Predictability hidden by Anomalous Observations in Financial Data

Abstract

Testing procedures for predictive regressions involving lagged autoregressive variables produce a suboptimal inference in presence of minor violations of ideal assumptions. A novel testing framework based on resampling methods that exhibits resistance to such violations and is reliable also in models with nearly integrated regressors is introduced. To achieve this objective, the robustness of resampling procedures for time series are defined by deriving new formulas quantifying their quantile breakdown point. For both the block bootstrap and subsampling, these formulas show a very low quantile breakdown point. To overcome this problem, a robust and fast resampling scheme applicable to a broad class of time series settings is proposed. This framework is also suitable for multi-predictor settings, particularly when the data only approximately conform to a predictive regression model. Monte Carlo simulations provide substantial evidence for the significant improvements offered by this robust approach. Using the proposed resampling methods, empirical coverages and rejection frequencies are very close to the nominal levels, both in the presence and absence of small deviations from the ideal model assumptions. Empirical analysis reveals robust evidence of market return predictability, previously obscured by anomalous observations, both in- and out-of-sample.