Entropy as an A Priori Indicator of Forecastability

The ability to accurately determine the a priori forecastability of a time series is an important endeavour for forecasting practitioners as it provides guidance on the potential for accurate forecasts and the associated degree of effort that is warranted. Measures of entropy, such as sample entropy, provide an assessment of the regularity or similarity within a time series. We posit that series with low in-sample entropy, i.e. high regularity, will positively correlate with low out-of-sample forecast error, as measured by the mean absolute scaled error (MASE). To assess this we adopt the 3003 time series used in the M3 forecasting competition spanning micro, industry, macro, finance, and demographic series. We calculate the in-sample sample entropy and out-of-sample MASE for all 3003 series using a common univariate forecasting method. We demonstrate that the a priori sample entropy is indeed a useful predictor of out-of-sample forecast performance, subject to the well-researched problem of structural breaks. We recommend that forecasting practitioners adopt such entropy measures, alongside well-established tests for seasonality and trend, to better understand the likelihood of successful forecasting outcomes.