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 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 1.Frame a model for change which describes what is expected to occur given knowledge of the known intervention; 2.Work out the appropriate data analysis based on that model; 3.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.

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

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

Simple Intervention Effect Model Transfer Function

Re-expression of Intervention Effect

Graph of the Intervention Effect Excel workbook demonstration