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 possiblities of zero coefficients at the begining 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, tmp.file=NULL)

Arguments

y a multivariate time series.
max.order upper limit of the order of AR model. Default is 2*sqrt(n), where n is the length of the time series y.
plot logical. If TRUE daic[[1]],...,daic[[d]] are plotted, where d is the dimention of the multivariate time series.
tmp.file a character string naming a file written intermediate results of AIC minimazation. If NULL (default) output no file.

Details

Multivariate autoregressive model is defined by

y(t) = A(1)y(t-1) + A(2)y(t-2) +...+ 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 = nlog(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(m) (m = 0,...,max.order).
aicmin minimum AIC.
daic AIC(m)-aicmin (m = 0,...,max.order).
order.maice order of minimum AIC.
v.maice innovation variance attained at m = order.maice.
np number of parameters.
jnd specification of i-th regressor.
subregcoef subset regression coefficients.
rvar residual variance.
aicf final estimate of AIC (=nlog(rvar)+2np).
respns instantaneous response.
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.Kiragawa, 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),3,3,byrow=TRUE)
  ar[,,2] <- matrix(c(0,  -0.3,  0.5,
                      0.7, -0.4,  1,
                      0,   -0.5,  0.3),3,3,byrow=TRUE)
  x <- matrix(rnorm(200*3),200,3)
  y <- mfilter(x,ar,"recursive")
  z <- mulmar(y, max.order=10)
  z$arcoef

[Package timsac version 1.2.1 Index]