Enhanced time series predictability with well-defined structures

For any given time series, how to optimize its forecast strategies and what prediction model is adopted are of great importance. In order to reach this goal, insight from analyzing predictability of series with known structure information is necessary. Time series generated by theoretical models with four kinds of known predictive structures, i.e., short-term correlation, long-term correlation, and multifractal and chaotic patterns, are applied to demonstrate that there is a well-defined relation between series' intrinsic predictability and prediction accuracy of any specific prediction model. And results show that both intrinsic predictability and prediction accuracy are enhanced by these well-defined structures. There are different regimes in the relation between intrinsic predictability and prediction accuracy for series with different known deterministic or stochastic predictive structures. These regimes in the relation between intrinsic predictability and prediction accuracy can guide us to preselect a suitable prediction model and forecast strategies for any underlying series by only analyzing the permutation entropy of a given series. Results from three pieces of climate series further confirm that insights from theoretical series with known structure information indeed work well.