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Old Apr 17th, 2012, 03:16 AM   #1
imtrader
 
 
Join Date: Mar 2009
Posts: 3
Hello everyone,

I have a query regarding Time series analysis. I have two series namely TS1 and TS2. I want to know which one of these series is dependent and which is independent. I was wondering what tests should be performed to find that out?

Thank you for your help.

Regards,
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Old Apr 18th, 2012, 11:13 PM   #2
PetaDollar
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Join Date: Mar 2003
Posts: 1,794
Great question.

Check out "The Mathematics of Technical Analysis" by the late Cliff Sherry. It's somewhat of a disaster in terms of organization, but it has the information you want.

There are a great many different kinds of tests for different kinds of dependencies. My favorite is to count the frequency of + or - price changes following + or - price changes and compare it to a random, independent "time series".

The "golden rule" is: compare to a random, independent time series.
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Old Apr 19th, 2012, 01:08 AM   #3
imtrader
 
 
Join Date: Mar 2009
Posts: 3
Hello Petadollar,

Thank you for your help. Will definitely try out the method you suggested.

Regards,
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Old Apr 19th, 2012, 04:09 AM   #4
athlonmank8
 
 
Join Date: May 2007
Location: Midwest
Posts: 3,145
Thanks for the info
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Old Apr 20th, 2012, 08:40 AM   #5
PetaDollar
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Join Date: Mar 2003
Posts: 1,794
Here is an example from the S&P 500 (e-mini futures) last fall, using some of the techniques from Sherry's book.


  • The graph across the top is the price.
  • Histogram "N" is the 5 minute prices changes (histogram of first differences
  • To the right of that is the differential spectrum test. It tells you if dependencies exist or not (but not what kind of dependencies). It tests for symmetry of the first-difference histogram.
  • Directly under the differential spectrum test is the digram test for serial price dependency. "1" means price decrease and "2" means increase. So "11" means a decrease followed by a decrease, "12" means decrease then increase, etc. "obs" is how many were seen in this time series and "exp" is how many are expected from a random, independent time series.
  • The two cdfs (cumulative distribution functions) plotted along the left-bottom are tests for stationarity (labelled stn) and randomness (labelled ran)

These results showed the price changes over 5 min intervals, for the S&P emini between Sept. 21 and Oct 14, were stationary, random, but dependent.

The dependency means that trends are in play and chart patterns can be useful. Random means that the historical prices don't completely determine the future prices. Good traders already knew all this. But it's nice to see proof. Furthermore, you can watch the markets change their behavior and also see difference in time frames with this kind of analysis.

The problem, I found, with studying dependencies there are not many statisticians who study dependencies. Useful material is difficult to come by.
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Old Apr 20th, 2012, 09:08 AM   #6
panzerman
 
 
Join Date: Aug 2006
Posts: 305
If you import any financial time series into Excel, and run the descriptive statistics function, you will find all distibutions have some degree of skew and kurtosis. There have been plenty of folks with Ph.D.s and even Nobel Prize winners who have failed to develop an economic model that comes close to accurately accounting for this skew and kurtosis.
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