Question

A popular brand of fly fishing rods has had the following demand history by quarters for the past 16 quarters.

Quarter	Demand	Quarter	Demand
1	52	9	81
2	46	10	108
3	56	11	74
4	75	12	49
5	92	13	59
6	65	14	79
7	50	15	102
8	60	16	73

a. Using the data above, forecast the demand for the next 8 quarters using Winter’s Seasonal Model. Use Minitab to find a good fitting seasonal model (you must decide whether to use an additive or multiplicative model; decide which values to use for model parameters α, β, γ.)

b. Conduct a sensitivity analysis to determine how the forecast accuracy measures (i.e. MAD, MAPE, MSE) change as the parameter settings change.

Answer 1

• This is a simple problem related to creation of a forecasting model with seasonal effects taken into account.

  This kind of a forecasting model is done with the help of Holt's winter's seasonal model which taken into account the seasonal impact on calculaton.

  To derive the desired forecast ,we use the following formula for Holt's winter model .

  

  The basic equations for their method are given by: s-α岩+(1.. α)(S,1+bel) yt OVER AL L SMOOTHING t-L bt-γ(S-St-ı) + (1-7)b-1 TREND SMOOTHING yt SEASONAL SMOOTHING FORECAST where y is the observation . S is the smoothed observation . b is the trend factor . I is the seasonal index .F is the forecast at m periods ahead t is an index denoting a time period and α, β, and γ are constants that must be estimated in such a way that the MSE of the error is minimized. This is best left to a good software package.

  Based on the formula application ,we have traced the forecast for the next 8 quarters along with the sensitivity analysis.

  Winter's Model
  	alpha =	0.50
  	beta =	0.30
  period	sales	level	trend	forecast	error	ABS(error)	Squared Error	Percent Error
  1	52	52	0	-	-	-	-	-
  2	46	52	0	52.00	-6.00	6.00	36.00	0.13
  3	56	49.00	-0.90	48.10	7.90	7.90	62.41	0.14
  4	75	52.05	0.28	52.34	22.67	22.67	513.70	0.30
  5	92	63.67	3.68	67.35	24.65	24.65	607.51	0.27
  6	65	79.68	7.38	87.06	-22.06	22.06	486.56	0.34
  7	50	76.03	4.07	80.10	-30.10	30.10	906.14	0.60
  8	60	65.05	-0.44	64.61	-4.61	4.61	21.24	0.08
  9	81	62.30	-1.13	61.17	19.83	19.83	393.19	0.24
  10	108	71.09	1.84	72.93	35.07	35.07	1230.16	0.32
  11	74	90.46	7.10	97.57	-23.57	23.57	555.31	0.32
  12	49	85.78	3.57	89.35	-40.35	40.35	1628.10	0.82
  13	59	69.17	-2.49	66.69	-7.69	7.69	59.13	0.13
  14	79	62.84	-3.64	59.21	19.79	19.79	391.80	0.25
  15	102	69.10	-0.67	68.43	33.57	33.57	1126.72	0.33
  16	73	85.22	4.37	89.58	-16.58	16.58	274.96	0.23
  17	89.58	81.29	1.88	83.17	6.41	6.41	41.13	0.07
  18	83.17	86.38	2.84	89.22	-6.05	6.05	36.56	0.07
  19	89.22	86.19	1.93	88.13	1.09	1.09	1.19	0.01
  20	88.13	88.67	2.10	90.77	-2.64	2.64	6.98	0.03
  21	90.77	89.45	1.70	91.15	-0.38	0.38	0.14	0.00
  22	91.15	90.96	1.64	92.60	-1.45	1.45	2.11	0.02
  23	92.60	91.87	1.43	93.30	-0.70	0.70	0.49	0.01
  24	93.30	92.95	1.32	94.27	-0.97	0.97	0.94	0.01
  					-1.51	21.53	585.48	0.32
  					BIAS	MAD	MSE	MAPE

  

  Forecast vs. Actual 120 100 80 650) 40 20 1 23 45 6 78 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 -sales-forecast