IDEAS home Printed from https://ideas.repec.org/p/bde/wpaper/1619.html
   My bibliography  Save this paper

A spectral EM algorithm for dynamic factor models

Author

Listed:
  • Gabriele Fiorentini

    (UNIVERSITÀ DI FIRENZE and RCEA)

  • Alessandro Galesi

    (Banco de España)

  • Enrique Sentana

    (CEMFI)

Abstract

We make two complementary contributions to efficiently estimate dynamic factor models: a frequency domain EM algorithm and a swift iterated indirect inference procedure for ARMA models with no asymptotic efficiency loss for any finite number of iterations. Although our procedures can estimate such models with many series without good initial values, near the optimum we recommend switching to a gradient method that analytically computes spectral scores using the EM principle. We successfully employ our methods to construct an index that captures the common movements of US sectoral employment growth rates, which we compare to the indices obtained by semiparametric methods

Suggested Citation

  • Gabriele Fiorentini & Alessandro Galesi & Enrique Sentana, 2016. "A spectral EM algorithm for dynamic factor models," Working Papers 1619, Banco de España.
    • Handle: RePEc:bde:wpaper:1619
    as

    Download full text from publisher

    File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/16/Fich/dt1619e.pdf
    File Function: First version, September 2016
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Danny Quah & Thomas J. Sargent, 1993. "A Dynamic Index Model for Large Cross Sections," NBER Chapters, in: Business Cycles, Indicators, and Forecasting, pages 285-310, National Bureau of Economic Research, Inc.
    2. Gabriele Fiorentini & Enrique Sentana, 2019. "Dynamic specification tests for dynamic factor models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 325-346, April.
    3. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2012. "A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1014-1024, November.
    4. Gabriele Fiorentini & Alessandro Galesi & Enrique Sentana, 2016. "Fast ML Estimation of Dynamic Bifactor Models: An Application to European Inflation," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 215-282, Emerald Group Publishing Limited.
    5. Demos, Antonis & Sentana, Enrique, 1998. "An EM Algorithm for Conditionally Heteroscedastic Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 357-361, July.
    6. Gregory, Allan W & Head, Allen C & Raynauld, Jacques, 1997. "Measuring World Business Cycles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 677-701, August.
    7. 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.
    8. R. H. Shumway & D. S. Stoffer, 1982. "An Approach To Time Series Smoothing And Forecasting Using The Em Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(4), pages 253-264, July.
    9. Mody, Ashoka & Taylor, Mark P., 2007. "Regional vulnerability: The case of East Asia," Journal of International Money and Finance, Elsevier, vol. 26(8), pages 1292-1310, December.
    10. Geweke, John F & Singleton, Kenneth J, 1981. "Maximum Likelihood "Confirmatory" Factor Analysis of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(1), pages 37-54, February.
    11. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
    12. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, vol. 119(2), pages 257-289, April.
    13. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    14. Lilien, David M, 1982. "Sectoral Shifts and Cyclical Unemployment," Journal of Political Economy, University of Chicago Press, vol. 90(4), pages 777-793, August.
    15. Rogerson, Richard, 1987. "An Equilibrium Model of Sectoral Reallocation," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 824-834, August.
    16. Enrique Sentana, 1998. "The relation between conditionally heteroskedastic factor models and factor GARCH models," Econometrics Journal, Royal Economic Society, vol. 1(RegularPa), pages 1-9.
    17. 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.
    18. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    19. 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.
    20. 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.
    21. Mardi Dungey & Vance L Martin & Adrian R Pagan, 2000. "A multivariate latent factor decomposition of international bond yield spreads," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 697-715.
    22. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    23. 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.
    24. Gabriele Fiorentini & Enrique Sentana, 2016. "Neglected serial correlation tests in UCARIMA models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 121-178, March.
    25. 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.
    26. Diebold, Francis X. & Rudebusch, Glenn D. & Borag[caron]an Aruoba, S., 2006. "The macroeconomy and the yield curve: a dynamic latent factor approach," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 309-338.
    27. Diebold, Francis X & Rudebusch, Glenn D, 1996. "Measuring Business Cycles: A Modern Perspective," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 67-77, February.
    28. Eric Ghysels & Lynda Khalaf & Cosmé Vodounou, 2003. "Simulation Based Inference In Moving Average Models," Annals of Economics and Statistics, GENES, issue 69, pages 85-99.
    29. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
    30. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409, National Bureau of Economic Research, Inc.
    31. Narasimhan Jegadeesh & George Pennacchi, 1996. "The behavior of interest rates implied by the term structure of Eurodollar future," Proceedings, Federal Reserve Bank of Cleveland, issue Aug, pages 426-451.
    32. Abraham, Katharine G & Katz, Lawrence F, 1986. "Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances?," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages 507-522, June.
    33. Peter Arcidiacono & John Bailey Jones, 2003. "Finite Mixture Distributions, Sequential Likelihood and the EM Algorithm," Econometrica, Econometric Society, vol. 71(3), pages 933-946, May.
    34. Bergstrom, A.R., 1984. "Continuous time stochastic models and issues of aggregation over time," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 20, pages 1145-1212, Elsevier.
    35. Maravall, Agustin, 1993. "Stochastic linear trends : Models and estimators," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 5-37, March.
    36. repec:adr:anecst:y:2003:i:69:p:04 is not listed on IDEAS
    37. Chambers, Marcus J. & Thornton, Michael A., 2012. "Discrete Time Representation Of Continuous Time Arma Processes," Econometric Theory, Cambridge University Press, vol. 28(1), pages 219-238, February.
    38. Lehmann, Bruce N. & Modest, David M., 1988. "The empirical foundations of the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 21(2), pages 213-254, September.
    39. repec:adr:anecst:y:2000:i:58:p:01 is not listed on IDEAS
    40. Borus Jungbacker & Siem Jan Koopman, 2015. "Likelihood‐based dynamic factor analysis for measurement and forecasting," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 1-21, June.
    41. Chumacero Rómulo A., 2001. "Estimating ARMA Models Efficiently," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(2), pages 1-14, July.
    42. Nidhan Choudhuri, 2004. "Contiguity of the Whittle measure for a Gaussian time series," Biometrika, Biometrika Trust, vol. 91(1), pages 211-218, March.
    43. James H. Stock & Mark W. Watson, 1993. "Business Cycles, Indicators, and Forecasting," NBER Books, National Bureau of Economic Research, Inc, number stoc93-1.
    44. Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 69-76, March.
    45. Stock, James H. & Watson, Mark W. (ed.), 1993. "Business Cycles, Indicators, and Forecasting," National Bureau of Economic Research Books, University of Chicago Press, edition 1, number 9780226774886, September.
    46. Enrique Sentana, 2000. "The Likelihood Function of Conditionally Heteroskedastic Factor Models," Annals of Economics and Statistics, GENES, issue 58, pages 1-19.
    47. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
    48. Watson, Mark W. & Kraft, Dennis F., 1984. "Testing the interpretation of indices in a macroeconomic index model," Journal of Monetary Economics, Elsevier, vol. 13(2), pages 165-181, March.
    49. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
    50. James H. Stock & Mark W. Watson, 1993. "A Procedure for Predicting Recessions with Leading Indicators: Econometric Issues and Recent Experience," NBER Chapters, in: Business Cycles, Indicators, and Forecasting, pages 95-156, National Bureau of Economic Research, Inc.
    51. Chris Heaton & Victor Solo, 2004. "Identification of causal factor models of stationary time series," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 618-627, December.
    52. Watson, Mark W. & Engle, Robert F., 1983. "Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models," Journal of Econometrics, Elsevier, vol. 23(3), pages 385-400, December.
    53. Hannan, E J & Nicholls, D F, 1972. "The Estimation of Mixed Regression, Autoregression, Moving Average, and Distributed Lag Models," Econometrica, Econometric Society, vol. 40(3), pages 529-547, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gabriele Fiorentini & Enrique Sentana, 2019. "Dynamic specification tests for dynamic factor models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 325-346, April.
    2. Gabriele Fiorentini & Alessandro Galesi & Enrique Sentana, 2016. "Fast ML Estimation of Dynamic Bifactor Models: An Application to European Inflation," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 215-282, Emerald Group Publishing Limited.
    3. Michael Creel, 2021. "Inference Using Simulated Neural Moments," Econometrics, MDPI, vol. 9(4), pages 1-15, September.
    4. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    5. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    6. Bastos, Guadalupe & García-Martos, Carolina, 2017. "BIAS correction for dynamic factor models," DES - Working Papers. Statistics and Econometrics. WS 24029, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised May 2024.
