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The Relation Between Conditionally Heteroskedastic Factor Models and Factor GARCH Models

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  • Enrique Sentana

Abstract

The factor GARCH model of Engle (1987) and the latent factor ARCH model of Diebold and Nerlove (1989) have become rather popular multivariate volatility parameterizations due to their parsimony, and the commonality in volatility movements across different financial series. Nevertheless, there is some confusion in the literature between them. The purpose of this note is to make clear their similarities and differences by providing a formal nesting of the two models, which can be exploited to analyze their statistical features in a more general context. At the same time, their differences may be important in the interpretation of empirical results.

Suggested Citation

  • Enrique Sentana, 1997. "The Relation Between Conditionally Heteroskedastic Factor Models and Factor GARCH Models," Working Papers wp1997_9719, CEMFI.
    • Handle: RePEc:cmf:wpaper:wp1997_9719
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    1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    2. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-186, January.
    3. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    5. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
    6. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    7. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
    8. Nijman, Theo & Sentana, Enrique, 1996. "Marginalization and contemporaneous aggregation in multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 71-87.
    9. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    10. Ng, Victor & Engle, Robert F. & Rothschild, Michael, 1992. "A multi-dynamic-factor model for stock returns," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 245-266.
    11. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
    12. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-380, October.
    13. Lin, Wen-Ling, 1992. "Alternative Estimators for Factor GARCH Models--A Monte Carlo Comparison," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 259-279, July-Sept.
    14. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-933, July.
    15. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    16. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
    17. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-395, October.
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    Cited by:

    1. Enrique Sentana & Giorgio Calzolari & Gabriele Fiorentini, 2004. "Indirect Estimation of Conditionally Heteroskedastic Factor Models," Working Papers wp2004_0409, CEMFI.
    2. Aaron Smith, 2005. "Partially overlapping time series: a new model for volatility dynamics in commodity futures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 405-422.
    3. Barigozzi, Matteo & Brownlees, Christian & Gallo, Giampiero M. & Veredas, David, 2014. "Disentangling systematic and idiosyncratic dynamics in panels of volatility measures," Journal of Econometrics, Elsevier, vol. 182(2), pages 364-384.
    4. Elena Andreou & Eric Ghysels, 2002. "Tests for Breaks in the Conditional Co-movements of Asset Returns," CIRANO Working Papers 2002s-59, CIRANO.
    5. Mohamed Saidane & Christian Lavergne, 2009. "Optimal Prediction with Conditionally Heteroskedastic Factor Analysed Hidden Markov Models," Computational Economics, Springer;Society for Computational Economics, vol. 34(4), pages 323-364, November.
    6. Fiorentini, Gabriele & Galesi, Alessandro & Sentana, Enrique, 2018. "A spectral EM algorithm for dynamic factor models," Journal of Econometrics, Elsevier, vol. 205(1), pages 249-279.
    7. Klaassen, F.J.G.M., 1999. "Have Exchange Rates Become More Closely Tied? Evidence from a New Multivariate GARCH Model," Other publications TiSEM af43cd1c-9656-4e45-bfd1-f, Tilburg University, School of Economics and Management.
    8. 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.
    9. Connor, Gregory & Korajczyk, Robert A. & Linton, Oliver, 2006. "The common and specific components of dynamic volatility," Journal of Econometrics, Elsevier, vol. 132(1), pages 231-255, May.
    10. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    11. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
    12. Catherine Doz & Eric Renault, 2004. "Conditionaly Heteroskedastic Factor Models : Identificationand Instrumental variables Estmation," THEMA Working Papers 2004-13, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. Antonis Demos & Sofia Parissi, 1998. "Testing Asset Pricing Models: The Case of Athens Stock Exchange," Multinational Finance Journal, Multinational Finance Journal, vol. 2(3), pages 189-223, September.
    14. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2004. "Likelihood-Based Estimation of Latent Generalized ARCH Structures," Econometrica, Econometric Society, vol. 72(5), pages 1481-1517, September.
    15. Fabrizio Cipollini & Giampiero Gallo & Alessandro Palandri, 2020. "A Dynamic Conditional Approach to Portfolio Weights Forecasting," Econometrics Working Papers Archive 2020_06, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    16. Antonis Demos & George Vasillelis, 2007. "U.K. Stock Market Inefficiencies and the Risk Premium," Multinational Finance Journal, Multinational Finance Journal, vol. 11(1-2), pages 97-122, March-Jun.
    17. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    18. Cipollini, Fabrizio & Gallo, Giampiero M. & Palandri, Alessandro, 2021. "A dynamic conditional approach to forecasting portfolio weights," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1111-1126.
    19. Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2006. "Generalized Dynamic Factor Model + GARCH Exploiting Multivariate Information for Univariate Prediction," LEM Papers Series 2006/13, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    20. Giorgio Calzolari & F. Di Iorio & G. Fiorentini, 1999. "Indirect Estimation of Just-Identified Models with Control Variates," Econometrics Working Papers Archive quaderno46, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    21. Enrique Sentana & Gabriele Fiorentini, 1997. "Identification, Estimation and Testing of Conditionally Heteroskedastic Factor Models.Versión Revisada," Working Papers wp1997_9709, CEMFI.
    22. Engle, Robert F. & Marcucci, Juri, 2006. "A long-run Pure Variance Common Features model for the common volatilities of the Dow Jones," Journal of Econometrics, Elsevier, vol. 132(1), pages 7-42, May.
    23. Mondher Bellalah & Marc Lavielle, 2002. "A Decomposition of Empirical Distributions with Applications to the Valuation of Derivative Assets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(2), pages 99-130, June.

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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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