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  • Junhui Qian (a1) and Liangjun Su (a2)

In this paper, we consider the problem of determining the number of structural changes in multiple linear regression models via group fused Lasso. We show that with probability tending to one, our method can correctly determine the unknown number of breaks, and the estimated break dates are sufficiently close to the true break dates. We obtain estimates of the regression coefficients via post Lasso and establish the asymptotic distributions of the estimates of both break ratios and regression coefficients. We also propose and validate a data-driven method to determine the tuning parameter. Monte Carlo simulations demonstrate that the proposed method works well in finite samples. We illustrate the use of our method with a predictive regression of the equity premium on fundamental information.

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*Address correspondence to Liangjun Su, School of Economics, Singapore Management University, 90 Stamford Road, Singapore 178903; e-mail:
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Andrews, D.W.K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821856.
Andrews, D.W.K. (2003) End-of-sample instability tests. Econometrica 71, 16611694.
Andrews, D.W.K. & Ploberger, W. (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 13831414.
Angelosante, D. & Giannakis, G.B. (2012) Group Lassoing change-points in piecewise-constant AR processes. EURASIP Journal on Advances in Signal Processing 1(70), 116.
Bai, J. (1995) Least absolute deviation estimation of a shift. Econometric Theory 11, 403436.
Bai, J. (1997a) Estimation of a change point in multiple regression models. Review of Economics and Statistics 79, 551563.
Bai, J. (1997b) Estimating multiple breaks one at a time. Econometric Theory 13, 315352.
Bai, J. (1998) Estimation of multiple-regime regressions with least absolute deviation. Journal of Statistical Planning and Inference 74, 103134.
Bai, J. (2010) Common breaks in means and variances for panel data. Journal of Econometrics 157, 7892.
Bai, J., Lumsdaine, R.L., & Stock, J. (1998) Testing and dating common breaks in multivariate time series. Review of Economic Studies 65, 395432.
Bai, J. & Perron, P. (1998) Estimating and testing liner models with multiple structural changes. Econometrica 66, 4778.
Bai, J. & Perron, P. (2003a) Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18, 122.
Bai, J. & Perron, P. (2003b) Critical values for multiple structural change tests. Econometrics Journal 6, 7278.
Bai, J. & Perron, P. (2006) Multiple structural change models: A simulation analysis. In Corbae, D., Durlauf, S.N., & Hansen, B.E. (eds.), Econometric Theory and Practice. Cambridge University Press.
Baltagi, B.H., Feng, Q., & Kao, C. (2014) Estimation of Heterogeneous Panels with Structural Breaks. Working paper, Syracuse University.
Belloni, A., Chernozhukov, V., & Hansen, C. (2012) Sparse models and methods for optimal instruments with an application to eminent domain. Econometrica 80, 23692429.
Belloni, A., Chernozhukov, V., & Hansen, C. (2014) Inference on treatment effects after selection amongst high-dimensional controls. Review of Economic Studies 81, 608650.
Bertsekas, D. (1995) Nonlinear Programming. Athena Scientific.
Bleakley, K. & Vert, J-P. (2011) The Group Fused Lasso for Multiple Change Point Detection. Working paper, INRIA Saclay, Orsay, France.
Caner, M. (2009) Lasso-type GMM estimator. Econometric Theory 25, 270290.
Caner, M. & Fan, M. (2011) A Near Minimax Risk Bound: Adaptive Lasso with Heteroskedastic Data in Instrumental Variable Selection. Working paper, North Carolina State University.
Caner, M. & Knight, K. (2013) An alternative to unit root tests: Bridge estimators differentiate between nonstationary versus stationary models and select optimal lag. Journal of Statistical Planning and Inference 143, 691715.
Chan, F., Mancini-Griffoli, T., & Pauwels, L.L. (2008) Stability Tests for Heterogenous Panel. Working paper, Curtin University of Technology.
Cheng, X., Liao, Z., & Schorfheide, F. (2014) Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities. NBER Working Paper No. 19792.
De Watcher, S. & Tzavalis, E. (2005) Monte Carlo comparison of model and moment selection and classical inference approaches to break detection in panel data models. Economics Letters 99, 9196.
De Watcher, S. & Tzavalis, E. (2012) Detection of structural breaks in linear dynamic panel data models. Computational Statistics and Data Analysis 56, 30203034.
Fan, J. & Peng, H. (2004) Nonconcave penalized likelihood with a diverging number of parameters. Annals of Statistics 32, 928961.
Friedman, J., Hastie, T., Höfling, H., & Tibshirani, R. (2007) Pathwise coordinate optimization. Annals of Applied Statistics 1, 302332.
