innov.spec: Spectrum of the innovation term epsilon.

In spate: Spatio-Temporal Modeling of Large Data Using a Spectral SPDE Approach

Spectrum of the innovation term epsilon.

Description

Spectrum of the innovation term epsilon.

Usage

innov.spec(wave,n,ns=4,rho0,sigma2,zeta,rho1,alpha,gamma,nu=1,dt=1,norm=TRUE)

Arguments

wave	Spatial wavenumbers.
n	Number of grid points on each axis. n x n is the total number of spatial points.
ns	Number of real Fourier functions that have only a cosine and no sine term. 'ns' is maximal 4.
rho0	Range of the Matern covariance funtion for the innovation term epsilon
sigma2	Marginal variance of the Matern covariance funtion for the innovation term epsilon
zeta	Damping parameter
rho1	Range parameter of the diffusion term
alpha	Parameter that determines the direction of anisotropy in the diffusion term
gamma	Parameter that determines the amount of anisotropy in the diffusion term
nu	Smoothness parameter of the Matern covariance function for the innovations. By default, this equals 1 corresponding to the Whittle covariance function.
dt	Temporal lag between two time points. By default, this equals 1.
norm	logical; if 'TRUE' the spectrum is multiplied by n*n so that after applying the real Fourier transform 'real.FFT' one has the correct normalization.

Value

Vector with the spectrum of the integrated innovation term epsilon hat.

Author(s)

Fabio Sigrist

Examples

n <- 100
spec <- innov.spec(wave=spate.init(n=n,T=1)$wave,n=n,rho0=0.05,sigma2=0.5,zeta=0.5,
                   rho1=0.05,alpha=pi/4,gamma=2,norm=TRUE)
sim <- real.fft(sqrt(spec)*rnorm(n*n),n=n,inv=FALSE)
image(1:n,1:n,matrix(sim,nrow=n),main="Sample from the integrated
stochastic innovation",xlab="",ylab="",col=cols())

spate documentation built on Oct. 3, 2023, 5:09 p.m.