[R-SIG-Finance] Where is my hedge ratio when testing for cointegration with Phillips-Ouliaris test?

[Eric Zivot]

For the hedge ratio, you need an estimate of the cointegrating vector
between the two series. When you use the PO cointegration test, the
cointegrating vector is estimated by ordinary least squares. However, except
in special cases the OLS estimate of the cointegrating vector has a finite
sample bias due to the dynamics in the data. It is preferred to use an
estimate of the cointegrating vector that is not subject to strong biases in
finite samples, such as the Stock-Watson dynamic OLS lead-lag estimator or
the Johansen MLE based on the VECM. The Johansen MLE has the advantage that
it is invariant to the normalization of the cointegrating vector (a subject
that Paul Teetor has discussed with his PCA estimator). OlS is not invariant
to normalization. You get different estimates of you regress y1 on y2 versus
if you regress y2 on y1. For Johansen, it doesn't matter.


Eric Zivot                  			               
Robert Richards Chaired Professor of Economics and Director of Outreach
Adjunct Professor of Finance                            
Adjunct Professor of Statistics
Adjunct Professor of Applied Mathematics 
Department of Economics
Box 353330                  email:  ezivot at u.washington.edu 
University of Washington    phone:  206-543-6715            
Seattle, WA 98195-3330
www:  http://faculty.washington.edu/ezivot                  



-----Original Message-----
From: r-sig-finance-bounces at r-project.org
[mailto:r-sig-finance-bounces at r-project.org] On Behalf Of Mark Breman
Sent: Friday, January 06, 2012 12:09 PM
To: r-sig-finance at r-project.org
Subject: [R-SIG-Finance] Where is my hedge ratio when testing for
cointegration with Phillips-Ouliaris test?

Hello List,

I'm testing multivariate timeseries for cointegration using the
Phillips-Ouliaris test from package urca (ca.po) i.e:

############################################# start example
################################
> library(quantmod)
> library(urca)
>
> getSymbols(c('GLD', 'GDX'), from="2006-01-01")
[1] "GLD" "GDX"
>
> prices=na.omit(cbind(Ad(GLD), Ad(GDX)))
>
> summary(ca.po(coredata(prices), type='Pz'))

########################################
# Phillips and Ouliaris Unit Root Test #
########################################

Test of type Pz
detrending of series none

Response GLD.Adjusted :

Call:
lm(formula = GLD.Adjusted ~ zr - 1)

Residuals:
    Min      1Q  Median      3Q     Max
-9.3422 -0.6212  0.0540  0.7783  8.6275

Coefficients:
                Estimate Std. Error t value Pr(>|t|)
zrGLD.Adjusted 1.0004786  0.0020531 487.295   <2e-16 ***
zrGDX.Adjusted 0.0001917  0.0047246   0.041    0.968
---
Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1

Residual standard error: 1.44 on 1414 degrees of freedom Multiple R-squared:
0.9998, Adjusted R-squared: 0.9998
F-statistic: 3.78e+06 on 2 and 1414 DF,  p-value: < 2.2e-16


Response GDX.Adjusted :

Call:
lm(formula = GDX.Adjusted ~ zr - 1)

Residuals:
    Min      1Q  Median      3Q     Max
-5.0164 -0.6497  0.0160  0.7325  4.7142

Coefficients:
               Estimate Std. Error t value Pr(>|t|)
zrGLD.Adjusted 0.001727   0.001608   1.074    0.283
zrGDX.Adjusted 0.996047   0.003701 269.116   <2e-16 ***
---
Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1

Residual standard error: 1.128 on 1414 degrees of freedom Multiple
R-squared: 0.9994, Adjusted R-squared: 0.9994
F-statistic: 1.162e+06 on 2 and 1414 DF,  p-value: < 2.2e-16



Value of test-statistic is: 11.1864

Critical values of Pz are:
                  10pct    5pct    1pct
critical values 33.9267 40.8217 55.1911

########################## end example ################################

Now my question is where is my hedge ratio? The estimates (coefficients)
don't look at all usable.
Do i have to do a manual OLS regression to get the hedge ratio or is it
hidden somewhere in the ca.po test results?

Thanks,

-Mark-

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