Grant, M., Boyd, S., & Ye, Y. (2009) CVX: Matlab Software for Disciplined Convex Programming. Mimeo.
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and its Applications. Academic Press.
Harchaoui, Z. & Lévy-Leduc, C. (2010) Multiple change-point estimation with a total variation penalty. Journal of the American Statistical Association 105, 14811493.
Hsu, C-C. & Lin, C-C. (2012) Change-Point Estimation for Nonstationary Panel. Working paper, National Central University.
Kim, D. (2011) Estimating a common deterministic time trend break in large panels with cross sectional dependence. Journal of Econometrics 164, 310330.
Kim, D. (2014) Common breaks in time trends for large panel data with a factor structure. The Econometrics Journal 17, 301337.
Knight, K. & Fu, W. (2000) Asymptotics for Lasso-type estimators. Annals of Statistics 28, 13561378.
Kock, A.B. (2013) Oracle efficient variable selection in random and fixed effects panel data models. Econometric Theory 29, 115152.
Kurozumi, E. (2012) Testing for Multiple Structural Changes with Non-Homogeneous Regressors. Working paper, Hitotsubashi University.
Kurozumi, E. & Arai, Y. (2006) Efficient estimation and inference in cointegrating regressions with structural breaks. Journal of Time Series Analysis 28, 545575.
Lam, C. & Fan, J. (2008) Profile-kernel likelihood inference with diverging number of parameters. Annals of Statistics 36, 22322260.
Leeb, H. & Pötscher, B.M. (2005) Model selection and inference: Facts and fiction. Econometric Theory 21, 2159.
Leeb, H. & Pötscher, B.M. (2008) Sparse estimators and the oracle property, or the return of the Hodges estimator. Journal of Econometrics 142, 201211.
Liao, Z. (2013) Adaptive GMM shrinkage estimation with consistent moment selection. Econometric Theory 29, 857904.
Liao, Z. & Phillips, P.C.B. (2014) Automated estimation of vector error correction models. Econometric Theory. Forthcoming.
Liao, W. & Wang, P. (2012) Structural Breaks in Panel Data Models: A Common Distribution Approach. Working paper, HKUST.
Liu, Q. & Watbled, F. (2009) Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random experiment. Stochastic Processes and Their Applications 119, 31013132.
Lu, X. & Su, L. (2013) Shrinkage Estimation of Dynamic Panel Data Models with Interactive Fixed Effects. Working paper, Singapore Management University.
Lu, X. & Su, L. (2015) Jackknife model averaging for quantile regressions. Journal of Econometrics 188, 4058.
Merlevède, F., Peligrad, M., & Rio, E. (2009) Bernstein inequality and moderate deviations under strong mixing conditions. IMS collections. High Dimensional Probability 5, 273292.
Merlevède, F., Peligrad, M., & Rio, E. (2011) A Bernstein type inequality and moderate deviations for weakly dependent sequences. Probability Theory and Related Fields 151, 435474.
Ohlsson, H., Ljung, L., & Boyd, S. (2010) Segmentation of ARX-models using sum-of-norms regularization. Automatica 46, 11071111.
Perron, P. (2006) Dealing with structural breaks. In Mills, T.C. & Patterson, K. (eds.), Palgrave Handbook of Econometrics, Econometric Theory, vol. 1, pp. 278352. Palgrave Macmillan.
Pötscher, B.M. & Leeb, H. (2009) On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding. Journal of Multivariate Analysis 100, 20652082.
Pötscher, B.M. & Schneider, U. (2009) On the distribution of the adaptive LASSO estimator. Journal of Statistical Planning and Inference 139, 27752790.
Qian, J. & Su, L. (2014) Shrinkage Estimation of Regression Models with Multiple Structural Changes. Working paper, Singapore Management University.
Qu, Z. & Perron, P. (2007) Estimating and testing structural changes in multiple regressions. Econometrica 75, 459502.
Rinaldo, A. (2009) Properties and refinement of the fused Lasso. Annals of Statistics 37, 29222952.
Su, L. & White, H. (2010) Testing structural change in partially linear models. Econometric Theory 26, 17611806.
Su, L., Xu, P., & Ju, H. (2013) Pricing for Goodwill: A Threshold Quantile Regression Approach. Working paper, Singapore Management University.
Tibshirani, R.J. (1996) Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society, Series B 58, 267288.
Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., & Knight, K. (2005) Sparsity and smoothness via the fused Lasso. Journal of the Royal Statistical Society, Series B 67, 91108.
Welch, I. & Goyal, A. (2008) A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies 21, 14551508.
White, H. (2001) Asymptotic Theory for Econometricians, 2nd ed. Emerald.
Yuan, M. & Lin, Y. (2006) Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society, Series B 68, 4967.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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