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TESTING FOR STRUCTURAL CHANGES IN FACTOR MODELS VIA A NONPARAMETRIC REGRESSION

Published online by Cambridge University Press:  12 May 2020

Liangjun Su  and
Xia Wang
Liangjun Su
Affiliation:
Tsinghua University and Singapore Management University
Xia Wang*
Affiliation:
Renmin University of China and Sun Yat-Sen University
*
Address correspondence to Xia Wang, School of Economics, Renmin University of China, Beijing 100872, China; e-mail: [email protected].
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Abstract

We propose a model-free test for structural changes in factor models. The basic idea is to regress the data on commonly estimated factors by local smoothing and compare the fitted values of time-varying factor loadings with those of time-invariant factor loadings estimated via principal component analysis. By construction, the test is designed to be powerful against both smooth structural changes and sudden structural breaks with a possibly unknown number of breaks and unknown break dates in the factor loadings. No restrictions on the form of alternatives or trimming of boundary regions near the beginning or end of the sample period is required for the test. The test has power to detect the usual nonparametric rate of local alternatives. Monte Carlo studies demonstrate excellent power of the test in detecting both smooth and sudden structural changes in the factor loadings. In an application using U.S. asset returns, we find significant evidence against time-invariant factor loadings.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 6 , December 2020 , pp. 1127 - 1158
Copyright
© Cambridge University Press 2020

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Footnotes

The authors sincerely thank the Editor Peter C.B. Phillips, the Co-Editor Patrik Guggenberger, and three anonymous referees for their constructive comments and suggestions on the early versions of the article. Su gratefully acknowledges the Singapore Ministry of Education for Tier-2 Academic Research Fund (AcRF) under Grant No. MOE2012-T2-2-021 and the funding support provided by the Lee Kong Chian Fund for Excellence. Wang acknowledges financial support from the National Science Foundation of China (No. 71873151, No. 71401160).

