ABSTRACT
The phenomenon of long memory was observed in applications long before appropriate stochastic models were known. Several heuristic methods to estimate the long-memory parameter Hwere suggested. Best known is the R/S statistic, which was first proposed by Hurst in a hydrological context. Other methods include the log-log correlogram, the log-log plot of var versus n, the semivariogram, and least squares regression in the spectral domain. In contrast, for short-memory processes, the log-log correlogram should show divergence to minus infinity at a rate that is at least exponential. For long-memory processes, partial correlations decay at the hyperbolic rate k-H-12. For short-memory processes, the partial correlations are bounded by an exponentially decaying bound. The log-log plot of partial correlations can be interpreted in an analogous way as the log-log correlogram. The variogram is often used in geostatistics. In particular, for spatial processes it is frequently used together with a methodology known under the name of kriging.
