mAr.est: Estimation of multivariate AR(p) model

In mAr: Multivariate AutoRegressive Analysis

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)

mAr documentation built on June 1, 2022, 1:07 a.m.