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Regression for Time Series Data – Part II

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

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  1. Regression for Time Series Data – Part II Modeling the Dynamic Effect of Independent Variables

  2. Intervention Analysis Box and Tiao, 1975

  3. Timeplot with Indication of Intervention Periods • Timeplot/ Freeze/ Line/Shade

  4. Data Generating Process • Datat = Intervention Effectt + Noiset Intervention Effect = Fixed Function of t Noise= Effect of all other factors (ARIMA is used for modeling)

  5. 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.

  6. Steps of Intervention Analysis • 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

  7. Definition of Intervention Series Let t = the time (known) the intervention has taken. • Pulse type intervention, represented by series • Step type intervention, represented by series

  8. Simple Intervention Effect Model • Transfer Function

  9. Re-expression of Intervention Effect

  10. Graph of the Intervention Effect • Excel workbook demonstration

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