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Detecting changes in functional linear models

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  • Horváth, Lajos
  • Reeder, Ron

Abstract

We observe two sequences of curves which are connected via an integral operator. Our model includes linear models as well as autoregressive models in Hilbert spaces. We wish to test the null hypothesis that the operator did not change during the observation period. Our method is based on projecting the observations onto a suitably chosen finite dimensional space. The testing procedure is based on functionals of the weighted residuals of the projections. Since the quadratic form is based on estimating the long-term covariance matrix of the residuals, we also provide some results on Bartlett-type estimators.

Suggested Citation

  • Horváth, Lajos & Reeder, Ron, 2012. "Detecting changes in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 310-334.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:310-334
    DOI: 10.1016/j.jmva.2012.04.007
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    References listed on IDEAS

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    1. 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.
    2. Wied, Dominik & Krämer, Walter & Dehling, Herold, 2012. "Testing For A Change In Correlation At An Unknown Point In Time Using An Extended Functional Delta Method," Econometric Theory, Cambridge University Press, vol. 28(3), pages 570-589, June.
    3. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    4. Horváth, Lajos & Husková, Marie & Kokoszka, Piotr, 2010. "Testing the stability of the functional autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 352-367, February.
    5. Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1218-1245, August.
    6. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1449-1459, December.
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    2. Liebl, Dominik & Walders, Fabian, 2019. "Parameter regimes in partial functional panel regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 105-115.

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