Regression for time series data part ii
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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 l.jpg

Regression for Time Series Data – Part II

Modeling the Dynamic Effect of Independent Variables

Intervention analysis l.jpg

Intervention Analysis

Box and Tiao, 1975

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Data Generating Process

  • Datat = Intervention Effectt + Noiset

    Intervention Effect = Fixed Function of t

    Noise= Effect of all other factors

    (ARIMA is used for modeling)

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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.

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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

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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

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Graph of the Intervention Effect

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