sfarima.est {DCSmooth}

Estimation of a SFARIMA-process

Description

Parametric Estimation of a SFARIMA(p, q, d)-process on a lattice.

Usage

sfarima.est(Y, model_order = list(ar = c(1, 1), ma = c(1, 1)))

Arguments

Y

A numeric matrix that contains the demeaned observations of the random field or functional time-series.

model_order

A list containing the orders of the SFARIMA model in the form model_order = list(ar = c(p1, p2), ma = c(q1, q2)). Default value is a SFARIMA((1, 1), (1, 1), d) model.

Value

The function returns an object of class "sfarima" including

Y	The matrix of observations, inherited from input.
innov The estimated innovations.
model	The estimated model consisting of the coefficient matrices ar and ma, the estimated long memory parameters d and standard deviation of innovations sigma.
stnry	An logical variable indicating whether the estimated model is stationary.

Details

The MA- and AR-parameters as well as the long-memory parameters

d

of a SFARIMA process are estimated by minimization of the residual sum of squares RSS. Lag-orders of SFARIMA(p, q, d) are given by p = (p_1, p_2), q = (q_1, q_2), where p_1, q_1 are the lags over the rows and p_2, q_2 are the lags over the columns. The estimated process is based on the (separable) model

\varepsilon_{ij} = \Psi_1(B) \Psi_2(B) \eta_{ij}

, where

\Psi_i = (1 - B_i)^{-d_i}\phi^{-1}_i(B_i)\psi_i(B_i), i = 1,2

.

See Also

sarma.est, sfarima.sim

Examples

# See vignette("DCSmooth") for examples and explanation

## simulation of SFARIMA process
ma <- matrix(c(1, 0.2, 0.4, 0.1), nrow = 2, ncol = 2)
ar <- matrix(c(1, 0.5, -0.1, 0.1), nrow = 2, ncol = 2)
d <- c(0.1, 0.1)
sigma <- 0.5
sfarima_model <- list(ar = ar, ma = ma, d = d, sigma = sigma)
sfarima_sim <- sfarima.sim(50, 50, model = sfarima_model)

## estimation of SFARIMA process
sfarima.est(sfarima_sim$Y)$model
sfarima.est(sfarima_sim$Y, 
           model_order = list(ar = c(1, 1), ma = c(0, 0)))$model