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Determining the number of factors after stationary univariate transformations

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  • Corona, Francisco
  • Poncela, Maria Pilar
  • Ruiz, Esther

Abstract

A very common practice when extracting factors from non-stationary multivariate timeseries is to differentiate each variable in the system. As a consequence, the ratiobetween variances and the dynamic dependence of the common and idiosyncraticdifferentiated components may change with respect to the original components. In thispaper, we analyze the effects of these changes on the finite sample properties of somepopular procedures to determine the number of factors. In particular, we consider theinformation criteria of Bai and Ng (2002), the edge distribution of Onastki (2010) andthe ratios of eigenvalues proposed by Ahn and Horenstein (2013). The performance ofthese procedures when implemented to differentiated variables depend on both theratios between variances and dependences of the differentiated factor and idiosyncraticnoises. Furthermore, we also analyze the role of the number of factors in the originalnon-stationary system as well as of its temporal and cross-sectional dimensions.

Suggested Citation

  • Corona, Francisco & Poncela, Maria Pilar & Ruiz, Esther, 2016. "Determining the number of factors after stationary univariate transformations," DES - Working Papers. Statistics and Econometrics. WS ws1602, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws1602
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    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. H. Wang, 2012. "Factor profiled sure independence screening," Biometrika, Biometrika Trust, vol. 99(1), pages 15-28.
    4. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    5. 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.
    6. 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.
    7. 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.
    8. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    9. 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.
    10. Jörg Breitung & In Choi, 2013. "Factor models," Chapters,in: 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.
    11. 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.
    12. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    13. 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.
    14. 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.
    15. Onatski, Alexei, 2015. "Asymptotic analysis of the squared estimation error in misspecified factor models," Journal of Econometrics, Elsevier, vol. 186(2), pages 388-406.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    26. 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.
    27. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    28. 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.
    29. 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.
    30. 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.
    31. 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.
    32. 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.
    33. 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.
    34. 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.
    35. 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.
    36. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    37. 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.
    38. 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.
    39. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
    40. 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.
    41. 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.
    42. repec:eme:aecozz:s0731-905320150000035013 is not listed on IDEAS
    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: Dynamic Factor Models, volume 35, pages 539-565 Emerald Publishing Ltd.
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    Cited by:

    1. Ruiz Ortega, Esther & Poncela, Pilar & Corona, Francisco, 2017. "Estimating non-stationary common factors : Implications for risk sharing," DES - Working Papers. Statistics and Econometrics. WS 24585, Universidad Carlos III de Madrid. Departamento de Estadística.

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    Dynamic Factor Model;

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