IDEAS home Printed from https://ideas.repec.org/p/fip/fedgfe/2017-111.html
   My bibliography  Save this paper

Common Factors, Trends, and Cycles in Large Datasets

Author

Abstract

This paper considers a non-stationary dynamic factor model for large datasets to disentangle long-run from short-run co-movements. We first propose a new Quasi Maximum Likelihood estimator of the model based on the Kalman Smoother and the Expectation Maximisation algorithm. The asymptotic properties of the estimator are discussed. Then, we show how to separate trends and cycles in the factors by mean of eigenanalysis of the estimated non-stationary factors. Finally, we employ our methodology on a panel of US quarterly macroeconomic indicators to estimate aggregate real output, or Gross Domestic Output, and the output gap.

Suggested Citation

  • Matteo Barigozzi & Matteo Luciani, 2017. "Common Factors, Trends, and Cycles in Large Datasets," Finance and Economics Discussion Series 2017-111, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2017-111
    DOI: 10.17016/FEDS.2017.111
    as

    Download full text from publisher

    File URL: https://www.federalreserve.gov/econres/feds/files/2017111pap.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.17016/FEDS.2017.111?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Kiley, Michael T., 2013. "Output gaps," Journal of Macroeconomics, Elsevier, vol. 37(C), pages 1-18.
    2. F. Vahid & R. F. Engle, 1993. "Common Trends And Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, October.
    3. Donald Robertson & Anthony Garratt & Stephen Wright, 2006. "Permanent vs transitory components and economic fundamentals," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 521-542.
    4. Giannone, Domenico & Reichlin, Lucrezia & Small, David, 2008. "Nowcasting: The real-time informational content of macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 55(4), pages 665-676, May.
    5. 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.
    6. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2016. "Non-Stationary Dynamic Factor Models for Large Datasets," Finance and Economics Discussion Series 2016-024, Board of Governors of the Federal Reserve System (U.S.).
    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. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2011. "A two-step estimator for large approximate dynamic factor models based on Kalman filtering," Journal of Econometrics, Elsevier, vol. 164(1), pages 188-205, September.
    9. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
    10. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    11. James Morley & Benjamin Wong, 2020. "Estimating and accounting for the output gap with large Bayesian vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 1-18, January.
    12. 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.
    13. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    14. Massimo Franchi, 2017. "On the structure of state space systems with unit roots," DSS Empirical Economics and Econometrics Working Papers Series 2017/4, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    15. 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.
    16. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, September.
    17. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    18. Del Negro, Marco & Schorfheide, Frank & Smets, Frank & Wouters, Rafael, 2007. "On the Fit of New Keynesian Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 123-143, April.
    19. Marco Lippi & Lucrezia Reichlin, 1994. "Diffusion of Technical Change and the Decomposition of Output into Trend and Cycle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 19-30.
    20. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2014. "Dynamic Factor Models, Cointegration and Error Correction Mechanisms," Working Papers ECARES ECARES 2014-14, ULB -- Universite Libre de Bruxelles.
    21. Matteo Luciani, 2015. "Monetary Policy and the Housing Market: A Structural Factor Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(2), pages 199-218, March.
    22. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    23. Choi, In, 2012. "Efficient Estimation Of Factor Models," Econometric Theory, Cambridge University Press, vol. 28(2), pages 274-308, April.
    24. Laura Coroneo & Domenico Giannone & Michele Modugno, 2016. "Unspanned Macroeconomic Factors in the Yield Curve," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 472-485, July.
    25. Ricardo Reis & Mark W. Watson, 2010. "Relative Goods' Prices, Pure Inflation, and the Phillips Correlation," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(3), pages 128-157, July.
    26. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    27. Bańbura, Marta & Giannone, Domenico & Lenza, Michele, 2015. "Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections," International Journal of Forecasting, Elsevier, vol. 31(3), pages 739-756.
    28. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    29. Juan Antolin-Diaz & Thomas Drechsel & Ivan Petrella, 2017. "Tracking the Slowdown in Long-Run GDP Growth," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 343-356, May.
    30. Robert Engle & Clive Granger, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    31. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    32. Kasa, Kenneth, 1992. "Common stochastic trends in international stock markets," Journal of Monetary Economics, Elsevier, vol. 29(1), pages 95-124, February.
