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Sequential testing for structural stability in approximate factor models

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  • Matteo Barigozzi
  • Lorenzo Trapani
Abstract
We develop an on-line monitoring procedure to detect a change in a large approximate factor model. Our statistics are based on a well-known property of the (r + 1)-th eigenvalue of the sample covariance matrix of the data (having defined r as the number of common factors): whilst under the null the (r + 1)-th eigenvalue is bounded, under the alternative of a change (either in the loadings, or in the number of factors itself) it becomes spiked. Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statistic in conjunction with sample conditioning, obtaining a sequence of i.i.d., asymptotically chi-square statistics which are then employed to build the monitoring scheme. Numerical evidence shows that our procedure works very well in finite samples, with a very small probability of false detections and tight detection times in presence of a genuine change-point.

Suggested Citation

  • Matteo Barigozzi & Lorenzo Trapani, 2018. "Sequential testing for structural stability in approximate factor models," Discussion Papers 18/04, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:18/04
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    1. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.
    2. Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 2007. "On sequential detection of parameter changes in linear regression," Statistics & Probability Letters, Elsevier, vol. 77(9), pages 885-895, May.
    3. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
    4. 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.
    5. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    6. Andreou, Elena & Ghysels, Eric, 2006. "Monitoring disruptions in financial markets," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 77-124.
    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. 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. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    10. Bandi, Federico M. & Corradi, Valentina, 2014. "Nonparametric Nonstationarity Tests," Econometric Theory, Cambridge University Press, vol. 30(1), pages 127-149, February.
    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. Bai, Zhidong & Yao, Jianfeng, 2012. "On sample eigenvalues in a generalized spiked population model," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 167-177.
    13. 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.
    14. Massacci, Daniele, 2017. "Least squares estimation of large dimensional threshold factor models," Journal of Econometrics, Elsevier, vol. 197(1), pages 101-129.
    15. 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.
    16. Aue, Alexander & Hörmann, Siegfried & Horváth, Lajos & Hušková, Marie & Steinebach, Josef G., 2012. "Sequential Testing For The Stability Of High-Frequency Portfolio Betas," Econometric Theory, Cambridge University Press, vol. 28(4), pages 804-837, August.
    17. 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.
    18. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2006. "Forecasting using a large number of predictors: is Bayesian regression a valid alternative to principal components?," Discussion Paper Series 1: Economic Studies 2006,32, Deutsche Bundesbank.
    19. Alexei Onatski & Marcelo Moreira J. & Marc Hallin, 2012. "Signal Detection in High Dmension: The Multispiked Case," Working Papers ECARES ECARES 2012-036, ULB -- Universite Libre de Bruxelles.
    20. 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.
    21. 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.
    22. Corradi, Valentina & Swanson, Norman R., 2006. "The effect of data transformation on common cycle, cointegration, and unit root tests: Monte Carlo results and a simple test," Journal of Econometrics, Elsevier, vol. 132(1), pages 195-229, May.
    23. 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(5), pages 1319-1347, October.
    24. Xu Cheng & Zhipeng Liao & Frank Schorfheide, 2016. "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1511-1543.
    25. Chihwa Kao & Lorenzo Trapani & Giovanni Urga, 2012. "Testing for Instability in Covariance Structures," Center for Policy Research Working Papers 131, Center for Policy Research, Maxwell School, Syracuse University.
    26. 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.
    27. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2017. "Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis," Journal of Econometrics, Elsevier, vol. 199(1), pages 74-92.
    28. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    29. Bai, Jushan, 2010. "Common breaks in means and variances for panel data," Journal of Econometrics, Elsevier, vol. 157(1), pages 78-92, July.
    30. Clifford Lam & Qiwei Yao & Neil Bathia, 2011. "Estimation of latent factors for high-dimensional time series," Biometrika, Biometrika Trust, vol. 98(4), pages 901-918.
    31. 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.
    32. Lam, Clifford & Yao, Qiwei & Bathia, Neil, 2011. "Estimation of latent factors for high-dimensional time series," LSE Research Online Documents on Economics 31549, London School of Economics and Political Science, LSE Library.
    33. Aue, Alexander & Horváth, Lajos, 2004. "Delay time in sequential detection of change," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 221-231, April.
    34. Jia Li & Viktor Todorov & George Tauchen & Huidi Lin, 2019. "Rank Tests at Jump Events," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 312-321, April.
    35. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    36. 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.
    37. Han, Xu & Inoue, Atsushi, 2015. "Tests For Parameter Instability In Dynamic Factor Models," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1117-1152, October.
    38. Lorenzo Trapani, 2018. "A Randomized Sequential Procedure to Determine the Number of Factors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1341-1349, July.
    39. 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.
    40. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    41. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2008. "Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?," Journal of Econometrics, Elsevier, vol. 146(2), pages 318-328, October.
    42. 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.
    43. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    44. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    45. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    46. 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.
    47. Guang-hui Cai, 2006. "Chover-type laws of the iterated logarithm for weighted sums of ρ ∗ -mixing sequences," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-7, April.
    48. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
    49. 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.
    50. Benaych-Georges, Florent & Nadakuditi, Raj Rao, 2012. "The singular values and vectors of low rank perturbations of large rectangular random matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 120-135.
    51. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-1065, September.
    52. 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.
    53. Hallin, Marc & Liska, Roman, 2011. "Dynamic factors in the presence of blocks," Journal of Econometrics, Elsevier, vol. 163(1), pages 29-41, July.
    54. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
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    Cited by:

    1. Matteo Barigozzi & Daniele Massacci, 2022. "Modelling Large Dimensional Datasets with Markov Switching Factor Models," Papers 2210.09828, arXiv.org, revised Jun 2024.
    2. Xin-Bing Kong & Yong-Xin Liu & Long Yu & Peng Zhao, 2022. "Matrix Quantile Factor Model," Papers 2208.08693, arXiv.org, revised Aug 2024.
    3. Lorenzo Trapani & Emily Whitehouse, 2020. "Sequential monitoring for cointegrating regressions," Papers 2003.12182, arXiv.org.
    4. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.

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    Keywords

    large factor model; change-point; sequential testing; randomised tests.;
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