by TACTICA » Sun Dec 28, 2008 2:49 pm
Hi,
I´ve found this from you....
Simple Moving Averages
The best-known forecasting method is the moving averages
method. It simply takes a certain number of past periods and
adds them together, then divides the result by the number of
periods. Simple Moving Averages (MA) is an effective and
efficient method provided the time series is stationary in
both mean and variance. The following formula is used in
finding the moving average of order n, MA(n) for a period
t+1:
MAt+1 = [Dt + Dt-1 + ... +Dt-n+1] / n
where n is the number of observations used in the calculation
Weighted Moving Averages
Very powerful and economical. It is widely used where
repeated forecasts requires methods like sum-of-the-digits
and trend adjustment methods. An example of a Weighted Moving
Averages calculation is as follows:
Weighted MA(3) = w1.Dt + w2.Dt-1 + w3.Dt-2
where the weights are any positive numbers such that: w1 + w2
\+ w3 =1. A typical weights for this example is, w1 = 3/(1 +
2 + 3) = 3/6, w2 = 2/6, and w3 = 1/6.
Exponential Smoothing Techniques
One of the most successful forecasting methods is the
exponential smoothing (ES) method. While the simple MA method
is a special case of the ES, the ES is more conservative in
its data usage. It also offers the following advantages:
§ can be modified to be used effectively for time series with
seasonal patterns
§ easy to adjust for past errors
§ easy to prepare follow-on forecasts, which is ideal for
situations where many forecasts must be prepared and several
different forms are used depending on the presence of trend
\or cyclical variations
In short, an ES is an averaging technique that uses unequal
weights, where the weights applied to past observations
decline in an exponential manner, as follows:
Ft+1 = a Dt + (1 - a) Ft
where:
Dt is the actual value
Ft is the forecasted value
a is the weighing factor, which ranges from 0 to 1
t is the current time period.
Notice that, the smoothed value becomes the forecast for
period t + 1.
A small a provides a lot of smoothing while a large a
provides a fast response to the recent changes in the time
series and a smaller amount of smoothing. Notice that the
exponential smoothing and simple moving average techniques
will generate forecasts having the same average age of
information if moving average of order n is the integer part
\of (2-a)/a.
An exponential smoothing over an already smoothed time series
is called <B>double-exponential smoothing</B>. In some cases,
it might be necessary to extend it to <B>triple-exponential
smoothing</B>. While simple exponential smoothing requires
stationary condition, the double-exponential smoothing can
capture linear trends and triple-exponential smoothing can
handle almost all other business time series.
And number of methods (for forecast) can be easily expanded if it required.
Can you?