IDEAS home Printed from https://ideas.repec.org/a/spr/empeco/v53y2017i1d10.1007_s00181-016-1158-5.html
   My bibliography  Save this article

Determining the number of factors after stationary univariate transformations

Author

Listed:
  • Francisco Corona

    (Universidad Carlos III de Madrid)

  • Pilar Poncela

    (European Commission, Joint Research Centre (JRC)
    Universidad Autónoma de Madrid)

  • Esther Ruiz

    (Universidad Carlos III de Madrid)

Abstract

A very common practice when extracting factors from non-stationary multivariate time series is to differentiate each variable in the system. As a consequence, the ratio between variances and the dynamic dependence of the common and idiosyncratic differentiated components may change with respect to the original components. In this paper, we analyze the effects of these changes on the finite sample properties of several procedures to determine the number of factors. In particular, we consider the information criteria of Bai and Ng (Econometrica 70(1):191–221, 2002), the edge distribution of Onatski (Rev Econ Stat 92(4):1004–1016, 2010) and the ratios of eigenvalues proposed by Ahn and Horenstein (Econometrica 81(3):1203–1227, 2013). The performance of these procedures when implemented to differentiated variables depends on both the ratios between variances and dependencies of the differentiated factor and idiosyncratic noises. Furthermore, we also analyze the role of the number of factors in the original non-stationary system as well as of its temporal and cross-sectional dimensions. Finally, we implement the different procedures to determine the number of common factors in a system of inflation rates in 15 euro area countries.

Suggested Citation

  • Francisco Corona & Pilar Poncela & Esther Ruiz, 2017. "Determining the number of factors after stationary univariate transformations," Empirical Economics, Springer, vol. 53(1), pages 351-372, August.
  • Handle: RePEc:spr:empeco:v:53:y:2017:i:1:d:10.1007_s00181-016-1158-5
    DOI: 10.1007/s00181-016-1158-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00181-016-1158-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00181-016-1158-5?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
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bräuning, Falk & Koopman, Siem Jan, 2014. "Forecasting macroeconomic variables using collapsed dynamic factor analysis," International Journal of Forecasting, Elsevier, vol. 30(3), pages 572-584.
    2. Bai, Jushan & Wang, Peng, 2014. "Identification theory for high dimensional static and dynamic factor models," Journal of Econometrics, Elsevier, vol. 178(2), pages 794-804.
    3. Kapetanios, George, 2010. "A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 397-409.
    4. H. Wang, 2012. "Factor profiled sure independence screening," Biometrika, Biometrika Trust, vol. 99(1), pages 15-28.
    5. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    6. 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.
    7. Kajal Lahiri & Wenxiong Yao, 2004. "A dynamic factor model of the coincident indicators for the US transportation sector," Applied Economics Letters, Taylor & Francis Journals, vol. 11(10), pages 595-600.
    8. Kajal Lahiri & George Monokroussos & Yongchen Zhao, 2016. "Forecasting Consumption: the Role of Consumer Confidence in Real Time with many Predictors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1254-1275, November.
    9. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    10. Altissimo, Filippo & Mojon, Benoit & Zaffaroni, Paolo, 2009. "Can aggregation explain the persistence of inflation?," Journal of Monetary Economics, Elsevier, vol. 56(2), pages 231-241, March.
    11. 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, Research Institute for Market Economy, Sogang University, revised Dec 2011.
    12. Pilar Poncela & Eva Senra & Lya Paola Sierra, 2014. "Common dynamics of nonenergy commodity prices and their relation to uncertainty," Applied Economics, Taylor & Francis Journals, vol. 46(30), pages 3724-3735, October.
    13. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    14. 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.
    15. Maximiano Pinheiro & António Rua & Francisco Dias, 2013. "Dynamic Factor Models with Jagged Edge Panel Data: Taking on Board the Dynamics of the Idiosyncratic Components," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(1), pages 80-102, February.
    16. Onatski, Alexei, 2015. "Asymptotic analysis of the squared estimation error in misspecified factor models," Journal of Econometrics, Elsevier, vol. 186(2), pages 388-406.
    17. Camacho Maximo & Lovcha Yuliya & Quiros Gabriel Perez, 2015. "Can we use seasonally adjusted variables in dynamic factor models?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(3), pages 377-391, June.
    18. Claudia M. Buch & Sandra Eickmeier & Esteban Prieto, 2014. "Macroeconomic Factors and Microlevel Bank Behavior," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 46(4), pages 715-751, June.
    19. Amengual, Dante & Watson, Mark W., 2007. "Consistent Estimation of the Number of Dynamic Factors in a Large N and T Panel," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 91-96, January.
    20. Jörg Breitung & Uta Pigorsch, 2013. "A Canonical Correlation Approach for Selecting the Number of Dynamic Factors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(1), pages 23-36, February.
    21. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    22. 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.
    23. Buch, Claudia M. & Eickmeier, Sandra & Prieto, Esteban, 2010. "Macroeconomic factors and micro-level bank risk," Discussion Paper Series 1: Economic Studies 2010,20, Deutsche Bundesbank.
    24. 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.
    25. 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.
    26. James H. Stock & Mark W. Watson, 2012. "Generalized Shrinkage Methods for Forecasting Using Many Predictors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 481-493, June.
    27. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    28. Jushan Bai & Serena Ng, 2006. "Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions," Econometrica, Econometric Society, vol. 74(4), pages 1133-1150, July.
    29. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    30. Karim Barhoumi & Olivier Darné & Laurent Ferrara, 2013. "Testing the Number of Factors: An Empirical Assessment for a Forecasting Purpose," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(1), pages 64-79, February.
    31. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January.
    32. Alvarez, Rocio & Camacho, Maximo & Perez-Quiros, Gabriel, 2016. "Aggregate versus disaggregate information in dynamic factor models," International Journal of Forecasting, Elsevier, vol. 32(3), pages 680-694.
    33. 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.
    34. 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.
    35. Kajal Lahiri & Xuguang Sheng, 2010. "Measuring forecast uncertainty by disagreement: The missing link," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 514-538.
    36. Mehmet Caner & Xu Han, 2014. "Selecting the Correct Number of Factors in Approximate Factor Models: The Large Panel Case With Group Bridge Estimators," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 359-374, July.
    37. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    38. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
    39. Jan Jacobs & Pieter Otter, 2008. "Determining the Number of Factors and Lag Order in Dynamic Factor Models: A Minimum Entropy Approach," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 385-397.
    40. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
    41. 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.
    42. Alessi, Lucia & Barigozzi, Matteo & Capasso, Marco, 2010. "Improved penalization for determining the number of factors in approximate factor models," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1806-1813, December.
    43. Davide Delle Monache & Ivan Petrella & Fabrizio Venditti, 2016. "Common Faith or Parting Ways? A Time Varying Parameters Factor Analysis of Euro-Area Inflation," Advances in Econometrics, in: Eric Hillebrand & Siem Jan Koopman (ed.), Dynamic Factor Models, volume 35, pages 539-565, Emerald Publishing Ltd.
    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.
    2. Francisco Corona & Graciela Gonz'alez-Far'ias & Jes'us L'opez-P'erez, 2021. "A nowcasting approach to generate timely estimates of Mexican economic activity: An application to the period of COVID-19," Papers 2101.10383, arXiv.org.

