The Moving Average Method Lecture 04

 The Moving Average Method 

Lecture 04

The moving average method analyzes the largest data divided into several pieces called k-periods. The k-period moving average method is "the average of the k consecutive values of the observed series, then repeating the operation by one value at the beginning and including the first value after the preceding total, and so on." Up until the latest k consecutive values have been averaged, this process is repeated.

Suppose we have the series 4, 5, 6, 8, and 10.

The 3-periods moving averages  are (4+5+6) / 3 = 5,   (5+6+8) / 3 = 3 = 6.88, and (6+8+10) / 3 = 8

Symbolically,

Each k-period moving average is placed against the middle value of its time period.

Centered moving average

When k is even, say k=4 periods. Then 4-period moving averages are computed as

a1 is placed against the second value of the series, and a2 immediately after a1. 

The 4-period centered moving averages can be computed as

Practice Question

Compute 3-, 5- and 7-years moving averages for the following data.

Year	1991	1992	1993	1994	1995	1996	1997	1998	1999
Profit (000,000)	10	18	15	17	24	30	28	25	34

Solution:

Year	Profit	3-years moving		5-years moving		7-years moving
		Total	Average	Total	Average	Total	Average
1991	10	-	-	-	-	-	-
1992	18	43	14.33	-	-	-	-
1993	15	50	16.67	84	16.80	-	-
1994	17	56	18.67	104	20.80	142	20.28
1995	24	71	23.67	114	22.80	157	22.43
1996	30	82	27.33	124	24.80	173	24.71
1997	28	83	27.67	141	28.20	-	-
1998	25	87	29.00	-	-	-	-
1999	34	-	-	-	-	-	-

Practice Question

Compute 4-year centred moving averages for the following data.

Year	1991	1992	1993	1994	1995	1996	1997	1998	1999
Profit (000,000)	10	18	15	17	24	30	28	25	34

Solution:

Year	Profit	4 years moving	4 years centred moving
			Total	Average
1991	10	-	-	-
1992	18	60	-	-
1993	15	74	134	16.75
1994	17	86	160	20.00
1995	24	99	185	23.12
1996	30	107	206	25.75
1997	28	117	224	28.00
1998	25	-	-	-
1999	34	-	-	-

Practice Question

The sale of an anti-allergic medicine in the various quarters is given below:

Year	Quarter- 1	Quarter-2	Quarter-3	Quarter-4
2008	59	58	62	60
2009	60	64	63	70
2010	62	70	65	56

Compute a 4-quarter centred moving average.

Solution:

Quarters		4 quarters moving		4 quarters centered moving
		Total	Average	Total	Average
2008        1	59	-	-	-	-
2	58	239	59.75	-	-
3	62	240	60.00	119.75	59.875
4	60	246	61.50	121.50	60.750
2009         1	60	247	61.75	123.26	61.625
2	64	257	64.25	126.00	63.000
3	63	259	64.75	129.00	64.500
4	70	265	66.25	131.00	65.500
2010         1	62	267	66.75	133.00	66.500
2	70	253	63.25	130.00	65.000
3	65	-	-	-	-
4	56	-	-	-	-

Moving Average Smoothing

The moving average is a simple and useful indicator to forecast the trend direction of an activity or phenomenon. This technique comes in handy if all consecutive periods of the variable (e.g., sale, demand, savings, cost, etc.) are available. The moving average techniques are used to estimate the next period value by averaging the value of the last couple of periods immediately prior. The businessmen and traders used it as an indicator to determine the direction of the trend, which is very helpful when deciding whether to sell or keep stock. This technique is called the moving average smoothing technique.

For example, the sales of a product in the last three months are given below:

Month	Sale (000,000)
January	12
February	14
March	15

The simplest approach would be to take the average of January through March and use that to estimate April’s sales:

(12 + 14 + 15) / 3 = 13.66

The sale forecast for the month of April is Rs. 130000 for the month of April. The actual sale of April is used to calculate the projection for May after receiving the actual sales data for April. The number of periods you utilise for moving average forecasting needs to be constant.

The forecast for the period for (t+1)

Where:

Ft+1: forecast for period t + 1

Yt-1: Value of period t-1.

The three-period, five-period moving average would be

Practice Question

Predict sales for 2008 by the 3-year moving average method, using the following data.

Year	sale	Forecast
2003	4	-
2004	3	-
2005	2	-
2006	1.5	3.00
2007	1	2.17
2008		1.50

Forecast for 2008

Practice Question

A company's sales over the last 25 weeks (in millions) are given below:

Week	1	2	3	4	5	6	7	8	9	10	11	12	13
Sale	5.3	4.4	5.4	5.8	5.6	4.8	5.6	5.6	5.4	6.5	5.1	5.8	5
week	14	15	16	17	18	19	20	21	22	23	24	25
sale	6.2	5.6	6.7	5.2	5.5	5.8	5.1	5.8	6.7	5.2	6	5.8

Solution:

Pros of Moving Average Method

i. The moving average method is simple to understand and calculate.

ii. The moving average method removes all subjective features.

iii. The estimation process is not affected by adding a new observation in the original data.

iv. The moving average method is used to measure seasonal, cyclical, and accidental variation.

Cons of Moving Average Method

i. The moving average method fails to determine the estimates of all values.

ii. There will be no functional relationship; therefore, the forecasting ability is limited.

• Read More: The Method of Least Squares