IDEAS home Printed from https://ideas.repec.org/p/aah/create/2022-10.html
   My bibliography  Save this paper

Parametric Estimation of Long Memory in Factor Models

Author

Listed:
  • Yunus Emre Ergemen

    (Aarhus University, Department of Economics and Business Economics, and CREATES)

Abstract

A dynamic factor model is proposed in that factor dynamics are driven by stochastic time trends describing arbitrary persistence levels. The proposed model is essentially a long memory factor model, which nests standard I(0) and I(1) behavior smoothly in common factors. In the estimation, principal components analysis (PCA) and conditional sum of squares (CSS) estimations are employed. For the dynamic model parameters, centered normal asymptotics are established at the usual parametric rates, and their small-sample properties are explored via Monte-Carlo experiments. The method is then applied to a panel of U.S. industry realized volatilities. JEL classifcation: C12, C13, C33 Key words: Factor models, long memory, conditional sum of squares, principal components analysis, realized volatility

Suggested Citation

  • Yunus Emre Ergemen, 2022. "Parametric Estimation of Long Memory in Factor Models," CREATES Research Papers 2022-10, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2022-10
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/22/rp22_10.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Choi, In, 2012. "Efficient Estimation Of Factor Models," Econometric Theory, Cambridge University Press, vol. 28(2), pages 274-308, April.
    2. Cristadoro, Riccardo & Forni, Mario & Reichlin, Lucrezia & Veronese, Giovanni, 2005. "A Core Inflation Indicator for the Euro Area," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 539-560, June.
    3. Pesaran, M. Hashem & Chudik, Alexander, 2014. "Aggregation in large dynamic panels," Journal of Econometrics, Elsevier, vol. 178(P2), pages 273-285.
    4. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    5. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    6. Kapetanios, George, 2004. "A note on modelling core inflation for the UK using a new dynamic factor estimation method and a large disaggregated price index dataset," Economics Letters, Elsevier, vol. 85(1), pages 63-69, October.
    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. Ray, Bonnie K & Tsay, Ruey S, 2000. "Long-Range Dependence in Daily Stock Volatilities," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 254-262, April.
    9. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    10. 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.
    11. Chauvet, Marcelle & Senyuz, Zeynep & Yoldas, Emre, 2015. "What does financial volatility tell us about macroeconomic fluctuations?," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 340-360.
    12. Morana, Claudio, 2009. "On the macroeconomic causes of exchange rate volatility," International Journal of Forecasting, Elsevier, vol. 25(2), pages 328-350.
    13. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    14. Scott R. Baker & Nicholas Bloom & Steven J. Davis, 2016. "Measuring Economic Policy Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1593-1636.
    15. Hallin, Marc & Mathias, Charles & Pirotte, Hugues & Veredas, David, 2011. "Market liquidity as dynamic factors," Journal of Econometrics, Elsevier, vol. 163(1), pages 42-50, July.
    16. repec:ulb:ulbeco:2013/136188 is not listed on IDEAS
    17. Robinson, Peter M. & Velasco, Carlos, 2015. "Efficient inference on fractionally integrated panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 185(2), pages 435-452.
    18. 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.
    19. Chambers, Marcus J, 1998. "Long Memory and Aggregation in Macroeconomic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1053-1072, November.
    20. 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.
    21. Dordonnat, Virginie & Koopman, Siem Jan & Ooms, Marius, 2012. "Dynamic factors in periodic time-varying regressions with an application to hourly electricity load modelling," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3134-3152.
    22. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    23. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
    24. Ergemen, Yunus Emre & Velasco, Carlos, 2017. "Estimation of fractionally integrated panels with fixed effects and cross-section dependence," Journal of Econometrics, Elsevier, vol. 196(2), pages 248-258.
    25. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    26. Michelacci, Claudio & Zaffaroni, Paolo, 2000. "(Fractional) beta convergence," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 129-153, February.
    27. Massimiliano Marcellino & Carlo A. Favero & Francesca Neglia, 2005. "Principal components at work: the empirical analysis of monetary policy with large data sets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 603-620.
