Answer to Question #153438 in Statistics and Probability for Shavetra

Question

1. Income at the architectural firm Spraggins and Yunes for the period February to July was as follows:

MONTH

FEBRUARY

MARCH

APRIL

MAY

JUNE

JULY

Income (in RM thousand)

70.0

68.5

64.8

71.7

71.3

72.8

Use trend-adjusted exponential smooting to forecast the firm’s August income. Assume February is RM65,000 and the initial trend adjustment is 0. The smooting constants selected are α = 0.1 and β = 0.2. 

Answer 1

Forecasting is the technique that helps to evaluate on the future aspects of the business or operation.

Forecast for month February to August using trend-adjusted exponential smoothing is given below:

The unadjusted forecast for February is given as $65 and trend estimate for February is 0.

The formula to compute the unadjusted forecast (F_t) is calculated by adding two values. First value is the multiple of smoothing constant α and the actual demand (income) of previous period. Second value is calculated by multiplying the value attained by subtracting trend estimate of previous period from the unadjusted forecast of previous period with the value attained by subtracting α from 1.

F_t = α(Actual demand of previous perio) + (1 - α)(Unadjusted forecast of previous period + Trend estimate of previous period)

F_t = α(A_t-1) + (1 – α)(F_t-1 + T_t-1)

The formula to compute the trend estimate (T_t) is calculated by adding two values. First value is the multiple of β and the value attained by subtracting the forecast of previous period from the present period. second value is the multiple of trend estimate of previous period and the value attained by subtracting β from 1.

T_t = β(Forecast of present period – Forecast of previous period) + (1 – β)(Trend estimate of previous period)

T_t = β(F_t – F_t-1)+(1 – β)(T_t-1)

The formula to compute the adjusted forecast (FIT_t ) is calculated by adding the unadjusted forecast and the trend estimate.

FIT_t = Unadjusted forecast + Trend estimate

FIT_t = F_t + T_t

Calculate the unadjusted forecast for August (F₇):

F₂ = α(A_7-1) + (1 – α)(F_7-1 + T_7-1)

$= (0.1 \times 72.8) + (1 -0.1)(67.31+0.33) \\ = 7.28 + (0.9 \times 67.64) \\ = 68.15$

The unadjusted forecast for August is 68.15

Calculate the trend estimate for August (T₇):

T₇ = β(F₇ – F_7-1)+(1 – β)(T_7-1)

$= 0.2(68.16-67.31) + (1 -0.2) \times 0.33 \\ = 0.17 + 1.65 \\ = 1.82$

The trend estimate for August is 1.82

Calculate the adjusted forecast for August (FIT₇):

FIT₇ = F₇ + T₇

= 68.15 + 1.82

= 69.97

The adjusted forecast of August is 69.97