Moving averages (MA) at a time index t estimates the average trend cycle component Ft and is calculated by taking average of over the time period of t ± k where k is the range of the MA:
Taking moving averages have an effect of smoothing the original time series by eliminating random noise. Commonly the total number of observations m = 2k + 1 is used to describe the moving average as m-order MA, which henceforth will be denoted as 
. Let us demonstrate moving averages and their smoothing effect through ...
