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Factor-driven two-regime regression. (English) Zbl 1475.62175

Summary: We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold effect shrinks to zero. In particular, we establish a phase transition that describes the effect of first-stage factor estimation as the cross-sectional dimension of panel data increases relative to the time-series dimension. Moreover, we develop bootstrap inference and illustrate our methods via numerical studies.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
62F12 Asymptotic properties of parametric estimators
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References:

[1] Andrews, D. W. K. (2002). Higher-order improvements of a computationally attractive \(k\)-step bootstrap for extremum estimators. Econometrica 70 119-162. · Zbl 1104.62315 · doi:10.1111/1468-0262.00271
[2] Bai, J. (1994). Least squares estimation of a shift in linear processes. J. Time Series Anal. 15 453-472. · Zbl 0808.62079 · doi:10.1111/j.1467-9892.1994.tb00204.x
[3] Bai, J. (2003). Inferential theory for factor models of large dimensions. Econometrica 71 135-171. · Zbl 1136.62354 · doi:10.1111/1468-0262.00392
[4] Bai, J. and Ng, S. (2006). Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions. Econometrica 74 1133-1150. · Zbl 1152.91721 · doi:10.1111/j.1468-0262.2006.00696.x
[5] Bai, J. and Ng, S. (2008). Extremum estimation when the predictors are estimated from large panels. Ann. Econ. Financ. 9 201-222.
[6] Bai, J. and Ng, S. (2009). Boosting diffusion indices. J. Appl. Econometrics 24 607-629. · doi:10.1002/jae.1063
[7] Bai, J. and Perron, P. (2003). Computation and analysis of multiple structural change models. J. Appl. Econometrics 18 1-22.
[8] Bertsimas, D., King, A. and Mazumder, R. (2016). Best subset selection via a modern optimization lens. Ann. Statist. 44 813-852. · Zbl 1335.62115 · doi:10.1214/15-AOS1388
[9] Chan, K. S. (1993). Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. Ann. Statist. 21 520-533. · Zbl 0786.62089 · doi:10.1214/aos/1176349040
[10] Cheng, X. and Hansen, B. E. (2015). Forecasting with factor-augmented regression: A frequentist model averaging approach. J. Econometrics 186 280-293. · Zbl 1332.62357 · doi:10.1016/j.jeconom.2015.02.010
[11] Fan, J., Liao, Y. and Mincheva, M. (2013). Large covariance estimation by thresholding principal orthogonal complements. J. R. Stat. Soc. Ser. B. Stat. Methodol. 75 603-680. · Zbl 1411.62138 · doi:10.1111/rssb.12016
[12] Gonçalves, S. and Perron, B. (2014). Bootstrapping factor-augmented regression models. J. Econometrics 182 156-173. · Zbl 1311.62040 · doi:10.1016/j.jeconom.2014.04.015
[13] Gonçalves, S. and Perron, B. (2020). Bootstrapping factor models with cross sectional dependence. J. Econometrics 218 476-495. · Zbl 1464.62318 · doi:10.1016/j.jeconom.2020.04.026
[14] Hall, P. (1992). The Bootstrap and Edgeworth Expansion. Springer Series in Statistics. Springer, New York. · Zbl 0829.62021 · doi:10.1007/978-1-4612-4384-7
[15] Hansen, B. E. (1997). Inference in TAR models. Stud. Nonlinear Dyn. Econom. 2 1-14. · Zbl 1078.91558 · doi:10.2202/1558-3708.1024
[16] Hansen, B. E. (2000). Sample splitting and threshold estimation. Econometrica 68 575-603. · Zbl 1056.62528 · doi:10.1111/1468-0262.00124
[17] Hawkins, D. L. (1986). A simple least squares method for estimating a change in mean. Comm. Statist. B. Simulation Comput. 15 655-679. · Zbl 0606.62028 · doi:10.1080/03610918608812531
[18] Horváth, L. and Kokoszka, P. (1997). The effect of long-range dependence on change-point estimators. J. Statist. Plann. Inference 64 57-81. · Zbl 0946.62078 · doi:10.1016/S0378-3758(96)00208-X
[19] Kim, J. and Pollard, D. (1990). Cube root asymptotics. Ann. Statist. 18 191-219. · Zbl 0703.62063 · doi:10.1214/aos/1176347498
[20] Lee, S., Liao, Y., Seo, M. H. and Shin, Y. (2021). Supplement to “Factor-driven two-regime regression.” https://doi.org/10.1214/20-AOS2017SUPP
[21] Ling, S. (1999). On the probabilistic properties of a double threshold ARMA conditional heteroskedastic model. J. Appl. Probab. 36 688-705. · Zbl 1109.62340 · doi:10.1017/s0021900200017502
[22] Ludvigson, S. C. and Ng, S. (2009). Macro factors in bond risk premia. Rev. Financ. Stud. 22 5027-5067.
[23] McKeague, I. W. and Sen, B. (2010). Fractals with point impact in functional linear regression. Ann. Statist. 38 2559-2586. · Zbl 1196.62116 · doi:10.1214/10-AOS791
[24] Merlevède, F., Peligrad, M. and Rio, E. (2011). A Bernstein type inequality and moderate deviations for weakly dependent sequences. Probab. Theory Related Fields 151 435-474. · Zbl 1242.60020 · doi:10.1007/s00440-010-0304-9
[25] Qu, Z. and Tkachenko, D. (2017). Global identification in DSGE models allowing for indeterminacy. Rev. Econ. Stud. 84 1306-1345. · Zbl 1471.91275 · doi:10.1093/restud/rdx007
[26] Seijo, E. and Sen, B. (2011). Change-point in stochastic design regression and the bootstrap. Ann. Statist. 39 1580-1607. · Zbl 1220.62043 · doi:10.1214/11-AOS874
[27] Seo, M. H. and Linton, O. (2007). A smoothed least squares estimator for threshold regression models. J. Econometrics 141 704-735. · Zbl 1418.62355 · doi:10.1016/j.jeconom.2006.11.002
[28] Seo, M. H. and Otsu, T. (2018). Local M-estimation with discontinuous criterion for dependent and limited observations. Ann. Statist. 46 344-369. · Zbl 1394.62058 · doi:10.1214/17-AOS1552
[29] Tong, H. (1990). Nonlinear Time Series: A Dynamical System Approach. Oxford Statistical Science Series 6. Oxford University Press, New York. · Zbl 0716.62085
[30] van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes: With Applications to Statistics. Springer Series in Statistics. Springer, New York · Zbl 0862.60002 · doi:10.1007/978-1-4757-2545-2
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