mAr.est {mAr}R Documentation

Estimation of multivariate AR(p) model

Description

Stepwise least-squares estimation of multivariate AR(p) model (based on Neumaier and Schneider 2001); given a minimal and maximal model order, the optimal model order is chosen based on Schwartz Bayesian Criterion (SBC).

Usage

mAr.est(x, pmin, pmax, ...)

Arguments

x matrix of multivariate time series
pmin minimal model order
pmax maximal model order
... additional arguments for specific methods

Details

Fits a m-variate AR(p) model given by

X[t]=w + A1 X[t-1] +...+ Ap X[t-p] +e[t]

where
X[t]=[X1(t)...Xm(t)]' is a vector of length m
w is a m-length vector of intercept terms
A=[A1 ... Ap] is a mp x m matrix of autoregressive coefficients
e(t) is a m-length uncorrelated noise vector with mean 0 and m x m covariance matrix C

Value

A list with components:

pHat order of the fitted model,chosen by SBC
SBC Schwartz Bayesian Criterion
wHat vector of intercept terms
AHat matrix of estimated autoregression coefficients for the fitted model
CHat noise covariance matrix
res residuals from the fitted model

Author(s)

S. M. Barbosa

References

Neumaier, A. and Schneider, T. (2001), Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Transactions on Mathematical Software, 27, 1, 27-57.

Schneider, T. and Neumaier, A. (2001), A Matlab package fo the estimation of parameters and eigenmodes of multivariate autoregressive models, 27, 1, 58-65.

Lutkepohl, H. (1993), Introduction to Multiple Time Series Analysis. Springer-Verlag, Berlin.

See Also

ar

Examples

data(pinkham)
y=mAr.est(pinkham,2,5)

[Package mAr version 1.0-3 Index]