Date:         Fri, 15 Dec 2006 08:42:58 -0800
Reply-To:     dave@AUTOBOX.COM
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From:         dave@AUTOBOX.COM
Organization: http://groups.google.com
Subject:      Re: association between 2 time series
Comments: To: sas-l@uga.edu
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Wensui Liu wrote:
> i am a little worried about the suggestion you are getting.
>
> if I were you, I will check the stationarity of 2 series first. if
> yes, I will check CCF between 2 series using proc arima.
>
> i might be wrong though.
>
>
>> --
> WenSui Liu
> (http://spaces.msn.com/statcompute/blog)
> Senior Decision Support Analyst
> Cincinnati Children Hospital Medical Center




Wensui,

I believe you are wrong. Converting or transforming the series to
stationarity is NECESSARY but not SUFFICIENT to identify structure. The
cross-correlation between two times series  even though may be
stationary may be meaningless due to autocorrelation structure within
the time series. This has been pointed out "time and time again" ( a
pun ! ) , notably by Yule in 1926 entitled "Why do we sometimes get
nonsense correlations with time series".

 More recently web pages such as
http://www.met.rdg.ac.uk/cag/stats/corr.html cite Yule in 1926 as a
primary source (excerpt follows) . Simply put if either x or y has
autocorrelative structure beware the use of the ccf as a tool to
identify structure recalling the multivariate normality assumption
requires marginal normality.

Suppose that X and Y are independent normal random variables. Then, in
the absence of temporal autocorrelation, the correlation coefficient,
r, between random samples of size n from X and Y has a probability
density function f(r) = ((1 - r^2)^0.5(n-4)) / B(0.5,0.5(n-2)) The
distribution has mean zero and a variance of (n-1)^-1. However, the
distribution is affected by the autocorrelation in X and Y, which
increases the variance of the distribution and so gives rise to
spurious large correlations. This problem was recognised for time
series as early as 1926 by Yule in his presidential address to the
Royal Statistical Society. In the discussion of the address which
followed, Edgeworth asked 'What about space ? Are there not nonsense
correlations in space ?' (Yule, 1926).

Other web sites point to Spurious Correlation. For example paste the
following into YAHOO
http://search.yahoo.com/search?p=yule+nonsense+correlation&fr=yfp-t-427&toggle=1&cop=mss&ei=UTF-8

Hope this helps ..

Dave Reilly
Automatic Forecasting Systems
http://www.autobox.com