COINT (version 0.0.2)

fmvar: 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)

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

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.

Author

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

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.

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