Small Sample Properties of GARCH Estimates and Persistence
It is shown that the ML estimates of the popular GARCH(1,1) model are significantly negatively biased in small samples and that in many cases converged estimates are not possible with Bollerslev's non-negativity conditions. Results also indicate that a high level of persistence in GARCH(1,1) models obtained using a large number of observations has autocorrelations lower than these ML estimates suggest in small samples. Considering the size of biases and convergence errors, it is proposed that at least 250 observations are needed for ARCH(1) models and 500 observations for GARCH(1,1) models. A simple measure of how much GARCH conditional volatility explains squared returns is proposed. The measure indicates that for a typical index return volatility whose ARCH parameter is very small, the conditional volatility hardly explains squared returns.
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- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, School of Economics and Management.
- Robert F. Engle & David F. Hendry & David Trumble, 1985. "Small-Sample Properties of ARCH Estimators and Tests," Canadian Journal of Economics, Canadian Economics Association, vol. 18(1), pages 66-93, February.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994.
"Multivariate Stochastic Variance Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(2), pages 247-64, April.
- Tom Doan, . "RATS programs to estimate multivariate stochastic volatility models," Statistical Software Components RTZ00093, Boston College Department of Economics.
- Drost, F.C. & Nijman, T.E., 1990.
"Temporal aggregation of GARCH processes,"
1990-66, Tilburg University, Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
- Daniel B. Nelson & Dean P. Foster, 1994.
"Asypmtotic Filtering Theory for Univariate Arch Models,"
NBER Technical Working Papers
0129, National Bureau of Economic Research, Inc.
- Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Merton, Robert C., 1980.
"On estimating the expected return on the market : An exploratory investigation,"
Journal of Financial Economics,
Elsevier, vol. 8(4), pages 323-361, December.
- Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
- Peter C.B. Phillips & Pierre Perron, 1986.
"Testing for a Unit Root in Time Series Regression,"
Cowles Foundation Discussion Papers
795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
- Jurgen A. Doornik & Marius Ooms, 2000.
"Multimodality and the GARCH Likelihood,"
Econometric Society World Congress 2000 Contributed Papers
0798, Econometric Society.
- repec:ner:tilbur:urn:nbn:nl:ui:12-153273 is not listed on IDEAS
- Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
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