DCSmooth (version 1.1.2)

sfarima.est: 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.	Y

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

# NOT RUN {
# 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

# }