fmvar: Fully-Modified VAR Estimator

In COINT: Unit Root Tests with Structural Breaks and Fully-Modified Estimators

Fully-Modified VAR Estimator

Description

Computes the Phillips' (1995) Fully-Modified" VAR estimator for cointegrated regressions, using OLS for the first stage regression.

Usage

fmvar(data,p=1,q=5,v=15,type=c("const","trend","season","all"),
                   ker_fun="parzen",aband=0,filter=0)

Arguments

data	The dependent variables for a VAR system.
p	The number of lags for dependent variables, as in a VAR(p).
q	The number of lagged innovation terms to include in the fitted FMVAR(p,q).
v	Number of autocovariance terms to compute the spectrum at frequency zero, default=15.
type	The deterministic parts in the regression. Please note that fmvar will "de-" before inclusion, for example, trend is to pre-detrend the data. const = intercept; trend = lnear trend; season = seasonal dummies, this option requires ts format; all = all three options, which requires ts format.
ker_fun	Set kernel function to one of the available kernels, default="parzen". See section details below.
aband	Whether to activate the automatic bandwidth selection. aband=1. To activate. aband=0. Do not activate.The default.
filter	Whether to use an AR(1) filter to compute the spectrum at frequency zero. filter=1. To use. filter=0. Do not use. The default.

Details

1. Available kernels. Technical details are referred to Brillinger (1981,P.55)
"parzen"=Parzen kernel
"bartlett"=Bartlett kernel
"dchlet"= Dirichlet kernel
"mdchlet"= Modified Dirichlet kernel
"tukham"=Tukey-Hamming kernel
"tukhan"=Tukey-Hanning kernel
"cauchy"=Cauchy kernel
"bohman"=Bohman kernel
"reisz"=Riesz,Bochner kernel
"gw"= Gauss-Weierstrass kernel
"qs"= Andrews (1991) Quadratic-Spectral

These kernels are written for FM procedures, technically different from those used in pp and kpss tests.

2. Andrews (1991) has developed data based (or automatic) bandwidth procedures for computing the spectrum. COINT implements these procedures for the Parzen, Bartlette, Tukey-Hamming, and the Quadratic-Spectral kernels. When aband is active, COINT ignores the value you specify for the band-width parameter and automatically substitutes the data-based value.
3. The aim of the AR(1) filter is to flatten the spectrum of residual around the zero frequency, thereby making it easier to estimate the true spectrum by simple averaging of the periodogram.

Value

beta	Coefficient estimates.
stderr	Standard error of the residuals.
tstat	t-statistics of parameter estimates.
vcov	Variance-covariance matrix for the parameter estimates.
fit	The fitted values, or conditional mean, of the regression.
resid	Estimated residuals.
data	The data used in fmvar
type	The type used in fmvar
p	The p argument used in fmvar
q	The q argument used in fmvar

Author(s)

Ho Tsung-wu <[e-mail]>, College of Management, National Taiwan Normal University.

References

Phillips, P. C. B (1995) Fully Modified Least Squares and Vector Autoregression. Econometrica, 63, 1023-1078.

Examples

data(macro)
out=fmvar(macro,p=1,q=6,v=15,type="trend",ker_fun="parzen",aband=0,filter=0)
out$beta
out$stderr
out$tstat
out$vcov
tail(out$data)
tail(out$resid)

ID1=grep(rownames(out$beta),pattern="_dL")
ID2=grep(rownames(out$beta),pattern="_L")
ID3=rownames(out$beta)[-c(ID1,ID2)]

out$beta[ID1,]; #innovation terms
out$beta[ID2,]; #VAR(1)
out$beta[ID3,]; #deterministic parts

COINT documentation built on Sept. 9, 2025, 5:51 p.m.