Bagging binary and quantile predictors for time series

Bootstrap aggregating or Bagging, introduced by Breiman (1996a. Bagging predictors. Machine Learning 24, 123–140), has been proved to be effective to improve on unstable forecast. Theoretical and empirical works using classification, regression trees, variable selection in linear and non-linear regression have shown that bagging can generate substantial prediction gain. However, most of the existing literature on bagging has been limited to the cross sectional circumstances with symmetric cost functions. In this paper, we extend the application of bagging to time series settings with asymmetric cost functions, particularly for predicting signs and quantiles. We use quantile predictions to construct a binary predictor and the majority-voted bagging binary prediction. We show that bagging may improve the binary prediction in small sample, but it does not improve in large sample. Various bagging forecast combination weights are used such as equal weighted and Bayesian model averaging (BMA) weighted combinations. For demonstration, we present results from Monte Carlo experiments and from empirical applications using monthly S&P500 and NASDAQ stock index returns.