timsac (version 1.3.8-4)

fpec: AR model Fitting for Control

Description

Perform AR model fitting for control.

Usage

fpec(y, max.order = NULL, control = NULL, manip = NULL)

Value

cov

covariance matrix rearrangement.

fpec

FPEC (AR model fitting for control).

rfpec

RFPEC.

aic

AIC.

ordermin

order of minimum FPEC.

fpecmin

minimum FPEC.

rfpecmin

minimum RFPEC.

aicmin

minimum AIC.

perr

prediction error covariance matrix.

arcoef

a set of coefficient matrices. arcoef[i,j,k] shows the value of \(i\)-th row, \(j\)-th column, \(k\)-th order.

Arguments

y

a multivariate time series.

max.order

upper limit of model order. Default is \(2 \sqrt{n}\), where \(n\) is the length of time series y.

control

controlled variables. Default is \(c(1:d)\), where \(d\) is the dimension of the time series y.

manip

manipulated variables. Default number of manipulated variable is \(0\).

References

H.Akaike and T.Nakagawa (1988) Statistical Analysis and Control of Dynamic Systems. Kluwer Academic publishers.

Examples

ar <- array(0, dim = c(3,3,2))
ar[, , 1] <- matrix(c(0.4,  0,   0.3,
                      0.2, -0.1, -0.5,
                      0.3,  0.1, 0), nrow = 3, ncol = 3, byrow = TRUE)
ar[, , 2] <- matrix(c(0,  -0.3,  0.5,
                      0.7, -0.4,  1,
                      0,   -0.5,  0.3), nrow = 3, ncol = 3, byrow = TRUE)
x <- matrix(rnorm(200*3), nrow = 200, ncol = 3)
y <- mfilter(x, ar, "recursive")
fpec(y, max.order = 10)