Nonparametric correction for serial correlation a la Phillli

[turkhanali]

Dear All,

For the past week, I am trying to apply the Phillips and Perron (1998) approach of auto-correlation correction in the test of Kapetanios et al (2003) nonlinear ESTAR unit root test. Kapetanios et al (2003) used the Dickey-Fuller augmentation, but I want to try to use the Phillips and Perron (1998) approach as proposed by Rothe and Sibbertsen (2006) and use the GLS detrending-based unit root test a la Kapetanios and Shin (2008)" GLS detrending-Based Unit root test in nonlinear STAR and SETAR model" Economics Letter 100(2008) 377-380.

After reading the reference guide on page 295 and the PPunit. SRC. However, I am facing problem in the last step, i.e.how to calculate the summation in the equation (3) and Equation (7) shown in the attached PDF file . In fact, I have read carefully the PPUNIT.SRC, I could not find how does it calculate the summation in the test, for example equation (3).

Your help on understanding the PPunit.SRC code and assistance in coding the test shown as Equation (7) in the attached PDF file is highly appreciated.

[TomDoan]

If you strip out the instructions for the notrend, t-test branches, you get this:

Code: Select all

linreg(noprint) series startl+1 endl resids
# series{1} constant
compute %seesq=%seesq*%ndf/%nobs
compute su=sqrt(%seesq)
compute tstat=(%beta(1)-1)/sqrt(%seesq*%xx(1,1))
stats(noprint) series startl endl-1
compute dxx=(%nobs-1)*%variance

mcov(lwindow=newey,lags=tlag) startl+1 endl resids
# constant
compute st=sqrt(%cmom(1,1)/%nobs)
compute vardiff=(st**2-su**2)
compute teststat=tstat*su/st-.5*vardiff*regnobs/(st*sqrt(dxx))

Quite a bit of this is to get divisors to match up; for instance, the su and the t-statistic are computed using a T divisor rather than the standard degrees of freedom corrected T-k. The MCOV computes the long-run variance; that's %cmom(1,1)/%nobs. The sums of the y{1}^2 and y{1}^6 needed in your formula are most easily computed using SSTATS:

Code: Select all

sstats startl+1 endl y{1}^2>>sumysq y{1}^6>>sumy6

[turkhanali]

Thank you, Tom.