QUESTION:

Please explain Intervention Analysis.

ANSWER:

Intervention Analysis can be conducted in two ways:

1. Assumed knowledge of the form of the intervention.

The user KNOWS the time and the form of the effect i.e. a pulse, a level shift or a time trend.

For example a law change may happen at a certain point in time and it may be assumed that there will be a

continuing effect thus the variable of interest would be

0,0,0,0,0,0,......,1,1,1,1,1,1,

The fatal flaw here is that there may be 'DEAD TIME" or a delayed response to the "de jure" date of

intervention OR a period where the system responded in ADVANCE of the known and assumed date. The

"de facto" date may not necessarily be equal to the "de jure " date. For those of us who are non-lawyers

"de jure" means by law while "de facto" means by date.

2. The modeler wishes to empirically, i.e. draw out of the data, the point in time and the form of the variable.

For example

a. There may be a one-time-only effect ( pulse)

b. The effect may occur or re-occur at fixed intervals of time (seasonal pulse)

c. Contiguous periods of time may be effected in a common way (level shift or step)

d. Starting at a point in time there may be a trend.

The fatal flaw in this is that absolute statements about the timing of permanent effects like level shifts or

time trends may, by chance, inexact. One can only say on or about when concluding.

To further complicate things the user or modeler should take into account other variables that have

effected the series in the past. For example you can't simply do marginal analysis of a reading or

observation at a particular time , one needs to assess or predict or estimate what that value should have

been in order to assess or measure the impact of a specific variable.

For example, if there is a trend in the history indicating steady growth and you introduce what you believe

to be a change at a point in time and you assume that this change will only impact the point in time where

the change is made you have to make a prediction as to what would have occurred in order to assess or

estimate the impact of the action.

For example if you had observed the following

1,3,1,3,1,3,1,5

The estimate of the INTERVENTION effect would be 2 or

BASELINE PREDICTED VALUE = 3

observed value = 5

-----------------------------

DIFFERENCE = 2

Note that if your baseline predicted value was based on a random walk ( use last value ) the estimated effect

would be a 4 while if your baseline predicted value was the average of the past (1+3+1+3+1+3+1)/7 = 13/7

= 1 + (6/7) the estimated effect would be 3 1/7 . The whole idea is to estimate the CONDITIONAL

IMPACT. The idea here is to construct and use a model based upon historical precedence.

Before assessing the unusual one has to assess or predict the usual.

In closing one uses either ARIMA , non-causal or TRANSFER FUNCTIONS (causal) models to develop a

base-line and then either assumes the form of the intervention variable or searches the sample space by

either visually or statistically examining the tentative model's residuals in order to construct the

appropriate intervention variable.

Intervention variables can be of the following form

1. a pulse 0,0,0,0,0,,,,,1,0,0,0,0,0,0

2. a step 0,0,0,0,0,....1,1,1,,,0,0,0 ( there may be multiple steps

of varying length)

3. a seasonal pulse

0,0,0,1,0,0,0,1,0,0,0,1.....(e.g. a quarterly pulse )

4. a local time trend

1,2,3,4,5........

or 0,0,0,1,2,3,4.....

or 0,0,0,1,2,3,4,0,0,0,0 ( there may be multiple time trends

time trends of varying length)

5. a transient effect

1,.5,.25.,.125 where a new level is asymptotically approached

and others