```Date: Fri, 15 Dec 2006 09:15:06 -0800 Reply-To: dave@AUTOBOX.COM Sender: "SAS(r) Discussion" From: dave@AUTOBOX.COM Organization: http://groups.google.com Subject: Re: association between 2 time series Comments: To: sas-l@uga.edu In-Reply-To: <1115a2b00612141423l5283997kd823cbaf0bf6f233@mail.gmail.com> Content-Type: text/plain; charset="us-ascii" 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, 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 . ```

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