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 study the small sample behaviour of two goodness-of-fit tests for time series models whichhave been proposed recently in the literature. Both tests are generalizations of the popular Box-Ljung-Pierce portmanteau test, one in the time domain and the other in the frequency domain.The tests are...

We present a goodness of fit test for time series models based on the discrete spectral averageestimator. Unlike current tests of goodness of fit, the asymptotic distribution of our test statisticallows the null hypothesis to be either a short or long range dependence model. Our test isin the...

We propose a new complex-valued taper and derive the properties of a tapered Gaussian semiparametric estimator of the long-memory parameter d Atilde; Acirc; Atilde; Acirc; (-0.5, 1.5). The estimator and its accompanying theory can be applied to generalized unit root testing. In the proposed method,...