    8. Martín Almuzara & Gabriele Fiorentini & Enrique Sentana, 2023. "Aggregate Output Measurements: A Common Trend Approach," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 3-33, Emerald Group Publishing Limited.
    9. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 401-434, Emerald Group Publishing Limited.
    10. Gabriele Fiorentini & Enrique Sentana, 2016. "Neglected serial correlation tests in UCARIMA models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 121-178, March.
    11. Dickhaus, Thorsten & Sirotko-Sibirskaya, Natalia, 2019. "Simultaneous statistical inference in dynamic factor models: Chi-square approximation and model-based bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 30-46.
    12. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Working Papers ECARES 2023-15, ULB -- Universite Libre de Bruxelles.
    13. Riccardo (Jack) Lucchetti & Ioannis A. Venetis, 2019. "Dynamic Factor Models in gretl. The DFM package," gretl working papers 7, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    14. Matteo Barigozzi & Matteo Luciani, 2019. "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Papers 1910.03821, arXiv.org, revised Sep 2024.
    15. Martín Almuzara & Dante Amengual & Enrique Sentana, 2019. "Normality tests for latent variables," Quantitative Economics, Econometric Society, vol. 10(3), pages 981-1017, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gabriele Fiorentini & Enrique Sentana, 2019. "Dynamic specification tests for dynamic factor models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 325-346, April.
    2. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    3. Gabriele Fiorentini & Alessandro Galesi & Enrique Sentana, 2016. "Fast ML Estimation of Dynamic Bifactor Models: An Application to European Inflation," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 215-282, Emerald Group Publishing Limited.
    4. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    5. Borus Jungbacker & Siem Jan Koopman, 2015. "Likelihood‐based dynamic factor analysis for measurement and forecasting," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 1-21, June.
    6. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    7. Borus Jungbacker & Siem Jan Koopman, 2008. "Likelihood-based Analysis for Dynamic Factor Models," Tinbergen Institute Discussion Papers 08-007/4, Tinbergen Institute, revised 20 Mar 2014.
    8. Koopman, Siem Jan & van der Wel, Michel, 2013. "Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model," International Journal of Forecasting, Elsevier, vol. 29(4), pages 676-694.
    9. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised May 2024.
    10. Borus Jungbacker & Siem Jan Koopman & Michel van der Wel, 0000. "Dynamic Factor Models with Smooth Loadings for Analyzing the Term Structure of Interest Rates," Tinbergen Institute Discussion Papers 09-041/4, Tinbergen Institute, revised 17 Sep 2010.
    11. Bork, Lasse, 2009. "Estimating US Monetary Policy Shocks Using a Factor-Augmented Vector Autoregression: An EM Algorithm Approach," Finance Research Group Working Papers F-2009-03, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    12. Gabriele Fiorentini & Enrique Sentana, 2009. "Dynamic Specification Tests for Static Factor Models," Working Papers wp2009_0912, CEMFI.
    13. Reichlin, Lucrezia, 2002. "Factor Models in Large Cross-Sections of Time Series," CEPR Discussion Papers 3285, C.E.P.R. Discussion Papers.
    14. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    15. Rua, António, 2017. "A wavelet-based multivariate multiscale approach for forecasting," International Journal of Forecasting, Elsevier, vol. 33(3), pages 581-590.
    16. Diebold, Francis X & Rudebusch, Glenn D, 1996. "Measuring Business Cycles: A Modern Perspective," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 67-77, February.
    17. George Kapetanios & Massimiliano Marcellino, 2009. "A parametric estimation method for dynamic factor models of large dimensions," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 208-238, March.
    18. Grace Lee, 2011. "Aggregate shocks decomposition for eight East Asian countries," Journal of the Asia Pacific Economy, Taylor & Francis Journals, vol. 16(2), pages 215-232.
    19. Gabriele Fiorentini & Enrique Sentana, 2012. "Tests for Serial Dependence in Static, Non-Gaussian Factor Models," Working Papers wp2012_1211, CEMFI.
    20. André Nunes Maranhão & Nicole Rennó Castro, 2023. "Dissecting Brazilian agriculture business cycles in high-dimensional and time-irregular span contexts," Empirical Economics, Springer, vol. 65(4), pages 1543-1578, October.

    More about this item

    Keywords

    indirect inference; Kalman filter; sectoral employment; spectral maximum likelihood; Wiener-Kolmogorov filter;
    All these keywords.

    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bde:wpaper:1619. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ángel Rodríguez. Electronic Dissemination of Information Unit. Research Department. Banco de España (email available below). General contact details of provider: https://edirc.repec.org/data/bdegves.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.