ARCH modeling. In: Doukhan P., Oppenheim G., and Taqqu M.S. (Eds). Long-Range Dependence: Theorey and Applications (2003), Birkhäuser, Boston 439-459
46. Mikosch T., and Stǎricǎ C. Change of structure in financial time series, long range dependence and the GARCH model. REVSTAT Statist. J. 2 (2004) 16-41
47. Perron P. The great crash, the oil shock and the unit root hypothesis. Econometrica 57 (1989) 1361-1401
48. Petrov V.V. Sums of Independent Random Variables (1975), Springer, New York
49. Philippe A., Surgailis D., and Viano M.-C. Invariance principle for a class of non stationary processes with long memory. C. R. Acad. Sci. Paris Ser. 1 342 (2006) 269-274
50. Philippe A., Surgailis D., and Viano M.-C. Almost periodically correlated processes with nonstationary long memory. In: Bertail P., Doukhan P., and Soulier Ph. (Eds). Dependence in Probability and Statistics, Lecture Notes in Statistics vol. 187 (2006), Springer, Berlin 159-194
51. A. Philippe, D. Surgailis, M.-C. Viano, Time varying fractionally integrated processes with nonstationary long memory, Theory Probab. Appl., forthcoming, 2007.
52. Robinson P.M. Efficient tests of nonstationary hypotheses. J. Amer. Statist. Assoc. 89 (1994) 1420-1437
53. Sibbertsen P. Log-periodogram estimation of the memory parameter of a long memory process under trend. Statist. Probab. Lett. 61 (2003) 261-268
54. Surgailis D. CLTs for polynomials of linear processes: diagram formula with illustrations. In: Doukhan P., Oppenheim G., and Taqqu M.S. (Eds). Long-Range Dependence: Theory and Applications (2003), Birkhäuser, Boston 111-127
55. Taqqu M.S. Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. verw. Geb. 31 (1975) 287-302
56. Taqqu M.S. Fractional Brownian motion and long-range dependence. In: Doukhan P., Oppenheim G., and Taqqu M.S. (Eds). Long-Range Dependence: Theory and Applications (2003), Birkhäuser, Boston 5-38
57. T. Teräsvirta, Two stylized facts and the GARCH (1, 1) model, Stockholm School of Economics, Working Paper Series in Economics and Finance, vol. 96, 1996.
58. Teyssière G. Interaction models for common long-range dependence in asset price volatility. In: Rangarajan G., and Ding M. (Eds). Processes with Long Range Correlations: Theory and Applications, Lecture Notes in Physics vol. 621 (2003), Springer, Berlin 251-269
59. Teyssière G., and Abry P. Wavelet analysis of nonlinear long-range dependent processes. Applications to financial time Series. In: Teyssière G., and Kirman A. (Eds). Long Memory in Economics (2005), Springer, Berlin 173-238