What is Exponential Smoothing Forecast Method?

 Exponential Smoothing Forecast Method: It is a time series used previous data to forecast future data. It is used to forecast short term data. It does not able to forecast future trend with the help of previous data. It is a simple method to forecast future demand with the help of past actual demand data and by using alpha.

Formula:

F_t = αA_t-1 + (1-α) F_t-1

Where,

F_t = Forecast demand for week t

Α_t-1 = previous period actual demand

F_t-1 = previous period forecast demand

And α =Smoothing constant

Common Measures of Error

Mean Absolute Deviation (MAD):

MAD = Ʃ ǀ actual –forecast ǀ / n

Mean Squared Error (MSE):

MSE = Ʃ (forecast errors) ² / n

Mean Absolute Percentage Error:

MAPE = 100* Ʃ ǀ actual _i –forecast _i ǀ/actual _i / n

Example: Find out the future demand with the help of using exponential smoothing forecast method. Alpha (α) is 0.2.

Time period	Actual Demand(At)	Forecast demand(Ft)
1	480	300
2	460	-
3	340	-
4	490	-
5	400	-
6	370	-
7	580	-

 Solution:

Time period	Actual Demand(At)	Forecast demand(Ft)	At-Ft	(At-Ft)2
1	480	300	180	32400
2	460	336	124	15376
3	340	360.8	-20.8	432.64
4	490	356.64	133.36	17784.89
5	400	383.31	16.69	278.5561
6	370	386.65	-16.65	277.2225
7	580	383.32	196.68	38683.02

 

F_t = αA_t-1 + (1-α) F_t-1

= 0.2(480) + (1-0.2)300

= 96 + 0.8*300

= 96+240

F₂=336

F_t = αA_t-1 + (1-α) F_t-1

= 0.2(460) + (1-0.2)336

= 92 + 268.8

F₃= 360.8

F_t = αA_t-1 + (1-α) F_t-1

= 0.2(340) + (1-0.2)360.8

= 68 + 288.64

= 356.64

F_t = αA_t-1 + (1-α) F_t-1

= 0.2(490) + (1-0.2)356.64

= 98 + 285.31

= 383.31

F_t = αA_t-1 + (1-α) F_t-1

= 0.2(400) + (1-0.2)383.31

= 80 + 306.65

= 386.65

F_t = αA_t-1 + (1-α) F_t-1

= 0.2(370) + (1-0.2)386.65

=74 + 309.32

= 383.32

Example: Find out the “α” with the help of given information:

Time	Actual demand (At)	Forecast demand (Ft)
1	80	80
2	72	80
3	85	76

 

Solutions: With the help of Forecast method we calculate “α”:

Let’s take F₃ value:

F_t = F_t-1 + α (A_t-1-F_t-1)

76 = 80 + α (72-80)

 76 = 80 + (-8α)

-4/-8= α

And α = 0.5

Example: Find out the mean squared error and mean absolute deviation with the help of following information:

Time period	Actual Demand(At)	Forecast demand(Ft)
1	265	290
2	325	300
3	340	320
4	280	360
5	400	260
6	320	275
7	220	330
8	260	290

 Solution:

Time period	Actual Demand(At)	Forecast demand(Ft)	At - Ft	ǀ At – Ft ǀ	(ǀ At – Ft ǀ)^2	(ǀ At – Ft ǀ / At)*100
1	265	290	-25	25	625	9.43
2	325	300	25	25	625	7.69
3	340	320	20	20	400	5.88
4	280	360	-80	80	6400	28.57
5	400	260	140	140	19600	35.00
6	320	275	45	45	2025	14.06
7	220	330	-110	110	12100	50.00
8	260	290	-30	30	900	11.54
Total				475	42675	162.18

MAD = Ʃ (ǀ actual –forecast ǀ)/ n

          = 475/8

          = 59.38

MSE = Ʃ (forecast errors) ² / n

        = 42675 /8

       = 5,334.38

MAPE = 100* Ʃ ǀ actual _i –forecast _i ǀ/actual _i / n

            = 162.18/8                                                  

           = 20.27