Joint forecasts of Dow Jones stocks under general multivariate loss function
When forecasts are assessed by a general loss (cost-of-error) function, the optimal point forecast is, in general, not the conditional mean, and depends on the conditional volatility--which, for stock returns, is time-varying. In order to provide forecasts of daily returns of 30 DJIA stocks under a general multivariate loss function, the following issues are addressed. We discuss what conditions define a multivariate loss function, and a simple class of such functions is proposed. Based on suitable combinations of univariate losses, the suggested multivariate functions are convenient for practical applications with many variables. To keep the computational aspect tractable, a flexible multivariate GARCH model is employed in estimating the conditional forecast distributions. The model easily copes with large number of series while allowing for skewness, fat tails, non-ellipticity, and tail dependence. Based on Engle's DCC GARCH, it uses multivariate affine generalized hyperbolic distributions as conditional probability law, and the number of parameters to be estimated simultaneously does not depend on the number of series. The model is fitted using daily data from 2002 to 2007 (keeping data from 2008 for out-of-sample forecasts), and a bootstrap procedure is used to derive point forecasts under several multivariate loss functions of the proposed type.
References listed on IDEAS
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.:
- Christoffersen & Diebold, .
"Further Results on Forecasting and Model Selection Under Asymmetric Loss,"
_059, University of Pennsylvania.
- Christoffersen, Peter F & Diebold, Francis X, 1996. "Further Results on Forecasting and Model Selection under Asymmetric Loss," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 561-71, Sept.-Oct.
- Allan Timmermann & Andrew Patton, 2004.
"Properties of Optimal Forecasts under Asymmetric Loss and Nonlinearity,"
wp04-05, Warwick Business School, Finance Group.
- Patton, Andrew J. & Timmermann, Allan, 2007. "Properties of optimal forecasts under asymmetric loss and nonlinearity," Journal of Econometrics, Elsevier, vol. 140(2), pages 884-918, October.
- Christoffersen, Peter F. & Diebold, Francis X., 1997.
"Optimal Prediction Under Asymmetric Loss,"
Cambridge University Press, vol. 13(06), pages 808-817, December.
- Christoffersen & Diebold, . "Optimal Prediction Under Asymmetric Loss," Home Pages 167, 1996., University of Pennsylvania.
- Peter F. Christoffersen & Francis X. Diebold, 1997. "Optimal prediction under asymmetric loss," Working Papers 97-11, Federal Reserve Bank of Philadelphia.
- Peter F. Christoffersen & Francis X. Diebold, 1994. "Optimal Prediction Under Asymmetric Loss," NBER Technical Working Papers 0167, National Bureau of Economic Research, Inc.
- Peter F. Christoffersen & Francis X. Diebold, . "Optimal Prediction Under Asymmetric Loss," CARESS Working Papres 97-20, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Komunjer, Ivana & OWYANG, MICHAEL, 2007.
"Multivariate Forecast Evaluation And Rationality Testing,"
University of California at San Diego, Economics Working Paper Series
qt81w8m5sf, Department of Economics, UC San Diego.
- Ivana Komunjer & Michael T. Owyang, 2012. "Multivariate Forecast Evaluation and Rationality Testing," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1066-1080, November.
- Ivana Komunjer & Michael T. Owyang, 2007. "Multivariate forecast evaluation and rationality testing," Working Papers 2007-047, Federal Reserve Bank of St. Louis.
- Clive W.J. Granger, 1999. "Outline of forecast theory using generalized cost functions," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 161-173.
- Liu, Yan & Luger, Richard, 2009. "Efficient estimation of copula-GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2284-2297, April.
- Bauwens, L. & Hafner, C.M. & Rombouts, J.V.K., 2007.
"Multivariate mixed normal conditional heteroskedasticity,"
Computational Statistics & Data Analysis,
Elsevier, vol. 51(7), pages 3551-3566, April.
- BAUWENS, Luc & HAFNER, Christian & ROMBOUTS, Jeroen, 2006. "Multivariate mixed normal conditional heteroskedasticity," CORE Discussion Papers 2006012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Luc, BAUWENS & C.M., HAFNER & J.V.K., ROMBOUTS, 2006. "Multivariate mixed normal conditional heteroskedasticity," Discussion Papers (ECON - Département des Sciences Economiques) 2006007, Université catholique de Louvain, Département des Sciences Economiques.
- BAUWENS, Luc & HAFNER, Christian M. & ROMBOUTS, Jeroen VK, . "Multivariate mixed normal conditional heteroskedasticity," CORE Discussion Papers RP 1906, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Palandri, Alessandro, 2009. "Sequential conditional correlations: Inference and evaluation," Journal of Econometrics, Elsevier, vol. 153(2), pages 122-132, December.
- Schmidt, Rafael & Hrycej, Tomas & Stutzle, Eric, 2006. "Multivariate distribution models with generalized hyperbolic margins," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2065-2096, April.
- Simon A. Broda & Marc S. Paolella, 2009.
"CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 7(4), pages 412-436, Fall.
- Simon A. BRODA & Marc S. PAOLELLA, 2006. "CHICAGO: A Fast and Accurate Method for Portfolio Risk Calculation," Swiss Finance Institute Research Paper Series 08-08, Swiss Finance Institute, revised Feb 2008.
- 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.
- Matei Demetrescu, 2007. "Optimal forecast intervals under asymmetric loss," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(4), pages 227-238.
- Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-46, October.
- Monica Billio & Massimiliano Caporin & Michele Gobbo, 2006. "Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 2(2), pages 123-130, March.
- Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
- Graham Elliott & Allan Timmermann & Ivana Komunjer, 2005. "Estimation and Testing of Forecast Rationality under Flexible Loss," Review of Economic Studies, Oxford University Press, vol. 72(4), pages 1107-1125.
- Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2008.
"Asymmetric multivariate normal mixture GARCH,"
CFS Working Paper Series
2008/07, Center for Financial Studies (CFS).
- BAUWENS, Luc & LAURENT, Sébastien, .
"A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models,"
CORE Discussion Papers RP
1793, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
- Capistran, Carlos, 2006. "On comparing multi-horizon forecasts," Economics Letters, Elsevier, vol. 93(2), pages 176-181, November.
- Ausin, M. Concepcion & Lopes, Hedibert F., 2010. "Time-varying joint distribution through copulas," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2383-2399, November.
- Chen, Ying & Härdle, Wolfgang & Spokoiny, Vladimir, 2010.
"GHICA -- Risk analysis with GH distributions and independent components,"
Journal of Empirical Finance,
Elsevier, vol. 17(2), pages 255-269, March.
- Ying Chen & Wolfgang Härdle & Vladimir Spokoiny, 2006. "GHICA - Risk Analysis with GH Distributions and Independent Components," SFB 649 Discussion Papers SFB649DP2006-078, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:54:y:2010:i:11:p:2360-2371. 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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.