Discriminating between Long Memory and Volatility Shifts
DOI:
https://doi.org/10.17713/ajs.v36i4.338Abstract
We develop a practical implementation of the test proposed in Berkes, Horv´ath, Kokoszka, and Shao (2006) designed to distinguish between a change-point model and a long memory model. Our implementation is calibrated to distinguish between a shift in volatility of returns and long memory in squared returns. It uses a kernel estimator of the long-run variance of squared returns with the maximal lag selected by a data driven procedure which depends on the sample size, the location of the estimated change point and the direction of the apparent volatility shift (increase versus decrease). In a simulations study, we also consider other long-run variance estimators, including the VARHAC estimator, but we find that they lead to tests with inferior performance. Applied to returns on indexes and individual stocks, our test indicates that even for the same asset, a change-point model may be preferable for a certain period of time, whereas there is evidence of long memory in another period of time. Generally there is stronger evidence for long memory in the eight years ending June 2006 than in the eight years starting January 1992. This pattern is most pronounced for US stock indexes and shares in the US financial sector.
References
Andersen, T. G., and Bollerslev, T. (1997). Heterogeneous information arrivals and return volatility dynamics: uncovering the long run in high frequency data. Journal
of Finance, 52, 975-1005.
Andreou, E., and Ghysels, E. (2002). Detecting multiple breaks in financial market volatility dynamics. Journal of Applied Econometrics, 17, 579-600.
Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59, 817-858.
Andrews, D. W. K., and Monahan, J. C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, 60, 953-966.
Baillie, R. T., Bollerslev, T., and Mikkelsen, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74,
-30.
Berkes, I., Horváth, L., Kokoszka, P., and Shao, Q.-M. (2006). On discriminating between long-range dependence and changes in mean. The Annals of Statistics, 34, 1140-
Bhattacharya, R. N., Gupta, V. K., andWaymire, E. (1983). The Hurst effect under trend. Journal of Applied Probability, 20, 649-662.
Bollerslev, T., and Mikkelsen, H. O. (1996). Modelling and pricing long memory in stock market volatility. Journal of Econometrics, 73, 151-184.
Bollerslev, T., and Wright, J. H. (2000). Semiparametric estimation of long memory volatility dependencies: The role of high frequency data. Journal of Econometrics,
, 81-106.
Bos, C., Franses, P. H., and Ooms, M. (1999). Long-memory and level shifts: reanalyzing inflation rates. Empirical Economics, 24, 427-449.
Cai, J. (1994). A Markov model of switching regime ARCH. Journal of Business and Economics Statistics, 12, 309-316.
Chambers, M. (1998). Long memory and aggregation in macroeconomic time series. International Economic Review, 39, 1053-1072.
Dacorogna, M., Müller, U., Nagler, R., Olsen, R., and Picket, O. (1993). A geographical model for the daily and weekly seasonal volatility in foreign exchange market.
Journal of International Money and Finance, 12, 413-438.
DenHaan, W. J., and Levin, A. (1996). Inference from parametric and non-parametric covariance matrix estimation procedures. National Bureau of Economic Research Technical Working Papers No. 195.
DenHaan, W. J., and Levin, A. (2000). Robust covarariance matrix estimation with data-dependent VAR prewhitening order. National Bureau of Economic Research Technical Working Papers No. 2000-11.
Diebold, F. (1986). Comment on ”Modeling the persistence of conditional variance”, by R. Engle and T. Bollerslev. Econometric Review, 5, 51-56.
Diebold, F., and Inoue, A. (2001). Long memory and structural change. Journal of Econometrics, 105, 131-159.
Ding, Z., Granger, C. W. J., and Engle, R. (1993). A long memory property of stock marked returns and a new model. Journal of Empirical Finance, 1, 83-106.
Doukhan, P., Oppenheim, G., and Taqqu, M. (Eds.). (2002). Theory and Applications of Long Range Dependence. Boston: Birkhäuser.
