A check-processing center uses exponential smoothing to forecast the number of i

Question

A check-processing center uses exponential smoothing to forecast the number of incoming checks each month. The number of checks received in June was 42 million, while the forecast was 43 million. A smoothing constant of 0 15 is used. Using exponential smoothing and given alpha, the forecast for the month of July = 42 85 million checks received (round your response to one decimal place). If the check-processing center received 45 million checks in the month of July, then using exponential smoothing and given alpha, the forecast for the month of August = million checks received (round your response to one decimal place).

Explanation / Answer

Exponential smoothing method

In exponential smoothing method, the new forecast is based on the previous forecast, plus a percentage of the difference between that forecast and the actual forecast of the series at that point.

Next forecast = Previous forecast + (Actual Previous forecast)

The equation is:

Ft = Ft-1 + (At-1 Ft-1)

Ft = Ft-1 + At-1 Ft-1

Ft = At-1 + (1 – )Ft-1

Where,

Ft = Forecast for time period t                                                   

Ft1 = Forecast for time period t1

At1 = Actual value in period (t1)

= Smoothing constant (percentage)

a)

For July month,

= 0.15, 1 = 0.85

Ajune = 42   and   Fjune = 43

Fjuly = 0.15Ajune + 0.85Fjune = 0.15 × 42 + 0.85 × 43 = 42.85

Fjuly = 42.85

b)

For August Month:

Ajuly = 45   and   Fjuly = 42.85

FAug = 0.15Ajuly + 0.85Fjuly = 0.15 × 45 + 0.85 × 42.85 = 43.17

FAug = 43.17

The forecast for month of August = 43.17 million checks to be received.

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