For long-memory time series, we show that the Toeplitz system sect;n(f)x = b can be solved inO(n log5=2 n) operations using a well-known version of the preconditioned conjugate gradient method, where sect;n(f) is the npound;n covariance matrix, f is the spectral density and b is a known vector....

We propose and derive the asymptotic distribution of a tapered narrow-band least squares estimator(NBLSE) of the cointegration parameter Atilde; Acirc; Atilde; Acirc;² in the framework of fractional cointegration.This tapered estimator is invariant to deterministic polynomial trends. In particular,...