Dueker, M. J. (1997). Markov switching in GARCH processes and mean reverting stock market volatility. Journal of Business and Economics Statistics, 15, 26-34.
Garcia, R., and Ghysels, E. (1998). Structural change and asset pricing in emerging markets. Journal of International Money and Finance,, 17, 455-473.
Giraitis, L., Kokoszka, P. S., and Leipus, R. (2001). Testing for long memory in the presence of a general trend. Journal of Applied Probability, 38, 1033-1054.
Glosten, L. R., Jagannathan, R., and Runkle, D. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of
Finance, 48, 1779-1801.
Granger, C. W. J., and Ding, Z. (1996). Varieties of long-memory models. Journal of Econometrics, 73, 61-77.
Hamilton, J. D. (1994). Time Series Analysis. Princeton, NJ: Princeton University Press.
Hamilton, J. D., and Susmel, R. (1994). Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics, 64, 307-333.
Henry, M., and Zaffaroni, P. (2002). The long-range dependence paradigm for macroeconomics and finance. In P. Doukhan, G. Oppenheim, and M. S. Taqqu (Eds.), Theory
and Applications of Long Range Dependence (p. 417-438). Boston: Birkhäuser.
Heyde, C. C., and Dai, W. (1996). On the robustness to small trends of estimation based on the smoothed periodogram. Journal of Time Series Analysis, 17, 141-150.
Hidalgo, J., and Robinson, P. M. (1996). Testing for structural change in a long-memory enviornment. Journal of Econometrics, 70, 159-174.
Jach, A., and Kokoszka, P. (2008). Wavelet domain test for long–range dependence in the presence of a trend. Statistics. (Forthcoming)
Krämer, W., and Sibbertsen, P. (2000). Testing for structural change in the presence of long-memory. International Journal of Business and Economics, 1, 235-242.
Krämer, W., Sibbertsen, P., and Kleiber, C. (2002). Long memory versus structural change in financial time series. Allgemeines Statistisches Archiv, 86, 83-96.
Künsch, H. (1986). Discrimination between monotonic trends and long-range dependence. Journal of Appllied Probability, 23, 1025-1030.
Lamoreaux, C. G., and Lastrapes, W. D. (1990). Persistence in variance, structural change and the garch model. Journal of Business and Economics Statistics, 8, 225-234.
Mikosch, T., and Stărică, C. (1999). Change of structure in financial time series, long range dependence and the GARCH model (Tech. Rep.). University of Groningen.
Mikosch, T., and Stărică, C. (2002). Long-range dependence effects and ARCH modeling. In P. Doukhan, G. Oppenheim, and M. S. Taqqu (Eds.), Theory and Applications of long-range Dependence (p. 439-459). Boston: Birkhäuser.
Morana, C., and Beltratti, A. (2004). Structural change and long range dependence in volatility of exchange rates: Either, Nither, or Both. Journal of Empirical Finance,
, 629-658.
Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: a new approach. Econometrica, 59, 347-370.
Pastor, L., and Stambaugh, R. F. (2001). Equity premium and structural breaks. Journal of Finance, 56, 1207-1239.
Press, H., and Tukey, J. W. (1956). Power spectral methods of analysis and their application to problems in airplane dynamics. In Flight Test Manual IV-C (p. 1-41). NATO Advisory Group for Aeronautical Research and Development. (Reprinted as Bell System Monograph No. 2606)
Sibbertsen, P., and Venetis, I. (2004). Distinguishing between long-range dependence and deterministic trends (Tech. Rep. No. SFB 475 TR 16-03). Universität Dortmund.
Stărică, C., and Granger, C. (2005). Nonstationarities in stock returns. The Review of Economics and Statistics, 87, 503-522.
Teyssiere, G., and Abry, P. (2006). Wavelet analysis of nonlinear long-range dependent processes. Applications to financial time series. In G. Teyssiere and A. Kirman (Eds.), Long Memory in Economics (p. 173-238). Springer.
Downloads
Published
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
How to Cite
