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?