Unformatted text preview: lve and see what
happens via MA(3) and MA(6).
happens Exponential Smoothing
It is a type of moving average forecasting technique
which weighs past data in an exponential manner so that
the most recent data carries more weight in the moving
average.
average.
1. New Forecast = α (most recent observation)
+ (1  α) (last forecast)
(1 α) (last
or
2. New Forecast = last forecast  α (last forecast error)
2.
where 0 < α < 1 is the smoothing constant and generally
where
is small for stability of forecasts (around .1 to .2).
is 10 Exponential Smoothing
Ft+1 = α Dt + (1  α ) Ft
(1
= α Dt + (1  α ) (α Dt1 + (1  α ) Ft1)
(1
= α Dt + (1  α )(α )Dt1 + (1  α)2 (α )Dt  2 +...
(1
)(
Hence the method applies a set of exponentially
Hence
declining weights to past data. It is easy to show that the
sum of the weights is exactly one.
sum
Simply;
Ft + 1 = Ft  α (Ft  Dt) Example
Example
α = 0.1 and from assumption we know that the
forecast for week 1 is 200.
forecast
Week
1
2
3
4
5
6
7
8 Failures
Forecast
200
200(assumption)
250
175
186
225
285
305
190 11 Example
Week
1
2
3
4
5
6
7
8 Failures
200
250
175
186
225
285
305
190 ES
200(assumption) error MA(3) error Comparison of ES and MA
Similarities
Similarities
Both methods are appropriate for stationary series
Both
Both methods depend on a single parameter
Both
Both methods lag behind a trend
Both
One can achieve the same distribution of forecast
error by setting α = 2/ ( N + 1).
2/
Differences
Differences...
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 Spring '14
 Forecasting, Regression Analysis, Time series analysis

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