sfar function

Estimation of an SFAR(1) Model

Estimation of an SFAR(1) Model

Estimate a seasonal functional autoregressive (SFAR) model of order 1 for a given functional time series.

sfar( X, seasonal, cpv = 0.85, kn = NULL, method = c("MME", "ULSE", "KOE"), a = ncol(Coefs)^(-1/6) )

Arguments

  • X: a functional time series.
  • 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 noise N <- 300 # the length of the series n <- 200 # the sample rate that each function will be sampled u <- seq(0, 1, length.out = n) # argvalues of the functions d <- 45 # the number of bases basis <- create.fourier.basis(c(0, 1), d) # the basis system sigma <- 0.05 # the std of noise norm Z0 <- matrix(rnorm(N * n, 0, sigma), nrow = n, nc = N) Z0[, 1] <- 0 Z_mat <- apply(Z0, 2, cumsum) # N standard Brownian motion Z <- smooth.basis(u, Z_mat, basis)$fd # Simulate random SFAR(1) data kr <- function(x, y) { (2 - (2 * x - 1)^2 - (2 * y - 1)^2) / 2 } s <- 5 # the period number X <- rsfar(kr, s, Z) plot(X) # SFAR(1) model parameter estimation: Model1 <- sfar(X, seasonal = s, kn = 1)