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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
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    1. 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.
    2. H. Wang, 2012. "Factor profiled sure independence screening," Biometrika, Biometrika Trust, vol. 99(1), pages 15-28.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Onatski, Alexei, 2015. "Asymptotic analysis of the squared estimation error in misspecified factor models," Journal of Econometrics, Elsevier, vol. 186(2), pages 388-406.
    11. 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.
    12. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    13. 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.
    14. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. 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.
    27. 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.
    28. 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.
    29. Eric Hillebrand & Siem Jan Koopman (ed.), 2016. "Dynamic Factor Models," Advances in Econometrics, Emerald Publishing Ltd, volume 35, number aeco.2016.35.
    30. 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.
    31. Clements, Michael P. & Hendry, David F. (ed.), 2011. "The Oxford Handbook of Economic Forecasting," OUP Catalogue, Oxford University Press, number 9780195398649, November.
    32. 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.
    33. 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.
    34. 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.
    35. 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.
    36. 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.
    37. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    38. 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.
    39. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    40. 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.
    41. 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.
    42. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    43. Tibor F. Liska, 2007. "The Liska model," Society and Economy, Akadémiai Kiadó, Hungary, vol. 29(3), pages 363-381, December.
    44. 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.
    45. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
    46. 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.
    47. 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.
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