Can GARCH models capture long-range dependence?

Studies in Nonlinear Dynamics and Econometrics

Volumn 9, Issue 4, 2005, Pages 1-43

  Maheu, John ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29144442127     PISSN: 15583708     EISSN: 10811826     Source Type: Journal    
DOI: 10.2202/1558-3708.1269     Document Type: Article

References (58)

1. AGIAKLOGLOU, C., P. NEWBOLD, AND M. WOHAR (1993): "Bias in an Estimator of the Fractional Difference Parameter," Journal of Time Series Analysis, 14(3), 235-246.
2. ANDERSEN, T. G., AND T. BOLLERSLEV (1997): "Heterogenous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, 52, 975-1005.
3. ANDERSEN, T. G., T. BOLLERSLEV, F. X. DIEBOLD, AND H. EBENS (2001): "The Distribution of Realized Stock Return Volatility," Journal of Financial Economics, 61, 43-76.
4. ANDERSEN, T. G., T. BOLLERSLEV, F. X. DIEBOLD, AND P. LABYS (2001): "The Distribution of Exchange Rate Volatility," Journal of the American Statistical Association, 96, 42-55.
5. BAILLIE, R. (1996): "Long Memory Processes and Fractional Integration in Econometrics," Journal of Econometrics, 73(5), 5-59.
6. BAILLIE, R. T., T. BOLLERSLEV, AND H. MIKKELSEN (1996): "Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, 14, 3-30.
7. BAILLIE, R. T., A. A. CECEN, AND Y. HAN (2000): "High Frequency Deutsche Mark-US Dollar Returns: FIGARCH Representations and Non Linearities," Multinational Finance Journal, 4(3-4), 247-67.
8. BELTRATTI, A., AND C. MORANA (1999): "Computing Value at Risk with High Frequency Data," Journal of Empirical Finance, 6(5), 431-55.
9. BERAN, J. (1994): Statistics for Long-Memory Processes, Monographs on Statistics and Applied Probability 61. Chapman and Hall.
10. BOLLERSLEV, T. (1986): "Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, 31, 309-328.
11. BOLLERSLEV, T., AND H. O. MIKKELSEN (1999): "Long-term Equity Anticipation Securities and Stock Market Volatility Dynamics," Journal of Econometrics, 92, 75-99.
12. BOLLERSLEV, T., AND J. M. WOOLDRIDGE (1992): "Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time-Varying Covariances," Econometric Reviews, 11, 143-172.
13. BOLLERSLEV, T., AND J. H. WRIGHT (2000): "Semiparametric Estimation of Long-memory volatility dependencies: The Role of High-Frequency Data," Journal of Econometrics, 98, 81-106.
14. BOUGEROL, P., AND N. PICARD (1992): "Stationarity of GARCH Processes and of some Nonnegative Time Series," Journal of Econometrics, 52(115-128).
15. BREIDT, F. J., N. CRATO, AND P. DE LIMA (1998): "The Detection and Estimation of Long Memory in Stochastic Volatility," Journal of Econometrics, 83, 325-348.
16. BRUNETTI, C., AND C. L. GILBERT (2000): "Bivariate FIGARCH and Fractional Cointegration," Journal of Empirical Finance, 7, 509-530.
17. CHEUNG, Y. (1993): "Tests for Fractional Integration: A Monte Carlo Investigation," Journal of Time Series Analysis, 14(4), 331-345.
18. DAVIS, R. A., AND T. MIKOSCH (1998): "The Sample Autocorrelations of Heavy Tailed Processes with Applications to ARCH," The Annals of Statistics, 26, 2049-2080.
19. DEO, R. S., AND C. M. HURVICH (2001): "On the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models," Econometric Theory, 17(686-710).
20. DIEBOLD, F. X., AND A. INOUE (2001): "Long memory and regime switching," Journal of Econometrics, 105(1), 131-159.
21. DING, Z., AND C. W. J. GRANGER (1996): "Modeling Volatility Persistence of Speculative Returns: A New Approach," Journal of Econometrics, 73, 185-215.
22. DING, Z., C. W. J. GRANGER, AND R. F. ENGLE (1993): "A Long Memory Property of Stock Market Returns and a New Model," Journal of Empirical Finance, 1, 83-106.
23. ENGLE, R. F. (1982): "Autoregressive Conditional Heteroskedasticity with Estimates of the UK inflation," Econometrica, 50, 987-1008.
24. ENGLE, R. F., AND T. BOLLERSLEV (1986): "Modelling the Persistence of Conditional Variances," Econometric Reviews, 5, 1-50.
25. ENGLE, R. F., AND G. G. J. LEE (1999): "A Long-Run and Short-Run Component Model of Stock Return Volatility," in Cointegration, Causality, and Forecasting, ed. by Engle, and White. Oxford University Press.
26. GEWEKE, J. (1998): "Comment on Real and Spurious Long-Memory Properties of Stock Market Data," Journal of Business & Economic Statistics, 16(3), 269-271.
27. GEWEKE, J., AND S. PORTER-HUDAK (1983): "The Estimation and Application of Long Memory Time Series Models," Journal of Time Series Analysis, 4(4), 221-238.
