Question

In: Statistics and Probability

Suppose that simple exponential smoothing with w=0.4 is used to forecast monthly wine sales at a...

Suppose that simple exponential smoothing with w=0.4 is used to forecast monthly wine sales at a liquor store. After April's Demand is observed, the forecasted Demand for May is 4500 bottles of wine.

a. At the beginning of May, What is the forecast of July's Wine Sales?

b. Suppose that actual Demands during May and June are as follows: May - 5000 bottles of wine and June - 4000 bottles of wine. After observing June's Demand, What is the forecast for July's Demand?

c. Based on the data of part b., The demands during May and June averages to 4500 bottles of wine. This is the same as the forecast of the monthly sales before we observed the May and June Data. Yet, after we we observe the May and June demands for wine, our forecast for July's Demand has decreased from what it was at the end of April. Why did this happen?

The process which leads to the answer is needed, not the guidance. Thanks a lot

Expert Solution

Answer

a) FORECAST FOR JULY'S WINE SALES AT THE BEGINNING OF MAY:

Given the simple exponential smoothing with . After the April's demand, the forecasted demand for May is 4500 bottles of wine. At the beginning of May, the forecast of July's wine sales is 4500. This is beacause for a stationary series, when we use simple exponential smoothing , the forecast for each future period remains constant until additional information is available.

b GIVEN THAT:

Forecasted demand for May=4500 bottles of wine

Actual demand for May=5000 bottles of wine

Actual demand for June=4000 bottles of wine

The formula to calculate forecasted value is where Y_t is actual value of previous time and F_t is forecasted value of previous time (either year, month or week).

FORECAST FOR JUNE:

The formula is where Y_t is actual value of May's demand and F_t is forecasted value of May's demand.

Forecasted value of June

FORECAST FOR JULY:

The formula is where Y_t is actual value of June's demand and F_t is forecasted value of June's demand.

Forecasted value of July

Thus forecasted value for July is 4420 bottles of wine

c) after we we observe the May and June demands for wine, our forecast for July's Demand has decreased from what it was at the end of April. was increased .

orchestra answered 2 years ago

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