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
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.