A semiparametric two-step estimator in a multivariate long memory model

This paper analyzes a two-step estimator of the long memory parameters of a vector process. The objective function considered is a semiparametric version of the multivariate Gaussian likelihood function in the frequency domain. In our context, semiparametric refers to the fact that only periodogram ordinates evaluated in a degenerating neighborhood of zero frequency are employed in the estimation procedure. Asymptotic normality is established under mild conditions that do not include Gaussianity. Furthermore, the simplicity of the form of the covariance matrix of the estimates facilitates statistical inference. We include an application of these estimates to exchange rate data.