Granger, C.W.J.

process transformation series long-memory long-memory parameter parameter autocorrelation time series gaussian proposition hermite function moment xt ~ i result hermite rank section yt z t granger memory table polynomial trend property proposition 1 power non-stationary error simulation square hermite polynomials j =0 t theory h z t time series analysis variance rescaled long-memory properties antipersistent distribution simulation results long-memory processes x t 2 estimate converge 0.2 figure covariance power transformations autocorrelation function nonlinear density observation regression rescaling frequency value point antipersistent process 0.2 437 95 c j t journal h +1 j 0.4 proof 0.01 g j 0 antipersistence hermite rank x c 2 2 divergence rate long-memory process gaussian process form t 4 table 2 table 3 2 c j nonlinear transformations non-stationary long-memory processes analysis