Long-memory time series
= Long-memory time series
A <weakly stationary process> can have very slowly decaying <autocovariance>, for example $\gamma(h)\sim Ch^{-\beta}$ with $C>0$ and $0<\beta<1$. Its sample mean can require a normalization different from $\sqrt T$. Long memory is dependence over long lags, rather than a changing marginal distribution.