smoothing by moving average

Post on 18-Jan-2018

224 views

Category:

Documents

Embed Size (px)

DESCRIPTION

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

TRANSCRIPT

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 MONTHPER MONTH MOVING AVERAGE Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- 103.3 88.3 95.0 78.3 85.0 105.0 110.0 MA3 = 3 i = 1 Di = = 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 ( ) /4 = 101,3 The n is established through trial and error. Note:Aprils forecast was way too high but the low sales corrected Mays 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