dpca.var {freqdom} | R Documentation |
Proportion of variance explained
Description
Computes the proportion of variance explained by a given dynamic principal component.
Usage
dpca.var(F)
Arguments
F |
|
Details
Consider a spectral density matrix \mathcal{F}_\omega
and let \lambda_\ell(\omega)
by the
\ell
-th dynamic eigenvalue. The proportion of variance described by the \ell
-th dynamic
principal component is given as
v_\ell:=\int_{-\pi}^\pi \lambda_\ell(\omega)d\omega/\int_{-\pi}^\pi \mathrm{tr}(\mathcal{F}_\omega)d\omega.
This function numerically computes the vectors (v_\ell\colon 1\leq \ell\leq d)
.
For more details we refer to Chapter 9 in Brillinger (2001), Chapter 7.8 in Shumway and Stoffer (2006) and to Hormann et al. (2015).
Value
A d
-dimensional vector containing the v_\ell
.
References
Hormann, S., Kidzinski, L., and Hallin, M. Dynamic functional principal components. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 77.2 (2015): 319-348.
Brillinger, D. Time Series (2001), SIAM, San Francisco.
Shumway, R.H., and Stoffer, D.S. Time Series Analysis and Its Applications (2006), Springer, New York.
See Also
dpca.filters
, dpca.KLexpansion
, dpca.scores