QUESTION:

Alright, so your computation of the standard deviation is more correct, explain why I need AUTOBOX to

detect level shifts, seasonal pulses and time trends.

ANSWER:

If one restricts OUTLIER DETECTION to detecting unusual values that are INDEPENDENTLY flagged,

one can miss important information. One man's signal is another man's noise is the best way that I can

put it. If you have an "UNUSUAL" value every December, this is "USUAL" since it represents a

predictable process. Software that INDEPENDENTLY evaluates each and every value based only upon IT's

characteristics can severely miss the boat in picking up quality information and predictable structure.

This is then the argument for Seasonal Pulse identification, a unique feature of AUTOBOX. The idea

here is to test for instantaneous and immediately disappearing changes in the mean of the errors. If the

mean of the errors changes to another "regime" this is called a level or a step shift. For example a series

1,1,1,1,1,2,2,2,2,2,2,2, would exhibit A STEP SHIFT or a change in the mean. AUTOBOX would identify

the need for a dummy variable that had 0,0,0,0,0,1,1,1,1,1,1,1 and when estimated the coefficient of

response would be a 1 with an intercept of 1. A step or level shift can be seen to be the integration of a

pulse, 1 1 0 1 0 1 0 1 0 2 when differenced 1 2 0 2 0 2 0 2 0 2 0 2 0. In the same spirit, a trend can be seen

to be the integration of a step 1 1 2 1 3 1 4 1 5 1 7 when differenced 2 9 2 11 2 13 2 15 2 17 2 19.

AUTOBOX can then detect the need for a TIME TREND VARIABLE which of course is nothing more

than the integration of a step or the double integration of a pulse.