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Today we will discuss different forecasting methods.
We estimate the single parameter of the model at time T
as average of the last m observations, where m
is the moving average interval.
Since the model assumes a constant underlying mean, the forecast
for any number of periods in the future is the same as the estimate
of the parameter:
Exponential smoothing:
As for the moving average, this method assumes that the time series follows a constant model.
The value of b is estimated as the weighted average
of the last observation and the last estimate. Here 
is a parameter in the interval [0, 1].
Rearranging, obtains an alternative form.
The new estimate is the old estimate plus a proportion of the
observed error.
Because we are supposing a constant model, the forecast is the same as the estimate.
Today we will discuss different forecasting methods.
What is forecasting?
Forecasting is the process of making predictions of the future based on past and present data and analysis of trends.
We have different methods to do that. Here are the two most used methods.
- Moving average
- Exponential smoothing
Moving average:
The moving average
forecast is based on the assumption of a constant model.
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In practice the moving average will provide a good estimate
of the mean of the time series if the mean is constant or slowly
changing. In the case of a constant mean, the largest value
of m will give the best estimates of the underlying
mean. A longer observation period will average out the effects
of variability.
For more Stat and Math of Moving average, please check this website.
Exponential smoothing:
As for the moving average, this method assumes that the time series follows a constant model.
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is a parameter in the interval [0, 1].  |
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Because we are supposing a constant model, the forecast is the same as the estimate.
For more Stat and Math of Exponential smoothing, please check this website.
References:
Note:
Find R code on forecasting here.
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