**Moving Averages**

In this method the next period's forecast is the average of the previous *n *actual values.

F_{t+1} = actual
data values for n previous periods / *n*)

i.e., F_{t+1} = (A_{t }+ A_{t-1} +
A_{t-2} + -------------- +A_{ t-(n-1)} ) / *n*

With this method the assumption is that the most recent events are the best indicators of the future with significant random fluctuations in the time series. This approach produces a moving average that is relatively more sensitive to recent movements in data and forecast responsiveness can be increased by reducing the value *n*. As this method uses only the most recent periods that are relevant, it greatly reduces the problem of forecast lag inherent in the simple averaging technique. The choice of the number of data values to be included in the moving average is arbitrary and is left to the judgment of the forecaster.

It should be noted, however, that while the moving average method uses the data from most recent periods, it still assigns equal
importance to all periods of data included in the base of the moving average. Consequently, even with this method there is bound
to be some forecast lag. This problem can be resolved to a certain extent by using an extension of the moving average called the **weighted
moving average. **In this method, the forecaster assigns more weight to most recent values in the time series. For example,
the most immediate observation might be assigned a value of 0.5, the next most recent value a weight of 0.3, and so on. The sum
of the weights, however, should be equal to 1. For example, the forecast using a weighted moving average with four recent periods
(*n* = 4) using weights of *w*_{1} = 0.5, *w*_{2} = 0.3, *w*_{3} =
0.2, *w*_{4} = 0.1, is given by:

F_{t+1} = F_{5} = *w*_{1}A_{4} + *w*_{2}A_{3} + *w*_{3}A_{2} + *w*_{4}A_{1} = 0.5A_{4} + 0.3A_{3} + 0.2A_{2} + 0.1A_{1 }