References

Ahn, S. & Horenstein, A. (2013) Eigenvalue ratio test for the number of factors. Econometrica 81, 1203–1227.Google Scholar
Andrews, W.K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821–856.CrossRefGoogle Scholar
Ang, A. & Kristensen, D. (2012) Testing conditional factor models. Journal of Financial Economics 106, 132–156.CrossRefGoogle Scholar
Bai, J. (2003) Inferential theory for factor models of large dimensions. Econometrica 71, 135–172.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2002) Determining the number of factors in approximate factor models. Econometrica 90, 191–221.CrossRefGoogle Scholar
Baltagi, B., Kao, C., & Wang, F. (2016) Estimating and Testing High Dimensional Factor Models with Multiple Structural Changes. Working Paper, Department of Economics, Syracuse University.Google Scholar
Banerjee, A., Marcellino, M., & Masten, I. (2008) Forecasting macroeconomic variables using diffusion indexes in short samples with structural change. Frontiers of Economics and Globalization 3, 149–194.CrossRefGoogle Scholar
Bates, B.J., Plagborg-Møller, M., Stock, J.H., & Watson, M.W. (2013) Consistent factor estimation in dynamic factor models with structural instability. Journal of Econometrics 177, 289–304.CrossRefGoogle Scholar
Breitung, J. & Eickmeier, S. (2011) Testing for structural breaks in dynamic factor models. Journal of Econometrics 163, 71–84.CrossRefGoogle Scholar
Cai, Z. (2007) Trending time-varying coefficient time series models with serially correlated errors. Journal of Econometrics 136, 163–188.CrossRefGoogle Scholar
Chen, J., Gao, J., & Li, D. (2012) Semiparametric testing for smooth structural changes in panel data models. Journal of Econometrics 171, 71–85.CrossRefGoogle Scholar
Chen, L., Dolado, J., & Gonzalo, J. (2014) Detecting big structural breaks in large factor models. Journal of Econometrics 180, 30–48.CrossRefGoogle Scholar
Cheng, X., Liao, Z., & Schorfheide, F. (2016) Shrinkage estimation of high-dimensional factor models with structural instabilities. Review of Economic Studies 83, 1511–1543.CrossRefGoogle Scholar
Corradi, V. & Swanson, N.R. (2014) Testing for structural stability of factor augmented forecasting models. Journal of Econometrics 182, 100–118.CrossRefGoogle Scholar
Del Negro, M., & Otrok, C. (2009) Dynamic Factor Models with Time-Varying Parameters: Measuring Changes in International Business Cycles. Staff Report No. 326. Federal Reserve Bank of New York.CrossRefGoogle Scholar
Eickmeier, S., Lemke, W., & Marcellino, M. (2015) Classical time varying factor-augmented vector auto-regressive models-estimation, forecasting and structural analysis. Journal of the Royal Statistical Society: Series A (Statistics in Society) 178, 493–533.CrossRefGoogle Scholar
Fan, J., Liao, Y., & Mincheva, M. (2013) Large covariance estimation by thresholding principal orthogonal complements. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 75, 603–680.CrossRefGoogle ScholarPubMed
Gao, J. & Gijbels, I. (2008) Bandwidth selection in nonparametric kernel testing. Journal of American Statistical Association 103, 1584–1594.CrossRefGoogle Scholar
Han, X. & Inoue, A. (2015) Tests for parameter instability in dynamic factor models. Econometric Theory 31, 1117–1152.CrossRefGoogle Scholar
Hong, Y. & Li, H. (2005) Nonparametric specification testing for continuous-time models with applications to term structure of interest rate. Review of Financial Studies 18, 37–84.CrossRefGoogle Scholar
Li, Q. & Racine, J.S. (2007) Nonparametric Econometrics: Theory and Practice. Princeton University Press.Google Scholar
Li, Y. & Yang, L. (2011) Testing conditional factor models: a nonparametric approach. Journal of Empirical Finance 18, 972–992.CrossRefGoogle Scholar
Ma, S., Lan, W., Su, L., & Tsai, C.-L. (2020) Testing alphas in conditional time-varying factor models with high dimensional assets. Journal of Business & Economic Statistics 38, 214–227.CrossRefGoogle Scholar
Ma, S. & Su, L. (2018) Estimation of large dimensional factor models with an unknown number of breaks. Journal of Econometrics 207, 1–29.CrossRefGoogle Scholar
Mikkelsen, J.G., Hillebrand, E., & Urga, G. (2015) Maximum Likelihood Estimation of Time-Varying Factor Loadings in High-Dimensional Factor Models. CREATES Research Paper 2015-16.Google Scholar
Moon, H. & Weidner, M. (2015) Linear regression for panel with unknown number of factors as interactive fixed effects. Econometrica 83, 1543–1579.CrossRefGoogle Scholar
Motta, C., Hafner, C.M., & von Sachs, R. (2011) Local stationary factor models: identification and nonparametric estimation. Econometric Theory 27, 1279–1319.CrossRefGoogle Scholar
Onatski, A. (2009) Testing hypotheses about the number of factors in large factor models. Econometrica 77, 1447–1479.Google Scholar
Onatski, A. (2010) Determining the number of factors from empirical distribution of eigenvalues. Review of Economics and Statistics 92, 1004–1016.CrossRefGoogle Scholar
Robinson, P.M. (2012) Nonparametric trending regression with cross-sectional dependence. Journal of Econometrics 169, 4–14.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2002) Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association 97, 1167–1179.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2009) Forecasting in dynamic factor models subject to structural instability. In Castle, J. & Shephard, N. (eds.), The Methodology and Practice of Econometrics: A Festschrift in Honour of Professor David F. Hendry, pp. 1–57. Oxford University Press.Google Scholar
Su, L. & Chen, Q. (2013) Testing homogeneity in panel data models with interactive fixed effects. Econometric Theory 29, 1079–1135.CrossRefGoogle Scholar
Su, L., Jin, S., & Zhang, Y. (2015) Specification test for panel data models with interactive fixed effects. Journal of Econometrics 185, 230–258.CrossRefGoogle Scholar
Su, L. & Wang, X. (2017) On time-varying factor models: Estimation and testing. Journal of Econometrics 198, 84–101.CrossRefGoogle Scholar
Sun, Y., Phillips, P., & Jin, S. (2008) Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing. Econometrica 76, 175–194.CrossRefGoogle Scholar
Yamamoto, Y. & Tanaka, S. (2015) Testing for factor loading structural change under common breaks. Journal of Econometrics 189, 187–206.CrossRefGoogle Scholar
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