sw: Stock-Watson Common Trends Statistic

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

Stock-Watson Common Trends Statistic

Description

Computes Stock and Watson (1988) common trends statistic for the null hypothesis that the data is a noncointegrated system (after allowing for a p-th order polynomial time trend).

Usage

sw(data,p,v=15,ker_fun="parzen",aband=0,filter=0)

Arguments

data	Matrix of k-time series variables.
p	Order of the time polynomial in the null hypothesis.
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 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
"fejer"=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

sw_stat	Test statistic. Reject the null of a unit root if the SW statistic < critical value
sw_cv	Critical values.

Author(s)

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

References

Stock, J. & M. K. Watson (1988) Testing for Common Trends. Journal of the American Statistical Association, 83, 1097-1107.

Examples

data(macro)
sw(macro,p=1,v=15)

COINT documentation built on Nov. 5, 2025, 6:30 p.m.