arh_rkhs function

Autoregressive Hilbertian Model using RKHS

Estimates an autoregresive Hilbertian model of order 1 for functional time series. The temporal dependence is estimated in the Hilbert projection space which has a reproducing kernel as proposed in Hernández et al (2021) arXiv:2105.13627 and Wang et al (2020) arXiv:2011.13993.

arh_rkhs(fdata)

Arguments

• fdata: an fdata object containing the functional objects and the lambda coefficients of the d dimensional RKHS representation.

Returns

• fdata: smoothed curves. - lambda_cent: centered coefficients of the d dimensional RKHS representation.

• lambda_ce: average coefficients of the d dimensional RKHS representation. - rho: autocorrelation operator computed as: Gamma_0$$Psi = $Gamma_1$. $Gamma_0$ correspond to the Covariance and $Gamma_0$ correspond to the Cross-Covariance (of lag 1) operators, both estimated using the coefficients $lambda$.

References

N. Hernández, J. Cugliari, J. Jacques. Simultaneous Predictive Bands for Functional Time Series using Minimum Entropy Sets. arXiv:2105.13627 (2021). D. Wang, Z. Zhao, R. Willett, C. Y. Yau, Functional autoregressive processes in reproducing kernel hilbert spaces, arXiv preprint arXiv:2011.13993 (2020).

Author(s)

N. Hernández and J. Cugliari