LARCH, Leverage, and Long Memory
AbstractWe consider the long-memory and leverage properties of a model for the conditional variance V-sub-t-super-2 of an observable stationary sequence X-sub-t, where V-sub-t-super-2 is the square of an inhomogeneous linear combination of X-sub-s, s < t, with square summable weights b-sub-j. This model, which we call linear autoregressive conditionally heteroskedastic (LARCH), specializes, when V-sub-t-super-2 depends only on X-sub-t - 1, to the asymmetric ARCH model of Engle (1990, Review of Financial Studies 3, 103--106), and, when V-sub-t-super-2 depends only on finitely many X-sub-s, to a version of the quadratic ARCH model of Sentana (1995, Review of Economic Studies 62, 639--661), these authors having discussed leverage potential in such models. The model that we consider was suggested by Robinson (1991, Journal of Econometrics 47, 67--84), for use as a possibly long-memory conditionally heteroskedastic alternative to i.i.d. behavior, and further studied by Giraitis, Robinson and Surgailis (2000, Annals of Applied Probability 10, 1002--1004), who showed that integer powers X-sub-t-super-ℓ, ℓ ≥ 2 can have long-memory autocorrelations. We establish conditions under which the cross-autocovariance function between volatility and levels, h-sub-t = cov
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Bibliographic InfoArticle provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.
Volume (Year): 2 (2004)
Issue (Month): 2 ()
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- Liudas Giraitis & Remigijus Leipus & Peter M Robinson & Donatas Surgailis, 2003. "LARCH, Leverage and Long Memory," STICERD - Econometrics Paper Series /2003/460, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Giraitis, Liudas & Leipus, Remigijus & Robinson, Peter M. & Surgailis, Donatas, 2004. "LARCH, leverage, and long memory," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- G. William Schwert, 1990.
"Stock Volatility and the Crash of '87,"
NBER Working Papers
2954, National Bureau of Economic Research, Inc.
- Eric Ghysels & Andrew Harvey & Éric Renault, 1995.
CIRANO Working Papers
- GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
- Wilfredo Palma & Mauricio Zevallos, 2004. "Analysis of the correlation structure of square time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 529-550, 07.
- Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
- Liudas Giraitis & Peter M Robinson, 2000.
"Whittle Estimation of ARCH Models,"
STICERD - Econometrics Paper Series
/2000/406, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Giraitis, Liudas & Robinson, Peter M., 2001. "Whittle estimation of ARCH models," Open Access publications from London School of Economics and Political Science http://eprints.lse.ac.uk/, London School of Economics and Political Science.
- Engle, Robert F & Ng, Victor K, 1993.
" Measuring and Testing the Impact of News on Volatility,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1749-78, December.
- Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
- Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
- M. Karanasos & J. Kim, 2003.
"Moments of the ARMA--EGARCH model,"
Royal Economic Society, vol. 6(1), pages 146-166, 06.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Sentana,E., 1995.
"Quadratic Arch Models,"
9517, Centro de Estudios Monetarios Y Financieros-.
- Fabienne Comte & Eric Renault, 1998.
"Long memory in continuous-time stochastic volatility models,"
Wiley Blackwell, vol. 8(4), pages 291-323.
- Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers 96.406, Toulouse - GREMAQ.
- Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996.
"Fractionally integrated generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 74(1), pages 3-30, September.
- Tom Doan, . "RATS programs to replicate Baillie, Bollerslev, Mikkelson FIGARCH results," Statistical Software Components RTZ00009, Boston College Department of Economics.
- He, Changli & Ter svirta, Timo & Malmsten, Hans, 2002. "Moment Structure Of A Family Of First-Order Exponential Garch Models," Econometric Theory, Cambridge University Press, vol. 18(04), pages 868-885, August.
- John Y. Campbell & Ludger Hentschel, 1991.
"No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns,"
NBER Working Papers
3742, National Bureau of Economic Research, Inc.
- Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
- Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
- Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1996.
"Modeling and pricing long memory in stock market volatility,"
Journal of Econometrics,
Elsevier, vol. 73(1), pages 151-184, July.
- Tom Doan, . "RATS program to replicate Bollerslev-Mikkelson(1996) FIEGARCH models," Statistical Software Components RTZ00173, Boston College Department of Economics.
- Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
- Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
- Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
- Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
- Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
- Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 345-357, 06.
- Agnieszka Jach & Piotr Kokoszka, 2010. "Empirical wavelet analysis of tail and memory properties of LARCH and FIGARCH models," Computational Statistics, Springer, vol. 25(1), pages 163-182, March.
- Francq, Christian & Zakoïan, Jean-Michel, 2010.
"Inconsistency of the MLE and inference based on weighted LS for LARCH models,"
Journal of Econometrics,
Elsevier, vol. 159(1), pages 151-165, November.
- Christian Francq & Jean-Michel Zakoïan, 2010. "Inconsistency of the MLE and inference based on weighted LS for LARCH models," Post-Print peer-00732536, HAL.
- Yuanhua Feng & Jan Beran & Keming Yu, 2007.
"Modelling financial time series with SEMIFAR-GARCH model,"
CoFE Discussion Paper
07-14, Center of Finance and Econometrics, University of Konstanz.
- Feng, Yuanhua & Beran, Jan & Yu, Keming, 2006. "Modelling financial time series with SEMIFAR-GARCH model," MPRA Paper 1593, University Library of Munich, Germany.
- Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.
- Mohamed Boutahar & Rabeh Khalfaoui2, 2011. "Estimation of the long memory parameter in non stationary models: A Simulation Study," Working Papers halshs-00595057, HAL.
- McAleer, Michael & Medeiros, Marcelo C., 2008.
"A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries,"
Journal of Econometrics,
Elsevier, vol. 147(1), pages 104-119, November.
- Michael McAller & Marcelo C. Medeiros, 2007. "A multiple regime smooth transition heterogeneous autoregressive model for long memory and asymmetries," Textos para discussÃ£o 544, Department of Economics PUC-Rio (Brazil).
- Conrad, Christian & Karanasos, Menelaos, 2006. "The impulse response function of the long memory GARCH process," Economics Letters, Elsevier, vol. 90(1), pages 34-41, January.
- Tomasz Wojtowicz & Henryk Gurgul, 2009. "Long memory of volatility measures in time series," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 1, pages 37-54.
- Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
- Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.
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