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Alessandro Casini and Pierre Perron

This article covers methodological issues related to estimation, testing, and computation for models involving structural changes. Our aim is to review developments as they relate to econometric applications based on linear models. Substantial advances have been made to cover models at a level of generality that allow a host of interesting practical applications. These include models with general stationary regressors and errors that can exhibit temporal dependence and heteroskedasticity, models with trending variables and possible unit roots and cointegrated models, among others. Advances have been made pertaining to computational aspects of constructing estimates, their limit distributions, tests for structural changes, and methods to determine the number of changes present. A variety of topics are covered including recent developments: testing for common breaks, models with endogenous regressors (emphasizing that simply using least-squares is preferable over instrumental variables methods), quantile regressions, methods based on Lasso, panel data models, testing for changes in forecast accuracy, factors models, and methods of inference based on a continuous records asymptotic framework. Our focus is on the so-called off-line methods whereby one wants to retrospectively test for breaks in a given sample of data and form confidence intervals about the break dates. The aim is to provide the readers with an overview of methods that are of direct use in practice as opposed to issues mostly of theoretical interest.


David E. Rapach and Guofu Zhou

Asset returns change with fundamentals and other factors, such as technical information and sentiment over time. In modeling time-varying expected returns, this article focuses on the out-of-sample predictability of the aggregate stock market return via extensions of the conventional predictive regression approach. The extensions are designed to improve out-of-sample performance in realistic environments characterized by large information sets and noisy data. Large information sets are relevant because there are a plethora of plausible stock return predictors. The information sets include variables typically associated with a rational time-varying market risk premium, as well as variables more likely to reflect market inefficiencies resulting from behavioral influences and information frictions. Noisy data stem from the intrinsically large unpredictable component in stock returns. When forecasting with large information sets and noisy data, it is vital to employ methods that incorporate the relevant information in the large set of predictors in a manner that guards against overfitting the data. Methods that improve out-of-sample market return prediction include forecast combination, principal component regression, partial least squares, the LASSO and elastic net from machine learning, and a newly developed C-ENet approach that relies on the elastic net to refine the simple combination forecast. Employing these methods, a number of studies provide statistically and economically significant evidence that the aggregate market return is predictable on an out-of-sample basis. Out-of-sample market return predictability based on a rich set of predictors thus appears to be a well-established empirical result in asset pricing.