Improved regression inference using a second overlapping regression model

Two time series of financial losses may be observed in different overlapping windows, serially dependent, heteroscedastic, and cross-sectionally dependent. Fitting a regression model to each of the two time series, we construct an improved least squares estimator in one series exploiting the cross-sectional dependence with the other series. We employ a random weight bootstrap method to define the new estimator and to establish its asymptotic normality. The developed inference is robust against heteroscedasticity as we do not estimate the GARCH errors. Simulations confirm the efficiency improvement through substantial variance reduction, especially when the cross-sectional dependence is strong and the second series is longer. We illustrate the usefulness of the method by analyzing mutual funds' returns.