sarma.est {DCSmooth}

Estimation of an SARMA-process

Description

Parametric Estimation of an SARMA(p, q)-process on a lattice.

Usage

sarma.est(Y, method = "HR", model_order = list(ar = c(1, 1), ma = c(1, 1)))

qarma.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.

method

Method used for estimation of the parameters. One of "HR", "sep", "RSS", default value is "HR"

model_order

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

Value

The function returns an object of class "sarma" 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 and standard deviation of innovations sigma.
stnry	An logical variable indicating whether the estimated model is stationary.

Details

The MA- and AR-parameters of a top-left quadrant ARMA process are estimated by the specified method. The lag-orders of the SARMA(p, q) 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 estimation process is based on the model

\phi(B_{1}B_{2})X_{i,j} = \theta(B_{1}B_{2})u_{i,j}

.

See Also

sarma.sim, sfarima.est

Examples

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

## simulation of SARMA 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)
sigma <- 0.5
sarma_model <- list(ar = ar, ma = ma, sigma = sigma)
sarma_simulated <- sarma.sim(100, 100, model = sarma_model)
sarma_simulated$model

## estimation of SARMA process
sarma.est(sarma_simulated$Y)$model
sarma.est(sarma_simulated$Y, 
           model_order = list(ar = c(1, 1), ma = c(1, 1)))$model