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Generalized Dynamic Factor Models and Volatilities: Consistency, rates, and prediction intervals

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  • Matteo Barigozzi
  • Marc Hallin
Abstract
Volatilities, in high-dimensional panels of economic time series with a dynamic factor structure on the levels or returns, typically also admit a dynamic factor decomposition. We consider a two-stage dynamic factor model method recovering the common and idiosyncratic components of both levels and log-volatilities. Specifically, in a first estimation step, we extract the common and idiosyncratic shocks for the levels, from which a log-volatility proxy is computed. In a second step, we estimate a dynamic factor model, which is equivalent to a multiplicative factor structure for volatilities, for the log-volatility panel. By exploiting this two-stage factor approach, we build one-step-ahead conditional prediction intervals for large $n \times T$ panels of returns. Those intervals are based on empirical quantiles, not on conditional variances; they can be either equal- or unequal- tailed. We provide uniform consistency and consistency rates results for the proposed estimators as both $n$ and $T$ tend to infinity. We study the finite-sample properties of our estimators by means of Monte Carlo simulations. Finally, we apply our methodology to a panel of asset returns belonging to the S&P100 index in order to compute one-step-ahead conditional prediction intervals for the period 2006-2013. A comparison with the componentwise GARCH benchmark (which does not take advantage of cross-sectional information) demonstrates the superiority of our approach, which is genuinely multivariate (and high-dimensional), nonparametric, and model-free.

Suggested Citation

  • Matteo Barigozzi & Marc Hallin, 2018. "Generalized Dynamic Factor Models and Volatilities: Consistency, rates, and prediction intervals," Papers 1811.10045, arXiv.org, revised Jul 2019.
    • Handle: RePEc:arx:papers:1811.10045
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    1. Rémy Chicheportiche & J-P Bouchaud, 2015. "A nested factor model for non-linear dependencies in stock returns," Post-Print hal-01339978, HAL.
    2. Mario Forni & Alessandro Giovannelli & Marco Lippi & Stefano Soccorsi, 2018. "Dynamic factor model with infinite‐dimensional factor space: Forecasting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(5), pages 625-642, August.
    3. Matteo Barigozzi & Marc Hallin & Stefano Soccorsi, 2019. "Identification of Global and Local Shocks in International Financial Markets via General Dynamic Factor Models," Journal of Financial Econometrics, Oxford University Press, vol. 17(3), pages 462-494.
    4. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    5. Wu, Wei Biao & Zaffaroni, Paolo, 2018. "Asymptotic Theory For Spectral Density Estimates Of General Multivariate Time Series," Econometric Theory, Cambridge University Press, vol. 34(1), pages 1-22, February.
    6. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2017. "Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis," Journal of Econometrics, Elsevier, vol. 199(1), pages 74-92.
    7. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    8. Hallin, Marc & Lippi, Marco, 2013. "Factor models in high-dimensional time series—A time-domain approach," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2678-2695.
    9. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2004. "The generalized dynamic factor model consistency and rates," Journal of Econometrics, Elsevier, vol. 119(2), pages 231-255, April.
    10. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    11. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    12. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
    13. Matteo Barigozzi & Marc Hallin, 2016. "Generalized dynamic factor models and volatilities: recovering the market volatility shocks," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 33-60, February.
    14. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    15. 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..
    16. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    17. Sentana, Enrique & Calzolari, Giorgio & Fiorentini, Gabriele, 2008. "Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks," Journal of Econometrics, Elsevier, vol. 146(1), pages 10-25, September.
    18. Barigozzi, Matteo & Hallin, Marc, 2017. "Generalized dynamic factor models and volatilities: estimation and forecasting," Journal of Econometrics, Elsevier, vol. 201(2), pages 307-321.
    19. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1319-1347, October.
    20. Connor, Gregory & Korajczyk, Robert A, 1993. "A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, September.
    21. Tiao, G. C. & Guttman, Irwin, 1980. "Forecasting contemporal aggregates of multiple time series," Journal of Econometrics, Elsevier, vol. 12(2), pages 219-230, February.
    22. Kyle Jurado & Sydney C. Ludvigson & Serena Ng, 2015. "Measuring Uncertainty," American Economic Review, American Economic Association, vol. 105(3), pages 1177-1216, March.
    23. 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.
    24. Fan, Jianqing & Han, Fang & Liu, Han & Vickers, Byron, 2016. "Robust inference of risks of large portfolios," Journal of Econometrics, Elsevier, vol. 194(2), pages 298-308.
    25. 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.
    26. 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.
    27. 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.
    28. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
    29. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    30. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 377-389, October.
    31. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2015. "Dynamic factor models with infinite-dimensional factor spaces: One-sided representations," Journal of Econometrics, Elsevier, vol. 185(2), pages 359-371.
    32. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    33. R. Chicheportiche & J.-P. Bouchaud, 2015. "A nested factor model for non-linear dependencies in stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1789-1804, November.
    34. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
    35. Francq, Christian & Zakoïan, Jean-Michel, 2020. "Virtual Historical Simulation for estimating the conditional VaR of large portfolios," Journal of Econometrics, Elsevier, vol. 217(2), pages 356-380.
    36. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
    37. Matteo Barigozzi & Marc Hallin, 2015. "Networks, Dynamic Factors, and the Volatility Analysis of High-Dimensional Financial Series," Papers 1510.05118, arXiv.org, revised Jul 2016.
    38. Marc Hallin & Jean-Marie Dufour & Ivan Mizera, 1998. "Generalized run tests for heteroscedastic time series," ULB Institutional Repository 2013/2077, ULB -- Universite Libre de Bruxelles.
    39. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    40. Aït-Sahalia, Yacine & Xiu, Dacheng, 2017. "Using principal component analysis to estimate a high dimensional factor model with high-frequency data," Journal of Econometrics, Elsevier, vol. 201(2), pages 384-399.
    41. 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.
    42. Forni, Mario & Lippi, Marco, 2011. "The general dynamic factor model: One-sided representation results," Journal of Econometrics, Elsevier, vol. 163(1), pages 23-28, July.
    43. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    44. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
    45. 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.
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    Cited by:

