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A perspective on recent methods on testing predictability of asset returns
LIAO Xiao-sai, CAI Zong-wu, CHEN Hai-qiang
Applied Mathematics-A Journal of Chinese Universities, 2018, 33(2): 127-.
https://doi.org/10.1007/s11766-018-3590-0
This paper highlights some recent developments in testing predictability of asset returns with focuses on linear mean regressions, quantile regressions and nonlinear regression models. For these models, when predictors are highly persistent and their innovations are contemporarily correlated with dependent variable, the ordinary least squares estimator has a finite-sample bias, and its limiting distribution relies on some unknown nuisance parameter, which is not consistently estimable. Without correcting these issues, conventional test statistics are subject to a serious size distortion and generate a misleading conclusion in testing predictability of asset returns in real applications. In the past two decades, sequential studies have contributed to this subject and proposed various kinds of solutions, including, but not limit to, the bias-correction procedures, the linear projection approach, the IVX filtering idea, the variable addition approaches, the weighted empirical likelihood method, and the double-weight robust approach. Particularly, to catch up with the fast-growing literature in the recent decade, we offer a selective overview of these methods. Finally, some future research topics, such as the econometric theory for predictive regressions with structural changes, and nonparametric predictive models, and predictive models under a more general data setting, are also discussed.
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Large Variable selection via generalized SELO-penalized linear regression models
SHI Yue-yong , CAO Yong-xiu , YU Ji-chang , JIAO Yu-ling
Applied Mathematics-A Journal of Chinese Universities, 2018, 33(2): 145-.
https://doi.org/10.1007/s11766-018-3496-x
The seamless-$L_0$ (SELO) penalty is a smooth function on $[0,\wq)$ that very closely resembles the $L_0$ penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, we first generalize SELO to a class of penalties retaining good features of SELO, and then propose variable selection and estimation in linear models using the proposed eneralized SELO (GSELO) penalized least squares (PLS) approach. We show that the GSELO-PLS procedure possesses the oracle property and consistently selects the true model under some regularity conditions in the presence of a diverging number of variables. The entire path of GSELO-PLS estimates can be efficiently computed through a smoothing quasi-Newton (SQN) method. A modified BIC coupled with a continuation strategy is developed to select the optimal tuning parameter. Simulation studies and analysis of a clinical data are carried out to evaluate the finite sample performance of the proposed method. In addition, numerical experiments involving simulation studies and analysis of a microarray data are also conducted for GSELO-PLS in the high-dimensional settings.
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8 articles
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