arh_rkhs {fpcb}

Autoregressive Hilbertian Model using RKHS

Description

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>.

Usage

arh_rkhs(fdata)

Arguments

fdata

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

Value

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_0Psi = 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.

Author(s)

N. Hernández and J. Cugliari

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).