Question

Would you please explain with details the followings:

*Moving average Time series is a useful process to describe events producing an immediate effects that lasts for short period of time.

Provide an example if it is possible, pleases

Answer 1

The classical method of time series decomposition originated in the 1920s and was widely used until the 1950s. It still forms the basis of many time series decomposition methods, so it is important to understand how it works. The first step in a classical decomposition is to use a moving average method to estimate the trend-cycle, so we begin by discussing moving averages.

Moving average smoothing

A moving average of order mm can be written as^Tt=1/m(∑yt+j),

where m=2k+1. That is, the estimate of the trend-cycle at the time it is obtained by averaging values of the time series within kk periods of it. Observations that are nearby in time are also likely to be close in value. Therefore, the average eliminates some of the randomnesses in the data, leaving a smooth trend-cycle component. We call this an mm-MA, meaning a moving average of order mm.

EXAMPLE

Calculating a 5-Year Moving Average Example

Sample Problem: Calculate a five-year moving average from the following data set:

Year	Sales ($M)
2003	4
2004	6
2005	5
2006	8
2007	9
2008	5
2009	4
2010	3
2011	7
2012	8

The mean (average) sales for the first five years (2003-2007) is calculated by finding the mean from the first five years (i.e. adding the five sales totals and dividing by 5). This gives you the moving average for 2005 (the center year) = 6.4M:

Year	Sales ($M)
2003	4
2004	6
2005	5
2006	8
2007	9

(4M + 6M + 5M + 8M + 9M) / 5 = 6.4M

The average sales for the second subset of five years (2004 – 2008), centered around 2006, is 6.6M:
(6M + 5M + 8M + 9M + 5M) / 5 = 6.6M

The average sales for the third subset of five years (2005 – 2009), centered around 2007, is 6.6M:
(5M + 8M + 9M + 5M + 4M) / 5 = 6.2M

Continue calculating each five-year average, until you reach the end of the set (2009-2013). This gives you a series of points (averages) that you can use to plot a chart of moving averages. The following Excel table shows you the moving averages calculated for 2003-2012 along with a scatter plot of the data: