Investigation of long range dependence in the annual rainfall structure from a global database

High scientific interest is raised around the hypothesis testing of long range dependence structure in geophysical data since Hurst discovered the phenomenon in 1951. Herein, we examine the hypothesis of long range dependence in the annual rainfall structure. A global data base of daily rainfall data GHCN (Global Historical Climatology Network) is processed along with the infilling of missing values. Based on length and quality criteria, 1265 rainfall stations are chosen for the estimation. Statistical properties of rainfall are also derived from the stations. In order to estimate the Hurst coefficient, the aggregated variance method as well as the LSSD (Least Squares based on Standard Deviation) method are applied to the data. Hypothesis testing for the existence of a common Hurst coefficient is conducted. In addition, the study of the autocorrelation function and the comparison with an AR(1) structure are performed as they provide a deeper insight on the matter. The results are in favor of the existence of long range dependence for the 3/4 of rainfall stations, although there exist considerable differences among them in the intensity of the phenomenon. In the future, the longer existing data lengths will perhaps enable a more certain estimation.