Quantifying and Estimating the Predictability Upper Bound of Univariate Numeric Time Series

The intrinsic predictability of a given time series indicates how well an (ideal) algorithm could potentially predict it when trained on the time series data. Being able to compute the intrinsic predictability helps the developers of prediction algorithms immensely in deciding whether there is further optimization potential, as it tells them how close they are to what is (theoretically) achievable. We call the intrinsic predictability the predictability upper bound ¶imax and propose a novel method for quantifying and estimating it for univariate numeric time series. So far, this has only been done for symbolic time series, even though most real-world time series are numeric by nature. We base our technique on the close relationship between entropy and predictability, utilizing the entropy rate of a time series to compute ¶imax . Since existing entropy rate estimators, such as those based on the Lempel-Ziv compression algorithm, only work for symbolic data, we develop new estimators using tolerance thresholds for matching numeric values. We demonstrate that ¶imax is an effective upper bound that characterizes the intrinsic predictability of a time series. We give formal proofs and we validate our arguments experimentally by comparing ¶imax with the prediction accuracy of different state-of-the-art models on various real-world datasets from different domains.