    33. 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.
    34. Gonzalo, Jesus & Granger, Clive W J, 1995. "Estimation of Common Long-Memory Components in Cointegrated Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 27-35, January.
    35. Luciana Juvenal & Ivan Petrella, 2015. "Speculation in the Oil Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 621-649, June.
    36. Antonello D’ Agostino & Domenico Giannone, 2012. "Comparing Alternative Predictors Based on Large‐Panel Factor Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(2), pages 306-326, April.
    37. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    38. Proietti, Tommaso, 1997. "Short-Run Dynamics in Cointegrated Systems," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(3), pages 405-422, August.
    39. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    40. 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.
    41. Marta Bańbura & Michele Modugno, 2014. "Maximum Likelihood Estimation Of Factor Models On Datasets With Arbitrary Pattern Of Missing Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(1), pages 133-160, January.
    42. Jeremy J. Nalewaik, 2012. "Estimating Probabilities of Recession in Real Time Using GDP and GDI," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(1), pages 235-253, February.
    43. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    44. S. J. Koopman & J. Durbin, 2000. "Fast Filtering and Smoothing for Multivariate State Space Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(3), pages 281-296, May.
    45. Tim Mahedy & Glenn D. Rudebusch & Daniel J. Wilson, 2015. "The puzzle of weak first-quarter GDP growth," FRBSF Economic Letter, Federal Reserve Bank of San Francisco.
    46. Dungey, Mardi & Jacobs, Jan P.A.M. & Tian, Jing & van Norden, Simon, 2015. "Trend In Cycle Or Cycle In Trend? New Structural Identifications For Unobserved-Components Models Of U.S. Real Gdp," Macroeconomic Dynamics, Cambridge University Press, vol. 19(4), pages 776-790, June.
    47. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    48. Roberto S. Mariano & Yasutomo Murasawa, 2003. "A new coincident index of business cycles based on monthly and quarterly series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 427-443.
    49. 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.
    50. Aruoba, S. Borağan & Diebold, Francis X. & Nalewaik, Jeremy & Schorfheide, Frank & Song, Dongho, 2016. "Improving GDP measurement: A measurement-error perspective," Journal of Econometrics, Elsevier, vol. 191(2), pages 384-397.
    51. Gonzalo, Jesus & Ng, Serena, 2001. "A systematic framework for analyzing the dynamic effects of permanent and transitory shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1527-1546, October.
    52. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
    53. Marek Jarociński & Michele Lenza, 2018. "An Inflation‐Predicting Measure of the Output Gap in the Euro Area," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(6), pages 1189-1224, September.
    54. Lippi, Marco & Reichlin, Lucrezia, 1994. "Common and uncommon trends and cycles," European Economic Review, Elsevier, vol. 38(3-4), pages 624-635, April.
    55. Aastveit, Knut Are & Trovik, Tørres, 2014. "Estimating the output gap in real time: A factor model approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 54(2), pages 180-193.
    56. repec:hal:journl:peer-00844811 is not listed on IDEAS
    57. Peña, Daniel & Poncela, Pilar, 1997. "Eigenstructure of nonstationary factor models," DES - Working Papers. Statistics and Econometrics. WS 6224, Universidad Carlos III de Madrid. Departamento de Estadística.
    58. Domenico Giannone & Lucrezia Reichlin & David Small, 2008. "Nowcasting: the real time informational content of macroeconomic data releases," ULB Institutional Repository 2013/6409, ULB -- Universite Libre de Bruxelles.
    59. Alvaro Escribano & Daniel Peña, 1994. "Cointegration And Common Factors," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 577-586, November.
    60. Jungbacker, B. & Koopman, S.J. & van der Wel, M., 2011. "Maximum likelihood estimation for dynamic factor models with missing data," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1358-1368, August.
    61. 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.
    62. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    63. Byeongchan Seong & Sung K. Ahn & Peter A. Zadrozny, 2013. "Estimation of vector error correction models with mixed-frequency data," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 194-205, March.
    64. Kurt Graden Lunsford, 2017. "Lingering Residual Seasonality in GDP Growth," Economic Commentary, Federal Reserve Bank of Cleveland, issue March.
    65. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    66. Engle, Robert F. & Issler, João Victor, 1993. "Common trends and common cycles in Latin America," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 47(2), April.
    67. 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.
    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. Francisco Corona & Pilar Poncela & Esther Ruiz, 2020. "Estimating Non-stationary Common Factors: Implications for Risk Sharing," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 37-60, January.

