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Estimation in Functional Lagged Regression

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  • Siegfried Hörmann
  • Łukasz Kidziński
  • Piotr Kokoszka

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.

Suggested Citation

  • Siegfried Hörmann & Łukasz Kidziński & Piotr Kokoszka, 2015. "Estimation in Functional Lagged Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 541-561, July.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:4:p:541-561
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    File URL: http://hdl.handle.net/10.1111/jtsa.12114
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    References listed on IDEAS

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    1. Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2010. "Tests for Error Correlation in the Functional Linear Model," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1113-1125.
    2. Comte, Fabienne & Johannes, Jan, 2012. "Adaptive functional linear regression," LIDAM Reprints ISBA 2012031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Chiou, Jeng-Min & Muller, Hans-Georg, 2007. "Diagnostics for functional regression via residual processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4849-4863, June.
    4. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    5. Hervé Cardot & Frédéric Ferraty & André Mas & Pascal Sarda, 2003. "Testing Hypotheses in the Functional Linear Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 241-255, March.
    6. Piotr Kokoszka & Matthew Reimherr, 2013. "Predictability of shapes of intraday price curves," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 285-308, October.
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    Cited by:

    1. Tomáš Rubín & Victor M. Panaretos, 2020. "Functional lagged regression with sparse noisy observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 858-882, November.
    2. Fang, Qin & Guo, Shaojun & Qiao, Xinghao, 2022. "Finite sample theory for high-dimensional functional/scalar time series with applications," LSE Research Online Documents on Economics 114637, London School of Economics and Political Science, LSE Library.

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