Estimation in Functional Lagged Regression

Siegfried Hörmann, Łukasz Kidziński and Piotr Kokoszka

Journal of Time Series Analysis, 2015, vol. 36, issue 4, 541-561

Abstract: type="main" xml:id="jtsa12114-abs-0001"> The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-super-2 in applications. A spectral approach to the estimation of these coefficients is proposed and asymptotically justified under a general nonparametric condition on the temporal dependence of the input series. Since the data are infinite-dimensional, the estimation involves a spectral-domain dimension-reduction technique. Consistency of the estimators is established under general data-dependent assumptions on the rate of the dimension-reduction parameter. Their finite-sample performance is evaluated by a simulation study that compares two ad hoc approaches to dimension reduction with an alternative, asymptotically justified method.

Date: 2015
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