    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. 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.
    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. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    4. 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.
    5. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2014. "Dynamic Factor Models, Cointegration and Error Correction Mechanisms," Working Papers ECARES ECARES 2014-14, ULB -- Universite Libre de Bruxelles.
    6. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised May 2024.
    7. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2016. "Non-Stationary Dynamic Factor Models for Large Datasets," Finance and Economics Discussion Series 2016-024, Board of Governors of the Federal Reserve System (U.S.).
    8. Francisco Corona & Pilar Poncela & Esther Ruiz, 2020. "Estimating Non-stationary Common Factors: Implications for Risk Sharing," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 37-60, January.
    9. Matteo Barigozzi & Matteo Luciani, 2019. "Quasi Maximum Likelihood Estimation of Non-Stationary Large Approximate Dynamic Factor Models," Papers 1910.09841, arXiv.org.
    10. Barigozzi, Matteo & Lippi, Marco & Luciani, Matteo, 2021. "Large-dimensional Dynamic Factor Models: Estimation of Impulse–Response Functions with I(1) cointegrated factors," Journal of Econometrics, Elsevier, vol. 221(2), pages 455-482.
    11. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    12. Kihwan Kim & Norman Swanson, 2013. "Diffusion Index Model Specification and Estimation Using Mixed Frequency Datasets," Departmental Working Papers 201315, Rutgers University, Department of Economics.
    13. Francisco Corona & Graciela González-Farías & Pedro Orraca, 2017. "A dynamic factor model for the Mexican economy: are common trends useful when predicting economic activity?," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 26(1), pages 1-35, December.
    14. Hindrayanto, Irma & Koopman, Siem Jan & de Winter, Jasper, 2016. "Forecasting and nowcasting economic growth in the euro area using factor models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1284-1305.
    15. Juho Koistinen & Bernd Funovits, 2022. "Estimation of Impulse-Response Functions with Dynamic Factor Models: A New Parametrization," Papers 2202.00310, arXiv.org, revised Feb 2022.
    16. Simona Delle Chiaie & Laurent Ferrara & Domenico Giannone, 2022. "Common factors of commodity prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 461-476, April.
    17. 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.
    18. Barigozzi, Matteo & Hallin, Marc & Luciani, Matteo & Zaffaroni, Paolo, 2024. "Inferential theory for generalized dynamic factor models," Journal of Econometrics, Elsevier, vol. 239(2).
    19. Karim Barhoumi & Olivier Darné & Laurent Ferrara, 2014. "Dynamic factor models: A review of the literature," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2013(2), pages 73-107.
    20. Marcellino, Massimiliano & Sivec, Vasja, 2016. "Monetary, fiscal and oil shocks: Evidence based on mixed frequency structural FAVARs," Journal of Econometrics, Elsevier, vol. 193(2), pages 335-348.

    More about this item

    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
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • E00 - Macroeconomics and Monetary Economics - - General - - - General

    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:fip:fedgfe:2017-111. 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: Ryan Wolfslayer ; Keisha Fournillier (email available below). General contact details of provider: https://edirc.repec.org/data/frbgvus.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.