Hurst Exponent with ARIMA and Simple Exponential Smoothing for Measuring Persistency of M3- Competition Series

The Hurst exponent is a metric used to evaluate whether a time series exhibits long-term memory, and it is used to identify its complexity. Besides, forecasting methods are tested using time series from Makridakis competition. Additionally, Exponential Smoothing is among the best forecasting methods of this competition, and ARIMA is one of the most used for many applications. Nevertheless, the quality of using the Hurst exponent in Makridakis M3-Competition for measuring how well Simple Exponential Smoothing and ARIMA are adapted to a specific time series is unknown. In this work, we show the impact of applying the Hurst exponent using the complete set of series from the M3-Competition. We used k-means as clustering algorithm for the 3003 Hurst exponent values of these series, improving the visualization of all of the data to identify a relationship between Hurst exponent with MAPE and sMAPE forecasting error of the Simple Exponential Smoothing and ARIMA. Finally, the experimentation shows that Hurst exponent and MAPE for the tested methods are inversely related in most of the cases and that there is a trend between them.