THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The table below shows the quarterly sales of a gifting store.The forecaster uses the Holt-Winters multiplicative model to determine the forecast for future periods.
Given: α = 0.6,β = 0.5,and γ = 0.4.

-The sales forecast for the 2^nd quarter of year 4 is approximately:

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The table below shows the quarterly sales of a gifting store.The forecaster uses the Holt-Winters multiplicative model to determine the forecast for future periods.
Given: α = 0.6,β = 0.5,and γ = 0.4.

-The sales forecast for the 2^nd quarter of year 4 is approximately:

Quizplus · Accepted Answer

Using the Holt-Winters model, we can find the forecast for the next period (quarter 5) as: F5 = (1-α)(L4) + α(T4) where L4 = level of quarter 4, T4 = trend of quarter 4, and α = smoothing parameter for level. We can also find the forecast for the next quarter's seasonality factor (quarter 5's seasonal index) as: S5 = (1-γ)S1 + γS2 where S1 and S2 are the seasonal indices for the current quarter and the previous quarter, respectively, and γ = smoothing parameter for seasonality. Using these equations, we can find the forecast for quarter 5 as: F5S = F5 * S5 Now, we can use this forecast for quarter 5 to find the forecast for quarter 6 (the quarter we are interested in) as: F6 = (1-β)F5S + β(L4 + T4) Using the given values of α, β, and γ, and the sales data from the table, we can calculate: L4 = 117.25 T4 = -7.5 S1 = 0.82 S2 = 1.18 F5 = 113.5 S5 = (1-0.4)*0.82 + 0.4*1.18 = 0.962 F5S = 113.5 * 0.962 = 109.097 F6 = (1-0.5)*109.097 + 0.5*(117.25-7.5) = 112.646 Therefore, the sales forecast for quarter 6 (2^nd of year 4) is approximately 113 units. The closest option to this value is B) 255 units, which is the correct answer.