LARCH, Leverage and Long Memory
AbstractWe consider the long memory and leverage properties of a model for the conditional variance of an observable stationary sequence, where the conditional variance is the square of an inhomogeneous linear combination of past values of the observable sequence, with square summable weights. This model, which we call linear ARCH (LARCH), specializes to the asymmetric ARCH model of Engle (1990), and to a version of the quadratic ARCH model of Sentana (1995), these authors having discussed leverage potential in such models. The model which we consider was suggested by Robinson (1991), for use as a possibly long memory conditionally heteroscedastic alternative to i.i.d. behaviour, and further studied by Giraitis, Robinson and Surgailis (2000), who showed that integer powers, of degree at least 2, can have long memory autocorrelation. We establish conditions under which the cross-autovariance function between volatility and levels decays in the manner of moving average weights of long memory processes. We also establish a leverage property and conditions for finiteness of third and higher moments.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2003/460.
Date of creation: Oct 2003
Date of revision:
Contact details of provider:
Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp
Leverage; long memory; linear ARCH; LARCH; finiteness of moments.;
Other versions of this item:
- NEP-ALL-2003-11-03 (All new papers)
- NEP-ECM-2003-11-03 (Econometrics)
- NEP-ETS-2003-11-03 (Econometric Time Series)
- NEP-MFD-2003-11-03 (Microfinance)
- NEP-RMG-2003-11-03 (Risk Management)
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.:
- GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995.
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.
- Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- 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.
- Schwert, G.W., 1989.
"Stock Volatility And The Crash Of '87,"
89-01, Rochester, Business - General.
- 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.
- 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.
- 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.
- 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.
- 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.
- Menelaos Karanasos & J. Kim, .
"Moments of the ARMA-EGARCH Model,"
00/29, Department of Economics, University of York.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Sentana, Enrique, 1995.
"Quadratic ARCH Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 62(4), pages 639-61, October.
- 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.
- 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.
- Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- 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).
- 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.
- Josu Arteche, 2012. "Standard and seasonal long memory in volatility: an application to Spanish inflation," Empirical Economics, Springer, vol. 42(3), pages 693-712, June.
- Axel Groß‐KlußMann & Nikolaus Hautsch, 2013.
"Predicting Bid–Ask Spreads Using Long‐Memory Autoregressive Conditional Poisson Models,"
Journal of Forecasting,
John Wiley & Sons, Ltd., vol. 32(8), pages 724-742, December.
- Axel Groß-Klußmann & Nikolaus Hautsch, 2011. "Predicting Bid-Ask Spreads Using Long Memory Autoregressive Conditional Poisson Models," SFB 649 Discussion Papers SFB649DP2011-044, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- 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.
- Christian Francq & Jean-Michel Zakoïan, 2010. "Inconsistency of the MLE and inference based on weighted LS for LARCH models," Post-Print hal-00732536, HAL.
- Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
- 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.
- Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.
- 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.
- 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.
- 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.
- 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.
- Mohamed Boutahar & Rabeh Khalfaoui2, 2011. "Estimation of the long memory parameter in non stationary models: A Simulation Study," Working Papers halshs-00595057, HAL.
- Iqbal Owadally, 2014. "Tail risk in pension funds: an analysis using ARCH models and bilinear processes," Review of Quantitative Finance and Accounting, Springer, vol. 43(2), pages 301-331, August.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.