sfarima.est: Estimation of a SFARIMA-process

In DCSmooth: Nonparametric Regression and Bandwidth Selection for Spatial Models

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 = (p1, p2), q = (q1, q2), where p1, q1 are the lags over the rows and p2, q2 are the lags over the columns. The estimated process is based on the (separable) model

\varepsilon_{ij} = Ψ_1(B) Ψ_2(B) η_{ij}

, where

Ψ_i = (1 - B_i)^{-d_i}φ^{-1}_i(B_i)ψ_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

DCSmooth documentation built on Oct. 21, 2021, 5:07 p.m.