Smoothing by moving average

The Moving Average Method Useful in smoothing time series to see its trend Basic method used in measuring seasonal fluctuation Applicable when time series follows fairly linear trend that have definite rhythmic pattern

Moving Averages Used for smoothing Series of arithmetic means over time Result dependent upon length of period chosen for computing means To smooth out seasonal variation, the number of periods should be equal to the number of seasons For quarterly data, number of periods = 4 For monthly data, number of periods = 12

Moving Average Method - Example

Three-year and Five-Year Moving Averages

3-month Simple Moving Average ORDERS MONTH PER MONTH MOVING AVERAGE Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - – 103.3 88.3 95.0 78.3 85.0 105.0 110.0 MA3 = 3 i = 1  Di = 90 + 110 + 130 = 110 orders for Nov Concentrates on most recent data. The more dynamic the environment, the smaller n is used. If we use n=2 (110+90) / 2 = 100 If we use n=4 (90+110+130+75) /4 = 101,3 The n is established through trial and error. Note: April’s forecast was way too high but the low sales corrected May’s forecast.

Moving Averages Example: Four-quarter moving average First average: (continued) Example: Four-quarter moving average First average: Second average: etc…

Seasonal Data … … Quarter Sales 1 2 3 4 5 6 7 8 9 10 11 etc… 23 40 25 27 32 48 33 37 50 … …

Calculating Moving Averages Average Period 4-Quarter Moving Average 2.5 28.75 3.5 31.00 4.5 33.00 5.5 35.00 6.5 37.50 7.5 38.75 8.5 39.25 9.5 41.00 Quarter Sales 1 23 2 40 3 25 4 27 5 32 6 48 7 33 8 37 9 10 50 11 etc… Each moving average is for a consecutive block of 4 quarters

Fools forecaster by appearing to identify a cycle when in fact no cycle was present in the actual data Any moving average is serially correlated as a number of periods have been averaged

Excel/Data Analysis/Moving Average