### Abstract

^{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.

Original language | Undefined/Unknown |
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Pages (from-to) | 541-561 |

Number of pages | 21 |

Journal | Journal of time series analysis |

Volume | 36 |

Issue number | 4 |

Publication status | Published - 2015 |

### Cite this

*Journal of time series analysis*,

*36*(4), 541-561.

**Estimation in Functional Lagged Regression.** / Hörmann, Siegfried; Kidzinski, Lukasz; Kokoszka, Piotr P.

Research output: Contribution to journal › Article › Research › peer-review

*Journal of time series analysis*, vol. 36, no. 4, pp. 541-561.

}

TY - JOUR

T1 - Estimation in Functional Lagged Regression

AU - Hörmann, Siegfried

AU - Kidzinski, Lukasz

AU - Kokoszka, Piotr P.

N1 - DOI: 10.1111/jtsa.12114

PY - 2015

Y1 - 2015

N2 - 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 L2 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.

AB - 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 L2 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.

M3 - Artikel

VL - 36

SP - 541

EP - 561

JO - Journal of time series analysis

JF - Journal of time series analysis

SN - 0143-9782

IS - 4

ER -