VARXFit {BigVAR}

Fit a VAR or VARX model by least squares

Description

Fit a VAR or VARX model by least squares

Usage

VARXFit(Y, p, IC, VARX = NULL)

Arguments

Y

a t \times k multivariate time series

p

maximum lag order

IC

Information criterion indicator, if set to NULL, it will fit a least squares VAR(X) of orders p and s. Otherwise, if set to 'AIC' or 'BIC' it return the model with lag orders that minimize the given IC.

VARX

a list of VARX specifications (as in constructModel (or NULL )

Details

This function uses a modified form of the least squares technique proposed by Neumaier and Schneider (2001). It fits a least squares VAR or VARX via a QR decomposition that does not require explicit matrix inversion. This results in improved computational performance as well as numerical stability over the conventional least squares approach.

Value

Returns a list with four entries:

• 'Bhat'Estimated k\times kp+ms coefficient matrix

• 'SigmaUEstimated k\times k residual covariance matrix

• 'phat'Selected lag order for VAR component

• 'shat'Selected lag order for VARX component

• 'Y'multivariate time series retained for prediction purposes

• 'Y'number of endogenous (modeled) time series

References

Neumaier, Arnold, and Tapio Schneider. 'Estimation of parameters and eigenmodes of multivariate autoregressive models.' ACM Transactions on Mathematical Software (TOMS) 27.1 (2001): 27-57.

See Also

constructModel, cv.BigVAR,BigVAR.fit

Examples

data(Y)
# fit a VAR_3(3)
mod <- VARXFit(Y,3,NULL,NULL)
# fit a VAR_3 with p= 6 and lag selected according to AIC
modAIC <- VARXFit(Y,6,'AIC',NULL)
# Fit a VARX_{2,1} with p=6, s=4 and lags selected by BIC
modXBIC <- VARXFit(Y,6,'BIC',list(k=1,s=4))