Accelerating GARCH and Score-Driven Models: Optimality, Estimation and Forecasting
We first consider an extension of the generalized autoregressive conditional heteroskedasticity (GARCH) model that allows for a more flexible weighting of financial squared-returns for the filtering of volatility. The parameter for the squared-return in the GARCH model is time- varying with an updating function similar to GARCH but with the squared-return replaced by the product of the volatility innovation and its lagged value. This local estimate of the first order autocorrelation of volatility innovations acts as an indicator of the importance of the squared-return for volatility updating. When recent volatility innovations have the same sign (positive autocorrelation), the current volatility estimate needs to adjust more quickly than in a period where recent volatility innovations have mixed signs (negative autocorrelation). The empirical relevance of the accelerated GARCH updating is illustrated by forecasting daily volatility in return series of all individual stocks present in the Standard & Poorâ€™s 500 index. Major improvements are reported for those stock return series that exhibit high kurtosis. The local adjustment in weighting new observational information is generalised to score-driven time-varying parameter models of which GARCH is a special case. It is within this general framework that we provide the theoretical foundations of accelerated updating. We show that acceleration in updating is more optimal in terms of reducing Kullback-Leibler divergence and in comparison to fixed updating. The robustness of our proposed extension is highlighted in a simulation study within a misspecified modelling framework. The score-driven acceleration is also empirically illustrated with the forecasting of US inflation using a model with time-varying mean and variance; we report significant improvements in the forecasting accuracy at a yearly horizon.
|Date of creation:||05 Jul 2017|
|Contact details of provider:|| Postal: Gustav Mahlerplein 117, 1082 MS Amsterdam|
Phone: +31 (0)20 598 4580
Web page: http://www.tinbergen.nl/
More information through EDIRC
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.:
- F. Blasques & S. J. Koopman & A. Lucas, 2015. "Information-theoretic optimality of observation-driven time series models for continuous responses," Biometrika, Biometrika Trust, vol. 102(2), pages 325-343.
- Raffaella Giacomini & Halbert White, 2006.
"Tests of Conditional Predictive Ability,"
Econometric Society, vol. 74(6), pages 1545-1578, November.
- Raffaella Giacomini & Halbert White, 2003. "Tests of conditional predictive ability," Boston College Working Papers in Economics 572, Boston College Department of Economics.
- Giacomini, Raffaella & White, Halbert, 2003. "Tests of Conditional Predictive Ability," University of California at San Diego, Economics Working Paper Series qt5jk0j5jh, Department of Economics, UC San Diego.
- Raffaella Giacomini & Halbert White, 2003. "Tests of Conditional Predictive Ability," Econometrics 0308001, EconWPA.
- Creal, Drew & Koopman, Siem Jan & Lucas, AndrÃ©, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
- Drew Creal & Siem Jan Koopman & AndrÃ© Lucas, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 552-563, October.
- Drew Creal & Siem Jan Koopman & André Lucas, 2010. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Tinbergen Institute Discussion Papers 10-032/2, Tinbergen Institute.
- Andrew Harvey & Alessandra Luati, 2014. "Filtering With Heavy Tails," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1112-1122, September.
- Harvey, A. & Luati, A., 2012. "Filtering with heavy tails," Cambridge Working Papers in Economics 1255, Faculty of Economics, University of Cambridge.
- Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
- Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-263, July.
- Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
- Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
- Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
- Tom Doan, "undated". "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 120-135.
- Irving Arturo De Lira Salvatierra & Andrew J. Patton, 2013. "Dynamic Copula Models and High Frequency Data," Working Papers 13-28, Duke University, Department of Economics.
- Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
- Amisano, Gianni & Geweke, John, 2009. "Optimal Prediction Pools," Working Paper Series 1017, European Central Bank.
- 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.
- Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2016. "Exploiting the errors: A simple approach for improved volatility forecasting," Journal of Econometrics, Elsevier, vol. 192(1), pages 1-18.
- Tim Bollerslev & Andrew J. Patton & Rogier Quaedvlieg, 2015. "Exploiting the Errors: A Simple Approach for Improved Volatility Forecasting," CREATES Research Papers 2015-14, Department of Economics and Business Economics, Aarhus University.
- James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, 02.
- James H. Stock & Mark W. Watson, 2006. "Why Has U.S. Inflation Become Harder to Forecast?," NBER Working Papers 12324, National Bureau of Economic Research, Inc.
- Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, 08.
- Ullah, Aman, 2002. "Uses of entropy and divergence measures for evaluating econometric approximations and inference," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 313-326, March.
- Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, 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. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20170059. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tinbergen Office +31 (0)10-4088900)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.