seasonal: a positive integer variable specifying the seasonality parameter.
cpv: a numeric with values in [0,1] which determines the cumulative proportion variance explained by the first kn eigencomponents.
kn: an integer variable specifying the number of eigencomponents.
method: a character string giving the method of estimation. The following values are possible: "MME" for Method of Moments, "ULSE" for Unconditional Least Square Estimation Method, and "KOE" for Kargin-Ontaski Estimation.
a: a numeric with value in [0,1].
Returns
A matrix of size p*p.
Examples
# Generate Brownian motion noiseN <-300# the length of the seriesn <-200# the sample rate that each function will be sampledu <- seq(0,1, length.out = n)# argvalues of the functionsd <-45# the number of basesbasis <- create.fourier.basis(c(0,1), d)# the basis systemsigma <-0.05# the std of noise normZ0 <- matrix(rnorm(N * n,0, sigma), nrow = n, nc = N)Z0[,1]<-0Z_mat <- apply(Z0,2, cumsum)# N standard Brownian motionZ <- smooth.basis(u, Z_mat, basis)$fd
# Simulate random SFAR(1) datakr <-function(x, y){(2-(2* x -1)^2-(2* y -1)^2)/2}s <-5# the period numberX <- rsfar(kr, s, Z)plot(X)# SFAR(1) model parameter estimation:Model1 <- sfar(X, seasonal = s, kn =1)