An investigation on the relationship between the Hurst exponent and the predictability of a rainfall time series

Rainfall prediction is a very challenging task due to its dependence on many meteorological parameters. Because of the complex nature of rainfall, the uncertainty associated with its predictability continues to be an issue in rainfall forecasting. The Hurst exponent is considered as a measure of persistence and it is believed that if a time series has persistence (as reflected by a Hurst exponent value greater than 0.5) it is also predictable. However, very limited studies have been carried out to demonstrate this hypothesis. This study, through experimental work on hypothetical data as well as real data, demonstrates that the Hurst exponent can be taken as an indicator for predictability provided that the exponent values at "smaller levels" of the time series are also significantly greater than 0.5 together with the Hurst exponent of the overall time series. It is also shown that it is better to predict the "similarity" aspect associated with a time series (and derive the predicted rainfall) than to predict the rainfall directly.