    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. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Eric Hillebrand & Siem Jan Koopman (ed.), Dynamic Factor Models, volume 35, pages 401-434, Emerald Publishing Ltd.
    2. 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.
    3. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," PSE Working Papers halshs-02262202, HAL.
    4. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers halshs-02262202, HAL.
    5. 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.
    6. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    7. 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.
    8. 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.
    9. Maldonado, Javier & Ruiz Ortega, Esther, 2017. "Accurate Subsampling Intervals of Principal Components Factors," DES - Working Papers. Statistics and Econometrics. WS 23974, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    11. Yunus Emre Ergemen & Carlos Vladimir Rodríguez-Caballero, 2016. "A Dynamic Multi-Level Factor Model with Long-Range Dependence," CREATES Research Papers 2016-23, Department of Economics and Business Economics, Aarhus University.
    12. Mao Takongmo, Charles Olivier & Stevanovic, Dalibor, 2015. "Selection Of The Number Of Factors In Presence Of Structural Instability: A Monte Carlo Study," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 177-233, Mars-Juin.
    13. Ergemen, Yunus Emre & Rodríguez Caballero, Carlos Vladimir, 2017. "Estimation of a Dynamic Multilevel Factor Model with possible long-range dependence," DES - Working Papers. Statistics and Econometrics. WS 24614, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Ruiz Ortega, Esther & Poncela, Pilar & Miranda Gualdrón, Karen Alejandra, 2021. "Dynamic factor models: does the specification matter?," DES - Working Papers. Statistics and Econometrics. WS 32210, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Francisco Corona & Pedro Orraca, 2019. "Remittances in Mexico and their unobserved components," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 28(8), pages 1047-1066, November.
    16. 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, Research Institute for Market Economy, Sogang University, revised Dec 2011.
    17. Nathan Bedock & Dalibor Stevanović, 2017. "An empirical study of credit shock transmission in a small open economy," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(2), pages 541-570, May.
    18. 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.
    19. 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.).
    20. Yoshimasa Uematsu & Takashi Yamagata, 2019. "Estimation of Weak Factor Models," DSSR Discussion Papers 96, Graduate School of Economics and Management, Tohoku University.

    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:spr:empeco:v:53:y:2017:i:1:d:10.1007_s00181-016-1158-5. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.springer.com .

    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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.