    1. Hallin, Marc & Trucíos, Carlos, 2023. "Forecasting value-at-risk and expected shortfall in large portfolios: A general dynamic factor model approach," Econometrics and Statistics, Elsevier, vol. 27(C), pages 1-15.
    2. Carlos Trucíos & João H. G. Mazzeu & Marc Hallin & Luiz K. Hotta & Pedro L. Valls Pereira & Mauricio Zevallos, 2022. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 40-52, December.
    3. Carlos Cesar Trucios-Maza & João H. G Mazzeu & Luis K. Hotta & Pedro L. Valls Pereira & Marc Hallin, 2019. "On the robustness of the general dynamic factor model with infinite-dimensional space: identification, estimation, and forecasting," Working Papers ECARES 2019-32, ULB -- Universite Libre de Bruxelles.
    4. Matteo Barigozzi & Marc Hallin, 2024. "The Dynamic, the Static, and the Weak Factor Models and the Analysis of High-Dimensional Time Series," Working Papers ECARES 2024-14, ULB -- Universite Libre de Bruxelles.
    5. Marc Hallin & Carlos Trucíos, 2020. "Forecasting Value-at-Risk and Expected Shortfall in Large Portfolios: a General Dynamic Factor Approach," Working Papers ECARES 2020-50, ULB -- Universite Libre de Bruxelles.
    6. Nummi, Patrik & Viitasaari, Lauri, 2024. "Necessary and sufficient conditions for continuity of hypercontractive processes and fields," Statistics & Probability Letters, Elsevier, vol. 208(C).
    7. Jianqing Fan & Ricardo Masini & Marcelo C. Medeiros, 2021. "Bridging factor and sparse models," Papers 2102.11341, arXiv.org, revised Sep 2022.
    8. Marc Hallin, 2022. "Manfred Deistler and the General-Dynamic-Factor-Model Approach to the Statistical Analysis of High-Dimensional Time Series," Econometrics, MDPI, vol. 10(4), pages 1-9, December.
    9. Matteo Barigozzi, 2023. "Asymptotic equivalence of Principal Components and Quasi Maximum Likelihood estimators in Large Approximate Factor Models," Papers 2307.09864, arXiv.org, revised Jun 2024.
    10. Trucíos, Carlos & Mazzeu, João H.G. & Hotta, Luiz K. & Valls Pereira, Pedro L. & Hallin, Marc, 2021. "Robustness and the general dynamic factor model with infinite-dimensional space: Identification, estimation, and forecasting," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1520-1534.
    11. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised May 2024.
    12. Liao, Gaoke & Li, Yanling & Wang, Mengxin, 2024. "Contagion network of idiosyncratic volatility: Does corporate environmental responsibility matter?," Energy Economics, Elsevier, vol. 129(C).
    13. Barigozzi, Matteo & Hallin, Marc & Luciani, Matteo & Zaffaroni, Paolo, 2024. "Inferential theory for generalized dynamic factor models," Journal of Econometrics, Elsevier, vol. 239(2).
    14. Gunawan, David & Kohn, Robert & Nott, David, 2021. "Variational Bayes approximation of factor stochastic volatility models," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1355-1375.
    15. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Working Papers ECARES 2023-15, ULB -- Universite Libre de Bruxelles.

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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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