How to obtain detrended data and demeaned data in Stata? I would like to run KSS test (KAPETANIOS, G. – SHIN, Y. – SNELL, A. 2003: Testing for a UnitRoot in the Nonlinear STAR Framework) , but I don't  know how to obtain demeaned data and detrended data. Could  you describe me the process in STATA?
 A: You can demean a variable as follows:
summarize x
generate x_demeaned = x - r(mean)

If you have a batch of variables, you can use a loop. Suppose that you have three variables called peter, paul and mary:
foreach v of varlist peter paul mary {
    summarize `v'
    generate `v'_demeaned = `v' - r(mean)
}

If you have missing values and you want to use the variables in a regression, you might want to do listwise deletion. This means that you don't take into account obsevrations that have missings for any of the variables. 
egen anymiss = rowmiss(peter paul mary) 
foreach v of varlist peter paul mary {
    summarize `v' if anymiss == 0
    generate `v'_demeaned = `v' - r(mean) if anymiss == 0
}

For detrending you have several possibilities. If you want to remove a linear trend from a variable y, you could do the following, supposing that t is the time index:
regress y t
predict y_detrended , resid

You can also have a look at
help tssmooth

as well as the following presentation:
http://ideas.repec.org/p/boc/asug06/2.html
