simple exponential smoothing model

[E. Bernardo]

(Sorry for cross-posting)

 

I have questions about the simple exponential smoothing model.  The model is mathematically expressed as follows:

 

Y_(t+m) = ALPHA*Y_(t) + (1 - ALPHA)*S_(t-1)

 

where:

 

Y_(t) is the observed value of the time series at period t;

Y_(t+m) is the predicted value at time m steps ahead;

ALPHA is between 0 and 1 such that the closer the alpha to 1 the larger the influence of the recent observations in forecasting the future values of the series;

S_(t-1) is called the smoothing level at time (t-1).

 

My questions focused on the (1-ALPHA)*S_(t-1) term.

 

1. What is meant by smoothing level?

2. Suppose ALPHA = .80. Then the equation is Y_(t+m) = .80*Y_(t) + .20*S_(t-1) .  How to interpret the .20*S_(t-1) term?

 

Thank you for any input.

Eins

 

 

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[Steve Simon, P.Mean Consulting]

Eins Bernardo wrote:

> I have questions about the simple exponential smoothing model.  The
> model is mathematically expressed as follows:
>
> Y_(t+m) = ALPHA*Y_(t) + (1 - ALPHA)*S_(t-1)
>
> where:
>
> Y_(t) is the observed value of the time series at period t;
> Y_(t+m) is the predicted value at time m steps ahead;
> ALPHA is between 0 and 1 such that the closer the alpha to 1 the larger
> the influence of the recent observations in forecasting the future
> values of the series;
> S_(t-1) is called the smoothing level at time (t-1).
>
> My questions focused on the (1-ALPHA)*S_(t-1) term.
>
> 1. What is meant by smoothing level?
> 2. Suppose ALPHA = .80. Then the equation is Y_(t+m) = .80*Y_(t) +
> .20*S_(t-1) .  How to interpret the .20*S_(t-1) term?

The Wikipedia entry on this topic is quite good and should explain
everything.

http://en.wikipedia.org/wiki/Exponential_smoothing
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