    28. Hande Karabiyik & Joakim Westerlund, 2021. "Forecasting using cross-section average–augmented time series regressions," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 315-333.
    29. Baltagi, Badi H. & Kao, Chihwa & Wang, Fa, 2021. "Estimating and testing high dimensional factor models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 220(2), pages 349-365.
    30. Yuzo Hosoya, 2005. "Fractional Invariance Principle," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 463-486, May.
    31. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 387-422.
    32. Fan, Jianqing & Ke, Yuan & Liao, Yuan, 2021. "Augmented factor models with applications to validating market risk factors and forecasting bond risk premia," Journal of Econometrics, Elsevier, vol. 222(1), pages 269-294.
    33. Cipollini, A. & Kapetanios, G., 2008. "A stochastic variance factor model for large datasets and an application to S&P data," Economics Letters, Elsevier, vol. 100(1), pages 130-134, July.
    34. Matteo Luciani & David Veredas, 2015. "Estimating and Forecasting Large Panels of Volatilities with Approximate Dynamic Factor Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(3), pages 163-176, April.
    35. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    36. Tobias Hartl, 2020. "Macroeconomic Forecasting with Fractional Factor Models," Papers 2005.04897, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    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. Ergemen, Yunus Emre, 2023. "Parametric estimation of long memory in factor models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1483-1499.
    2. Ergemen, Yunus Emre & Rodríguez-Caballero, C. Vladimir, 2023. "Estimation of a dynamic multi-level factor model with possible long-range dependence," International Journal of Forecasting, Elsevier, vol. 39(1), pages 405-430.
    3. In Choi & Hanbat Jeong, 2019. "Model selection for factor analysis: Some new criteria and performance comparisons," Econometric Reviews, Taylor & Francis Journals, vol. 38(6), pages 577-596, July.
    4. Forni, Mario & Cavicchioli, Maddalena & Lippi, Marco & Zaffaroni, Paolo, 2016. "Eigenvalue Ratio Estimators for the Number of Common Factors," CEPR Discussion Papers 11440, C.E.P.R. Discussion Papers.
    5. In Choi & Dukpa Kim & Yun Jung Kim & Noh‐Sun Kwark, 2018. "A multilevel factor model: Identification, asymptotic theory and applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 355-377, April.
    6. Yunus Emre Ergemen, 2016. "System Estimation of Panel Data Models under Long-Range Dependence," CREATES Research Papers 2016-02, Department of Economics and Business Economics, Aarhus University.
    7. Jörg Breitung & In Choi, 2013. "Factor models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 11, pages 249-265, Edward Elgar Publishing.
      • In Choi & Jorg Breitung, 2011. "Factor models," Working Papers 1121, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy), revised Dec 2011.
    8. 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.
    9. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    10. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    11. Mario Forni & Marc Hallin & Marco Lippi & Paolo Zaffaroni, 2011. "One-Sided Representations of Generalized Dynamic Factor Models," Working Papers ECARES ECARES 2011-019, ULB -- Universite Libre de Bruxelles.
    12. 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.
    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. Bai, Jushan & Liao, Yuan, 2017. "Inferences in panel data with interactive effects using large covariance matrices," Journal of Econometrics, Elsevier, vol. 200(1), pages 59-78.
    15. 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.
    16. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised May 2024.
    17. 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.
    18. Matteo Barigozzi & Antonio M. Conti & Matteo Luciani, 2014. "Do Euro Area Countries Respond Asymmetrically to the Common Monetary Policy?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(5), pages 693-714, October.
    19. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    20. Fan, Jianqing & Ke, Yuan & Liao, Yuan, 2021. "Augmented factor models with applications to validating market risk factors and forecasting bond risk premia," Journal of Econometrics, Elsevier, vol. 222(1), pages 269-294.

    More about this item

    Keywords

    factor models; long memory; conditional sum of squares; principal components analysis; realized volatility;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

    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:aah:create:2022-10. 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: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    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.