Studying the impact of fluctuations, spikes and rare events in time series through a wavelet entropy predictability measure

Data has become one of the most crucial sources of human life. In particular, the ability to predict the future through data is a widely studied topic. In finance, as an instance, increased volatility, fluctuations, low-frequency events, and rare events negatively affect the predictability of data, thus increasing the level of risk. As a consequence, the inability to make accurate predictions on future events increases the uncertainty and variability of a given scenario, indicating a consequent increase in risk. In this paper, we analyse data predictability introducing a new measure based on entropy and the wavelet transform. In particular, we show that the data are less predictable than one might expect due to the mentioned fluctuations and low-frequency events. Furthermore, we apply our tool to real data, in particular to time series of commodities. As a result, thanks to this new measure, we can observe that the price time series under analysis exhibit a significant level of unpredictability due to increased volatility, fluctuations, and the influence of low-frequency events.