Regression for Time Series Data

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 StrategyIterative, 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