Analyzing Time-Series Data: What Model to Use?

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To analyze the effect of data points across 36 time periods, regression analysis is suggested as a suitable model, particularly for its predictive capabilities. Chi-Square tests are not appropriate due to the lack of expected frequencies in this context. A regression model can be structured as y(i, t) = a + b y(i, t-1), allowing for the assessment of changes from one period to the next. Outlier detection is typically included in standard regression analysis tools. Utilizing a robust statistical package will enhance the analysis of time-series data effectively.
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I want to test a series of 36 time periods and 10 data points for each one of those periods. The goal is to see which data points have the biggest effect on change from one period to the next.

I thought Chi-Square was the way to go, but I do not have any expected frequencies here. Regression analysis is more of a prediction/forecasting model? What statistical model should I use here?
 
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A decent stats package will provide outlier detection as part of their basic regression subroutine.

For SAS, see:http://www2.sas.com/proceedings/sugi24/Infovis/p161-24.pdf and http://www2.tltc.ttu.edu/westfall/images/5349/outliers_what_to_do.htm

Your regression model could be y(i, t) = a + b y(i, t-1) where y(i,t) (i = 1, ..., 10) corresponds to the 10 different observations in period t. (Similarly for t-1.)
 
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