mulmar {timsac} | R Documentation |
Multivariate Case of Minimum AIC Method of AR Model Fitting
Description
Fit a multivariate autoregressive model by the minimum AIC procedure. Only the possibilities of zero coefficients at the beginning and end of the model are considered. The least squares estimates of the parameters are obtained by the householder transformation.
Usage
mulmar(y, max.order = NULL, plot = FALSE)
Arguments
y |
a multivariate time series. |
max.order |
upper limit of the order of AR model, less than or equal to
|
plot |
logical. If |
Details
Multivariate autoregressive model is defined by
where is order of the model and
is Gaussian white noise
with mean
and variance matrix
matv
. AIC is defined by
where is the number of data,
is the estimate of innovation
variance matrix,
is the determinant and
is the number of
free parameters.
Value
mean |
mean. |
var |
variance. |
v |
innovation variance. |
aic |
AIC. |
aicmin |
minimum AIC. |
daic |
AIC-aicmin. |
order.maice |
order of minimum AIC. |
v.maice |
MAICE innovation variance. |
np |
number of parameters. |
jnd |
specification of |
subregcoef |
subset regression coefficients. |
rvar |
residual variance. |
aicf |
final estimate of AIC ( |
respns |
instantaneous response. |
regcoef |
regression coefficients matrix. |
matv |
innovation variance matrix. |
morder |
order of the MAICE model. |
arcoef |
AR coefficients. |
aicsum |
the sum of aicf. |
References
G.Kitagawa and H.Akaike (1978) A Procedure for The Modeling of Non-stationary Time Series. Ann. Inst. Statist. Math., 30, B, 351–363.
H.Akaike, G.Kitagawa, E.Arahata and F.Tada (1979) Computer Science Monograph, No.11, Timsac78. The Institute of Statistical Mathematics.
Examples
# Example 1
data(Powerplant)
z <- mulmar(Powerplant, max.order = 10)
z$arcoef
# Example 2
ar <- array(0, dim = c(3,3,2))
ar[, , 1] <- matrix(c(0.4, 0, 0.3,
0.2, -0.1, -0.5,
0.3, 0.1, 0), nrow = 3, ncol = 3, byrow = TRUE)
ar[, , 2] <- matrix(c(0, -0.3, 0.5,
0.7, -0.4, 1,
0, -0.5, 0.3), nrow = 3, ncol = 3,byrow = TRUE)
x <- matrix(rnorm(200*3), nrow = 200, ncol = 3)
y <- mfilter(x, ar, "recursive")
z <- mulmar(y, max.order = 10)
z$arcoef