Norberto Lobato Garcia, Ignacio
(1995)
Multivariate analysis of long memory series in the frequency domain.
PhD thesis, London School of Economics and Political Science.
Abstract
This thesis examines some statistical procedures in the frequency domain to analyze long-memory series. We define a long-memory series and review part of the literature. Then we proceed by analyzing different estimation procedures for H, the parameter that characterizes the existence of long-memory. Parametric estimates have as a main drawback that they can lead to inconsistent estimates of H if the parametric model is misspecified. Therefore we focus on semiparametric estimates in the frequency domain. In our case, semiparametric means that we only need to assume a parametric model for the spectral density in a neighbourhood of zero frequency. We focus mainly on a multivariate framework. First we analyze estimates based on the average periodogram. We prove the consistency of the average cross-periodogram for the cumulative cross-spectrum. We also establish the asymptotic distribution in the scalar case. Then we focus on an implicit estimate based on a discrete approximation of the Gaussian likelihood in a neighbourhood of zero frequency. We prove the consistency and asymptotic normality of this estimate. Based on this estimate we establish a Lagrange multiplier test for weak dependence. We finish with an application of these methods to financial data.
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