[R-SIG-Finance] Number of data points required for Cointigration

[Paul Teetor]

Amol,
I don't have a formula or a guideline for determining the number of data points. But I can share two experiences.
First, when I traded mean-reverting spreads, I used 3 to 5 years of daily data. That's 750 to 1,250 data points. Less data did not work well for my spreads.
Second, in my experience, the ADF test was quite unstable. That is, it might fail to reject for a while, then start rejecting the null hypothesis when the market showed some trending back to the mean. Then it would fail to reject again as the market wandered away.
Perhaps smarter people than I have had better luck trading with the ADF, but for me, it did not provide a complete answer to the question of mean-reversion.
Paul Paul Teetor, Elgin, IL USAhttp://quantdevel.com/public
      From: amol gupta <amolgupta87 at gmail.com>
 To: "r-sig-finance at r-project.org" <r-sig-finance at r-project.org> 
 Sent: Friday, January 23, 2015 3:24 AM
 Subject: [R-SIG-Finance] Number of data points required for Cointigration
   
Hi
I need help in figuring out the length of historical data that I should use. I took stock prices(daily close) for two tickers from yahoo(200 days).I tried finding regression coefficient using PCA and I use 150 points for PCA. I find a coefficient Beta.

Now to see whether the spread is mean reverting or not I use ADF. If I use 150 point long spread, It comes out to be nonstationary. If I use 200 points data the outcome is stationary
I again used 200 points to do the PCA and find regression. The spread comes out to be non stationary. From all these observation I think that this is not a stable relationship.
So following are my questions   
   - Is there a way to decide length of historical data to use?
   - Some relationship may be more stable than others. Is there away to quantify it?
Any other insight in this regard will be appreciated(time frame, pairs vs basket). I have attached the plot and the script that was used to generate the plot.

-- 
Regards
Amol

If all the seas were ink,
And all the reeds were pens,
And all the skies were parchment,
And all the men could write,
These would not suffice
To write down all the red tape
Of this Government.


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