Locally stationary volatility modelling
The increasing works on parameter instability, structural changes and regime switches lead to the natural research question whether the assumption of stationarity is appropriate to model volatility processes. Early econometric studies have provided testing procedures of covariance stationarity and have shown empirical evidence for the unconditional time-variation of the dependence structure of many financial time series.After a review of several econometric tests of covariance stationarity, this survey paper focuses on several attempts in the literature to model the time-varying second- order dependence of volatility time series. The approaches that are summarized in this discussion paper propose various specification for this time-varying dynamics. In some of them an explicit variation over time is suggested, such as in the spline GARCH model. Larger classes of nonstationary models have also been proposed, in which the variation of the parameters may be more general such as in the so-called locally stationary models. In another approach that is called â€œadaptiveâ€, no explicit global model is assumed and local parametric model are adaptively fitted at each point over time. Multivariate extensions are also visited. A comparison of these approaches is proposed in this paper and some illustrations are provided on the two last decades of data of the Dow Jones Industrial Average index.
|Date of creation:||01 Oct 2011|
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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.:
- Perron, P, 1988.
"The Great Crash, The Oil Price Shock And The Unit Root Hypothesis,"
338, Princeton, Department of Economics - Econometric Research Program.
- Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
- Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
- Giuseppe Cavaliere, 2005.
"Unit Root Tests under Time-Varying Variances,"
Taylor & Francis Journals, vol. 23(3), pages 259-292.
- Silvennoinen, Annastiina & Teräsvirta, Timo, 2007.
"Multivariate GARCH models,"
SSE/EFI Working Paper Series in Economics and Finance
669, Stockholm School of Economics, revised 18 Jan 2008.
- Francesco Audrino & Peter Bühlmann, 2007.
"Splines for Financial Volatility,"
University of St. Gallen Department of Economics working paper series 2007
2007-11, Department of Economics, University of St. Gallen.
- Richard Paap & Philip Hans Franses & Marco Van Der Leij, 2002. "Modelling and forecasting level shifts in absolute returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 601-616.
- Amado, Cristina & Teräsvirta, Timo, 2013.
"Modelling volatility by variance decomposition,"
Journal of Econometrics,
Elsevier, vol. 175(2), pages 142-153.
- Cristina Amado & Timo Teräsvirta, 2011. "Modelling Volatility by Variance Decomposition," NIPE Working Papers 01/2011, NIPE - Universidade do Minho.
- Cristina Amado & Timo Teräsvirta, 2011. "Modelling Volatility by Variance Decomposition," CREATES Research Papers 2011-01, School of Economics and Management, University of Aarhus.
- Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
- Phillips, P C B, 1987.
"Time Series Regression with a Unit Root,"
Econometric Society, vol. 55(2), pages 277-301, March.
- Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- Christian M. Hafner & Oliver Linton, 2009.
"Efficient Estimation of a Multivariate Multiplicative Volatility Model,"
STICERD - Econometrics Paper Series
541, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Hafner, Christian M. & Linton, Oliver, 2010. "Efficient estimation of a multivariate multiplicative volatility model," Journal of Econometrics, Elsevier, vol. 159(1), pages 55-73, November.
- Christian M. Hafner & Oliver Linton, 2010. "Efficient estimation of a multivariate multiplicative volatility model," Post-Print hal-00732539, HAL.
- P. Č�žek & W. H�rdle & V. Spokoiny, 2009. "Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 248-271, 07.
- Hamilton, James D. & Susmel, Raul, 1994.
"Autoregressive conditional heteroskedasticity and changes in regime,"
Journal of Econometrics,
Elsevier, vol. 64(1-2), pages 307-333.
- Tom Doan, . "RATS programs to estimate Hamilton-Susmel Markov Switching ARCH model," Statistical Software Components RTZ00083, Boston College Department of Economics.
- BAUWENS, Luc & HAFNER, Christian & LAURENT, SÃ©bastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
- Lucrezia Reichlin & Peter Rappoport, 1989.
"Segmented trends and non-stationary time series,"
ULB Institutional Repository
2013/10169, ULB -- Universite Libre de Bruxelles.
- Lo, Andrew W. (Andrew Wen-Chuan), 1989.
"Long-term memory in stock market prices,"
3014-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Marianne Sensier & Dick van Dijk, 2004.
"Testing for Volatility Changes in U.S. Macroeconomic Time Series,"
The Review of Economics and Statistics,
MIT Press, vol. 86(3), pages 833-839, August.
- M Sensier & D van Dijk, 2003. "Testing for Volatility Changes in US Macroeconomic Time Series," Centre for Growth and Business Cycle Research Discussion Paper Series 36, Economics, The Univeristy of Manchester.
- White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
- Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
- Van Bellegem, Sebastien & von Sachs, Rainer, 2004. "Forecasting economic time series with unconditional time-varying variance," International Journal of Forecasting, Elsevier, vol. 20(4), pages 611-627.
- Sébastien Van Bellegem & Rainer Dahlhaus, 2006. "Semiparametric estimation by model selection for locally stationary processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 721-746.
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