On Out-of-Sample Statistics for Time-Series

This paper studies an out-of-sample statistic for time-series prediction that is analogous to the widely used R2 in-sample statistic. We propose and study methods to estimate the variance of this out-of-sample statistic. We suggest that the out-of-sample statistic is more robust to distributional and asymptotic assumptions behind many tests for in-sample statistics. Furthermore we argue that it may be more important in some cases to choose a model that generalizes as well as possible rather than choose the parameters that are closest to the true parameters. Comparative experiments are performed on a financial time-series (daily and monthly returns of the TSE300 index). The experiments are performed for varying prediction horizons and we study the relation between predictibility (out-of-sample R2), variability of the out-of-sample R2 statistic, and the prediction horizon.
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