ABSTRACT
There is a long history of studying long-range dependent models for strictly stationary time series. Hurst (1951), Mandelbrot and Van Ness (1968), Granger and Joyeux (1980), and Geweke and Porter-Hudak (1983) were among the first to study time series models with long-range dependence through using the spectral density approach. Attention has recently been given to two single-parameter models in which the spectral density function is proportional to ω−γ , 1 < γ < 2, for ω near zero, and the asymptotic decay of the autocorrelation function is proportional to τγ−1. Because the spectral density function is unbounded at ω = 0equivalently, the autocorrelation function is not summable, these are long-range dependent (LRD) (long memory; strong dependent) models. A recently published survey of long-range dependence literature up to about 1994 is Beran (1994). See also Robinson (1994), Baillie and King (1996), Anh and Heyde (1999) and Robinson (2003) for recent developments of long-range dependence in econometrics and statistics.
