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Simultaneous multiple change-point and factor analysis for high-dimensional time series

Author

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  • Barigozzi, Matteo
  • Cho, Haeran
  • Fryzlewicz, Piotr

Abstract

We propose the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure. We operate under the most flexible definition of piecewise stationarity, and estimate the number and locations of change-points consistently as well as identifying whether they originate in the common or idiosyncratic components. Through the use of wavelets, we transform the problem of change-point detection in the second-order structure of a high-dimensional time series, into the (relatively easier) problem of change-point detection in the means of high-dimensional panel data. Also, our methodology circumvents the difficult issue of the accurate estimation of the true number of factors in the presence of multiple change-points by adopting a screening procedure. We further show that consistent factor analysis is achieved over each segment defined by the change-points estimated by the proposed methodology. In extensive simulation studies, we observe that factor analysis prior to change-point detection improves the detectability of change-points, and identify and describe an interesting ‘spillover’ effect in which substantial breaks in the idiosyncratic components get, naturally enough, identified as change-points in the common components, which prompts us to regard the corresponding change-points as also acting as a form of ‘factors’. Our methodology is implemented in the R package factorcpt, available from CRAN.

Suggested Citation

  • Barigozzi, Matteo & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
  • Handle: RePEc:eee:econom:v:206:y:2018:i:1:p:187-225
    DOI: 10.1016/j.jeconom.2018.05.003
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    as
    1. Jan J. J. Groen & George Kapetanios & Simon Price, 2013. "Multivariate Methods For Monitoring Structural Change," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 250-274, March.
    2. Bates, Brandon J. & Plagborg-Møller, Mikkel & Stock, James H. & Watson, Mark W., 2013. "Consistent factor estimation in dynamic factor models with structural instability," Journal of Econometrics, Elsevier, vol. 177(2), pages 289-304.
    3. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
    4. Gonçalves, Sílvia & Perron, Benoit, 2014. "Bootstrapping factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 182(1), pages 156-173.
    5. 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.
    6. repec:bla:jorssc:v:66:y:2017:i:3:p:581-605 is not listed on IDEAS
    7. 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.
    8. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    9. 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(05), pages 1319-1347, October.
    10. Chen, Liang & Dolado, Juan J. & Gonzalo, Jesús, 2014. "Detecting big structural breaks in large factor models," Journal of Econometrics, Elsevier, vol. 180(1), pages 30-48.
    11. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    12. Xu Cheng & Zhipeng Liao & Frank Schorfheide, 2016. "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities," Review of Economic Studies, Oxford University Press, vol. 83(4), pages 1511-1543.
    13. 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.
    14. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters,in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230 National Bureau of Economic Research, Inc.
    15. James H. Stock & Mark W. Watson, 2003. "Has the business cycle changed?," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 9-56.
    16. Haeran Cho & Piotr Fryzlewicz, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 475-507, March.
    17. 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.
    18. Massacci, Daniele, 2017. "Least squares estimation of large dimensional threshold factor models," Journal of Econometrics, Elsevier, vol. 197(1), pages 101-129.
    19. Matteo Barigozzi & Marc Hallin, 2017. "A network analysis of the volatility of high dimensional financial series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(3), pages 581-605, April.
    20. 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.
    21. Andrew Patton & Dimitris Politis & Halbert White, 2009. "Correction to “Automatic Block-Length Selection for the Dependent Bootstrap” by D. Politis and H. White," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 372-375.
    22. Jianqing Fan & Jinchi Lv & Lei Qi, 2011. "Sparse High-Dimensional Models in Economics," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 291-317, September.
    23. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    24. 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.
    25. repec:bla:jorssb:v:80:y:2018:i:1:p:57-83 is not listed on IDEAS
    26. G. P. Nason & R. Von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    27. Y. Yu & T. Wang & R. J. Samworth, 2015. "A useful variant of the Davis–Kahan theorem for statisticians," Biometrika, Biometrika Trust, vol. 102(2), pages 315-323.
    28. Onatski, Alexei, 2015. "Asymptotic analysis of the squared estimation error in misspecified factor models," Journal of Econometrics, Elsevier, vol. 186(2), pages 388-406.
    29. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    30. repec:eee:econom:v:201:y:2017:i:2:p:384-399 is not listed on IDEAS
    31. Shujie Ma & Liangjun Su, 2016. "Estimation of Large Dimensional Factor Models with an Unknown Number of Breaks," Working Papers 05-2016, Singapore Management University, School of Economics.
    32. P. Fryzlewicz & S. Subba Rao, 2014. "Multiple-change-point detection for auto-regressive conditional heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(5), pages 903-924, November.
    33. Corradi, Valentina & Swanson, Norman R., 2014. "Testing for structural stability of factor augmented forecasting models," Journal of Econometrics, Elsevier, vol. 182(1), pages 100-118.
    34. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    35. 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.
    36. Trapani, Lorenzo, 2013. "On bootstrapping panel factor series," Journal of Econometrics, Elsevier, vol. 172(1), pages 127-141.
    37. 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.
    38. Fryzlewicz, Piotr & Nason, Guy P., 2006. "Haar-Fisz estimation of evolutionary wavelet spectra," LSE Research Online Documents on Economics 25227, London School of Economics and Political Science, LSE Library.
    39. Baltagi, Badi H. & Kao, Chihwa & Wang, Fa, 2017. "Identification and estimation of a large factor model with structural instability," Journal of Econometrics, Elsevier, vol. 197(1), pages 87-100.
    40. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    41. Piotr Fryzlewicz & Guy P. Nason, 2006. "Haar–Fisz estimation of evolutionary wavelet spectra," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 611-634, September.
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    Cited by:

    1. Matteo Barigozzi & Marc Hallin & Stefano Soccorsi, 2019. "Time-Varying General Dynamic Factor Models and the Measurement of Financial Connectedness," Working Papers 257939806, Lancaster University Management School, Economics Department.

    More about this item

    Keywords

    Piecewise stationary factor model; Change-point detection; Principal component analysis; Wavelet transformation; Double CUSUM binary segmentation;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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