mulmar: Multivariate Case of Minimum AIC Method of AR Model Fitting

In timsac: Time Series Analysis and Control Package

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 n/2d where n is the length and d is the dimension of the time series y. Default is min(2 \sqrt{n}, n/2d).
plot	logical. If TRUE, daic[[1]], \ldots , daic[[d]] are plotted.

Details

Multivariate autoregressive model is defined by

y(t) = A(1)y(t-1) + A(2)y(t-2) +\ldots+ A(p)y(t-p) + u(t),

where p is order of the model and u(t) is Gaussian white noise with mean 0 and variance matrix matv. AIC is defined by

AIC = n \log(det(v)) + 2k,

where n is the number of data, v is the estimate of innovation variance matrix, det is the determinant and k 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 i-th regressor.
subregcoef	subset regression coefficients.
rvar	residual variance.
aicf	final estimate of AIC (=n\log(rvar)+2np).
respns	instantaneous response.
regcoef	regression coefficients matrix.
matv	innovation variance matrix.
morder	order of the MAICE model.
arcoef	AR coefficients. arcoef[i,j,k] shows the value of i-th row, j-th column, k-th order.
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

timsac documentation built on Sept. 30, 2023, 5:06 p.m.