Re: Hypothesis testing, two different rates

Adam ,

The correlation between to time series can be computed. To test the
significance of a correlation coefficient using "standard procedures"
one needs to have independent samples. When you have time series data,
as you have , this is seldom the case. The reasons for "spurious
correlation" can be found at http://www.autobox.com ... select SEARCH
.....search for SPURIOUS .

Furthermore if there are unusual values ( Pulses, Level Shifts,
Seasonal Pulses) then the "standard proceedures" are of little use as
one needs to normalize for the anomalies via either manually
adjustments of the incorporation of Intervention Variables.

Please see

http://www.autobox.com/pdfs/regvsbox.pdf

Also you might google "why do we sometimes get nonsense correlations
between time series"

@ARTICLE{Yule26:Sometimes,
AUTHOR="G. U. Yule",
TITLE="Why do we sometimes get nonsense-correlations between
time-series? - A study in sampling and the nature of time-series",
JOURNAL=jrss,
PAGES="1-29",
YEAR=1926,
KEYWORDS="Correlation; time series analysis; sampling",


In short to test the "correlation" between two time series , one may
have to augment the OLS model that other posters suggested using with
either ARIMA structure or Intervention Variables in order to assess the
relationship.

See the Spring 2005 article in the Jpurnal of Business Forecasting

http://www.autobox.com/pdfs/Pickett.pdf

Hope this helps ..

p.s. In specific ARREST RATE is significantly related to OD rate in the
following manner

Y(T) = 1120.2

+[X1(T)][(- 57.2722 + 51.6551 B** 1)]
+[X2(T)][(- 191.24 )]
+[X3(T)][(- 143.13 )]
+ [A(T)]

Wher all coefficients are significant at p=.03 and x2 represents a
PULSE at 1992 and X3 is a PULSE at 1999 ... thus two distortions or
unusual values

Furthermore the "relationship" is not only significant
contemporaneously ( coeff = -.57 ) BUT there is also a significant
lagged relationship suggesting the the prior year's OD rate can
significantly help the prediction of the current years ARREST RATE (
coeff = +.51)

Simplifying yields that ARREST RATE = .5 * first differences in OD RATE

so that it is changes in OD RATE that is SIGNIFICANTLY correlated with
the ARREST RATE .

Any questions or comments on this please give me a call ..

Dave Reilly
AFS 215-675-0652

.

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