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A0224
Title: Robust test of stock return predictability under heavy-tailed innovations Authors:  Cheng-Der Fuh - ()
Hsinchieh Wong - National Central University, Taiwan (Taiwan) [presenting]
Menghua Chung - National Central University, Taiwan (Taiwan)
Abstract: Conventional tests of the predictability of stock returns are usually based on the normal innovation assumption, which does not fit the empirical data well. To remedy this ideal assumption, we consider a predictive regression model $Y_t=\beta_0+\beta_1 X_{t-1}+u_t,~ X_t=\rho X_{t-1}+e_t$ with heavy tails. That is, $\{u_t, t\ge 1\}$ and $\{e_t, t\ge 1\}$ are two sequences of random variables, in which the distributions are in the domain of attraction of the normal law with zero means and possibly infinite variances. To construct a robust statistic based on this model, we study asymptotic behavior of the estimators of $\beta_0$, $\beta_1$ and $(\beta_0,beta_1)^T$ for stationary as well as local to unity cases. Our results show that when $|\rho|< 1$ or $\rho$ tends to unity but slowly enough, the proposed robust statistic is indeed pivotal, and can be used directly to test the predictability of stock returns. Next, under the dependent structure of $u_t$ and $e_t$, in the case of local to unity, we propose a modified test based on the celebrated Bonferroni Q-test and present the efficiency of this test. Finally, based on our theoretical results, we study the relationships among heavy-tails, unit root and predictability. Numerical simulations and empirical studies are given for illustration.