Question

The following data are monthly sales of jeans at a local department store. The buyer would like to forecast sales of jeans for the next month, July.

(a) Forecast sales of jeans for March through June using the naïve method, a two-period moving average, and exponential smoothing with an ? = 0.2. (Hint: Use naïve to start the exponential smoothing process.)
(b) Compare the forecasts using MAD and decide which is best.
(c) Using your method of choice, make a forecast for the month of July.

Month	Sales
January	45
February	30
March	40
April	50
May	55
June	47

Answer 1

Please refer below table highlighting relevant calculations :

Month	Actual sales	Forecast ( Naïve method)	Absolute deviation	Forecast ( 2 period moving average)	Absolute deviation	Forecast ( Exponential smoothing)	Absolute deviation
January	45
February	30	45	15			45
March	40	30	10	37.5	2.5	42	2.00
April	50	40	10	35	15	41.6	8.40
May	55	50	5	45	10	43.28	11.72
June	47	55	8	52.5	5.5	45.62	1.38
July		47		51		45.90
		SUM =	48		33		23.50

Following to be noted :

Forecasted value as per Naïve method :

Ft = At-1    , Ft = Forecast for period t and At-1 = Actual sales for period t-1

Forecasted value as per 2 period moving average :

Ft =   ( At-1 + At-2 ) /2 , Ft = forecast for period t , At-1 , At-2 = actual sales for period t-1 and t-2 respectively

Forecasted value as per exponential smoothing method :

First we determine forecasted value for February = 45 as per Naïve method

Subsequently :

Ft = alpha x At-1 + ( 1 – alpha) x Ft-1

      = 0.2 x At-1 + 0.8 x Ft-1

Where, alpha = exponential smoothing forecast = 0.2

Also to be noted:

Absolute deviation = Absolute difference between actual sales value and forecasted value

Mean absolute deviation ( MAD) = Sum of absolute deviation / Corresponding number of observations

Based on above definition of MAD ,

MAD for forecast as per Naïve method = 48/5 = 9.6

MAD for forecast as per 2 period moving average = 33/ 4 = 8.25

MAD for forecast as per exponential smoothing method = 23.5 / 4 = 5.875

Since MAD for exponential smoothing forecast is the LOWEST , Exponential smoothing forecast is the best

FORECAST FOR JULY AS PER NAÏVE METHOD = 47

FORECAST FOR JULY AS PER 2 PERIOD MOVING AVERAGE = 51

FORECAST FOR JULY AS PER EXPONENTIAL SMOOTHING METHOD = 45.90