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 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, Quote
 Apr 18th, 2012, 11:13 PM #2 PetaDollar Moderator   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. Quote
 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, Quote
 Apr 19th, 2012, 04:09 AM #4 athlonmank8     Join Date: May 2007 Location: Midwest Posts: 3,142 Thanks for the info Quote
Apr 20th, 2012, 08:40 AM   #5
PetaDollar
Moderator

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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 Apr 20th, 2012, 09:08 AM #6 panzerman     Join Date: Aug 2006 Posts: 304 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. Quote
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