COINT (version 0.0.2)

fm: Fully-Modified OLS Estimator

Description

Computes the Phillips-Hansen (1990) Fully-Modified estimator for cointegrated regressions, using OLS for the first stage regression.

Usage

fm(y,
    x,
    type=c("const","trend","season","all"),
    v=15,
    ker_fun="parzen",
    aband=0,
    filter=0,
    sb_start=0.15)

Value

coefTable

Coefficients table.

vcov

Variance-covariance matrix for the parameter estimates.

sigma

Standard error of the residuals.

rss

Residual sum of squares.

fit

The fitted values, or conditional mean, of the regression.

stests

3x1 vector containing Hansen's (1992) Lc, MeanF, and SupF (in this order) statistics for testing the null hypothesis that the cointegrating vector is stable over the sample period.

resid

Estimated residuals.

Arguments

y

The data of dependent variable in a regression.

x

The data of independent variables in a regression.

type

The deterministic parts in the regression.
const = intercept;
trend = lnear trend;
season = seasonal dummies, this option requires ts format;
all = all three options, which requires ts format.

v

Number of autocovariance terms to compute the spectrum at frequency zero, default=15.

ker_fun

Set kernel function to one of the available kernels, default="parzen". See section details below.

aband

Whether to use the automatic bandwidth selection.
aband=1. To use.
aband=0. Do not use.The default.

filter

Whether to activate an AR(1) filter to compute the spectrum at frequency zero.
filter=1. To activate.
filter=0. Do not activate.The default.

sb_start

The percentage specifies the beginning of sub-sample for stability test, and the end sample is (1-sb_start).

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

Andrews, D. W. K. (1991) Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.Econometrica, 59: 817-858.

Brillinger, David R. (1981) Time Series Data Analysis and Theory. San Francisco, CA: Holden-Day.

Hansen, B. E. (1992) Tests for Parameter Instability in Regressions with I(1) Processes. Journal of Business and Economic Statistics, 10, 321-335.

Phillips, P. C. B. and Hansen B. E.(1990) Statistical Inference in Instrumental Variables Regression with I(1) Processes. Review of Economic Studies, 57, 99-125.

Examples

data(macro)
y=macro[,1]
x=macro[,-1]
out=fm(y,x,type=c("const","trend","season","all")[2],v=15,ker_fun="parzen")
out$coefTable
out$vcov
out$stests
tail(out$fit)
tail(out$resid)