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

[R. Michael Weylandt]

Slightly beyond the scope of your question, but this might be of
interest: http://quanttrader.info/public/betterHedgeRatios.pdf

Michael

On Fri, Jan 6, 2012 at 2:08 PM, Mark Breman <breman.mark at gmail.com> wrote:
> 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-
>
>        [[alternative HTML version deleted]]
>
>
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