mAr.est {mAr}

Estimation of multivariate AR(p) model

Description

Stepwise least-squares estimation of a multivariate AR(p) model based on the algorithm of Neumaier and Schneider (2001).

Usage

mAr.est(x, p, ...)

Arguments

x

matrix of multivariate time series

p

model order

...

additional arguments for specific methods

Details

Fits by stepwise least squares an 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:

SBC

Schwartz Bayesian Criterion

wHat

vector of intercept terms

AHat

matrix of estimated autoregression coefficients for the fitted model

CHat

noise covariance matrix

resid

residuals from the fitted model

Author(s)

S. M. Barbosa

References

Barbosa S.M., Silva M.E., Fernandes M.J. (2006), Multivariate autoregressive modelling of sea level time series from TOPEX/Poseidon satellite altimetry. Nonlinear Processes in Geophysics, 13, 177-184.

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.

Examples

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