[R] Regression output labels

[Pfaff, Bernhard]

> Hello to all-
>  	1.	When I run a regression which implements the 
> augmented Dickey-Fuller
> test, I am confused about the names given to the regressors 
> in the output.
> I understand what "xGE" stands for in a standard "lm" test 
> involving an
> independent variable GE for instance, but if I lags and or 
> differences are
> included in the model, what do the following "output" stand for:
> 	 	"xlag(x,-1)GE"
>   		"xD.GE"
>   		"xD.lag(diff(x), -i)GE"
>   		"xD.D.lag(diff(x), -i)GE"
> 	Thanks for the clarifications -- I don't want to 
> "misspeculate" on the
> actual interpretations, here...
> 

Hello rwatkins,

I assume that you are referring to the function:
http://www.econ.uiuc.edu/~econ472/adf.R.txt


"adf"<-
function(x, L = 2, int = T, trend = T)
{
#Construct Data for Augmented Dickey Fuller Model with L lags.
#This is a modified version for R, in which the command rts was substituted
by ts.
        x <- ts(x)
        D <- diff(x)
        if(L > 0) {
                for(i in 1:L)
                        D <- ts.intersect(D, lag(diff(x),  - i))
        }
        D <- ts.intersect(lag(x, -1), D)
        if(trend == T)
                D <- ts.intersect(D, time(x))
        y <- D[, 2]
        x <- D[, -2]
        if(int == T)
                summary(lm(y ~ x))
        else summary(lm(y ~ x - 1))
}

As you can see by the code the lagged differences of the series are produced
repetitively in the for-loop; the function argument "L" sets the maximum
number of lagged differences of the time series to be tested for unit root.
After the for-loop the one period lag of the original variable is included
to "D" as first columne. In case of a trend inclusion, this variable is
included as last columne:

xD.lag(x, -1): is the one period lag of the original series;
xD.D.D.lag(diff(x), -i): is the one period lag of the differenced series;
xD.D.lag(diff(x), -i): is the two period lag of the differenced series and
xtime(x): is the linear time trend.  

Pls. note, that you should include as many lagged differenced x series
(function argument "L") until the residuals of the test regression do not
contain any significant autocorrelations (check their acfs and/or pacfs). 
> Also...
> 	2.	When an Engle-Granger test is run on multiple 
> independent variables,
> only one cointegration vector is returned.  Can one tell 
> "which vector" --
> or what two variables' relationship  -- is being identified for the R
> output.  Likewise, if I run a Johansen test, does R "tell me" 

To which function are you referring in particular?

> specifically
> which pairs of variables are cointegrated or do I just get the rank?
> 
> 	Thanks to all for your time and consideration.
> 

If you apply the Engle-Granger Two-Step-procedure in case of more than two
I(1) variables and if more than one cointegration-relationship exists you
are estimating a linear combination of the latter. In case you apply a
Johansen test (rank- or trace-test) you are only testing the space of
cointegrating vectors. In order to draw inferences about the
cointegration-relationships you must test these specifically.

As a suggestion for reading and further elaboration let me allow you to hint
you to the following literature:

1)
Hamilton, James D. (1994). Time Series Analysis. Princeton N.J.: Princeton
University
Press.

2)
Engle, Robert F., and Clive W. J. Granger. (1987). Co-Integration and Error
Correction:
Representation, Estimation and Testing. Econometrica. Vol. 55, pp. 251-276.

3)
Johansen, Søren. (1991). Estimation and Hypotheses Testing of Cointegrating
Vectors
in Gaussian Vector Autoregressive Models. Econometrica. Vol. 59, pp.
1551-1580.

4)
Johansen, Søren. (1995). Likelihood-Based Inference in Cointegrated Vector
Autoregressive
Models. Oxford: Oxford University Press.

HTH,
Bernhard


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