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Regression for Time Series Data – Part II. Modeling the Dynamic Effect of Independent Variables. Intervention Analysis. Box and Tiao, 1975. Timeplot with Indication of Intervention Periods . Timeplot/ Freeze/ Line/Shade. Data Generating Process. Data t = Intervention Effect t + Noise t

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### Regression for Time Series Data – Part II

Modeling the Dynamic Effect of Independent Variables

### Intervention Analysis

Box and Tiao, 1975

• Datat = Intervention Effectt + Noiset

Intervention Effect = Fixed Function of t

Noise= Effect of all other factors

(ARIMA is used for modeling)

Intervention Modeling Strategy:Iterative, Trial and Error - Box-Tiao

• Frame a model for change which describes what is expected to occur given knowledge of the known intervention;

• Work out the appropriate data analysis based on that model;

• If diagnostic checks show no inadequacy in the model, make appropriate inferences; if serious deficiencies are uncovered, make appropriate model modification, repeat the analysis, etc.

• Define the series to represent the intervention

• Formulate a “transfer function” that translates the series of intervention to a series of response

• Identify a reasonable model for the noise

Let t = the time (known) the intervention has taken.

• Pulse type intervention, represented by series

• Step type intervention, represented by series

• Transfer Function

• Excel workbook demonstration