Prediction analysis of long-term memory effect for calamity gray series

Abstract

It is adequate to use the gray theory for modeling and forecasting short-term calamity series. The forecast of calamity gray series is equivalent to predicting an extraordinary event in nature. In order to look for the regularity, the calamity date series, created from the threshold for a fixed time-interval series, are studied. In this paper, the Hurst exponent is applied to defining the long-term memory effect of the simulated calamity series, and is tested for the feasibility of using it as pre-requisite information before the gray modeling and forecasting. Based on the fractional Brownian motion (fBm) model, the time series with a definite length or quantity of data are derived assuming that various kinds of memory effect exist. Different threshold values are defined to yield or to analogize the calamity date series that are required in the prediction of the gray calamity events. After case study, both of the simulated and real seismic data show that the Hurst exponents are greater than 0.5 and, therefore, indicate that the long-term memory ef-fect exists. The correlation between the Hurst exponent and the gray modeling parameter, a, provides criteria for the classification of the forecast.