If the estimate of the trend component is 160.2, the estimate of the seasonal component is 94%, the estimate of the cyclical component is 105%, and the estimate of the irregular component is 98%, then the multiplicative model will produce a forecast of
A) 1.55.
B) 147.58.
C) 154.96.
D) 154,960,532.

Question

Quizplus · Accepted Answer

The multiplicative model for time series forecasting is given by:
Y(t) = T(t) ×  S(t) × C(t) × I(t)
where Y(t) is the observed value at time t, T(t) is the trend component at time t, S(t) is the seasonal component at time t, C(t) is the cyclical component at time t, and I(t) is the irregular or random component at time t.

Given the estimates of the components, the forecast can be obtained by multiplying the estimates together as follows:
Y(f) = T(f) × S(f) × C(f) × I(f)
where Y(f) is the forecasted value, T(f) is the estimated trend component, S(f) is the estimated seasonal component, C(f) is the estimated cyclical component, and I(f) is the estimated irregular component.

Substituting the given estimates, we get:
Y(f) = 160.2 × 0.94 × 1.05 × 0.98
Y(f) = 154.95996 ≈ 154.96

Therefore, the multiplicative model will produce a forecast of 154.96. Option C is the correct answer.

If the Estimate of the Trend Component Is 160