28. GIRAITIS, L., P. KOKOSZKA, AND R. LEIPUS (2000): "Stationary ARCH Models: Dependence Structure and Central Limit Theorem," Econometric Theory, 16, 3-22.
29. GOURIEROUX, C. (1997): ARCH Models and Financial Applications. Springer Series in Statistics.
30. GOURIEROUX, C., AND J. JASIAK (2001): "Memory and Infrequent Breaks," Economics Letters, 70, 29-41.
31. GOURIEROUX, C., AND C. Y. ROBERT (2001): "Tails and Extremal Behaviour of Stochastic Unit Root Models," manuscript, Dept. of Economics, University of Toronto.
32. GRANGER, C. W., AND Y. JEON (2001): "The Distributional Properties of Shocks to a Fractional I(d) Process Having a Marginal Exponential Distribution," Applied Financial Economics, 11(5), 469-74.
33. GRANGER, C. W. J. (1980): "Long Memory Relationships and the Aggregation of Dynamic Models," Journal of Econometrics, 14, 227-238.
34. GRANGER, C. W. J., AND Z. DING (1996): "Varieties of Long Memory Models," Journal of Econometrics, 73, 61-77.
35. GRANGER, C. W. J., AND N. HYUNG (1999): "Occasional Structural Breaks and Long Memory," Discussion Paper 99-14, Dept. of Economics, University of California, San Diego.
36. GRANGER, C. W. J., AND R. JOYEUX (1980): "An Introduction to Long Memory Time Series Models and Fractional Differencing," Journal of Time Series Analysis, 1, 15-39.
37. GRANGER, C. W. J., AND T. TERÄSVIRTA (1999): "A Simple Nonlinear Time Series Model with Missleading Linear Proporties," Economics Letters, 62, 161-165.
38. HE, C., AND T. TERASVIRTA (1999): "Fourth Moment Structure of the GARCH(p,q) Process," Econometric Theory, 15, 824-846.
39. HOSKING, J. R. M. (1981): "Fractional Differencing," Biometrika, 68, 165-176.
40. HURVICH, C. M., R. S. DEO, AND J. BRODSKY (1998): "The Mean Squared Error of Geweke and Porter-Hudak's Estimator of the Memory Parameter of a Long-Memory Time Series," Journal of Time Series Analysis, 19(1), 19-46.
41. HWANG, Y. (2001): "Asymmetric Long Memory GARCH in Exchange Return," Economics Letters, 73(1), 1-5.
42. KARANASOS, M. (1999): "The Second Moment and the Autocovariance Function of the Squared Errors of the GARCH Model," Journal of Econometrics, 90, 63-76.
43. LEBARON, B. (2001): "Stochastic Volatility as a Simple Generator of Apparent Financial Power Laws and Long Memory," Quantitative Finance, 1, 621-631.
44. LIU, M. (2000): "Modeling Long Memory in Stock Market Volatility," Journal of Econometrics, 99, 139-171.
45. LJUNG, L., AND G. Box (1978): "On a Measure of Lack of Fit in Time-Series Models," Biometrika, 67, 297-303.
46. LOBATO, I. N., AND N. E. SAVIN (1998): "Real and Spurious Long-Memory Properties of Stock Market Data," Journal of Business & Economic Statistics, 16(3), 261-268.
47. MCCURDY, T. H., AND P. K. MICHAUD (1997): "Capturing Long Memory in the Volatility of Equity Returns: a Fractionally Integrated Asymmetric Power ARCH Model," manuscript, Rotman School of Managment, University of Toronto.
48. MIKOSCH, T., AND C. STARICA (2000): "Limit Theory for the Sample Autocorrelations and Extremes of a GARCH(1,1) Process," The Annals of Statistics.
49. _ (2003): "Long Range Dependence Effects and ARCH Modeling," in Theory and Applications of Long Range Dependence, ed. by Doukhan, Oppenheim, and Taqqu. Springer Verlag.
50. NELSON, D. B. (1990): "ARCH Models as Diffusion Approximations, " Journal of Econometrics, 45, 7-39.
51. PALM, F. C. (1996): GARCH Models of Volatility chap. 7, Handbook of Statistics vol. 14. Elsevier Science.
52. RAY, B. K., AND R. S. TSAY (2000): "Long-Range Dependence in Daily Stock Volatilities," Journal of Business & Economic Statistics, 18(2), 254-262.
53. ROBINSON, P. M. (1995a): "Gaussian Semiparametric Estimation of Long Range Dependence," The Annals of Statistics, 23(5), 1630-1661.
54. _ (1995b): "Log-Periodogram regression of time Series with Long Range Dependence," The Annals of Statistics, 23(3), 1048-1072.
55. ROBINSON, P. M., AND M. HENRY (1999): "Long and Short Memory Conditional Heteroskedaticity in Estimating the Memory Parameter of Levels," Econometric Theory, 15(299-336).
56. TAQQU, M. S., AND V. TEVEROVSKY (1996): "Semi-Parametric Graphical Estimation Techniques for Long-Memory Data," in Time Series Analysis in Memory of E. J. Hannan, ed. by P. Robinson, and M. Rosenblatt. Springer-Verlag.
57. VELASCO, C. (1999): "Non-stationary Log-periodogram Regression," Journal of Econometrics, 91, 325-371.
58. WRIGHT, J. H. (2002): "Log-Periodograrn Estimation of Long Memory Volatility Dependencies with Conditionally Heavy Tailed Returns," Econometric Reviews, 21, 397-417.