The time-series multiplicative model is used for forecasting, where $T _ { t } , C _ { t } , S _ { t },$ and $R _ { t }$ are respectively the trend, cyclical, seasonal and random variation components of the time series, and $y _ { t }$ is the value of the time series at time t. The following estimates are obtained: $\hat { T _ { 1 } }$ = 125, $\hat { C } _ { t }$ = 1.03, $\hat { S } _ { t }$ = 1.02, $\hat { R } _ { t }$ = 0.97. The model will produce a forecast of:
A)122.659.
B)131.325.
C)118.980.
D)127.385.

Question

Quizplus · Accepted Answer

In the multiplicative model, the forecast $\hat{y}_t$ is calculated as the product of the estimates of its components: $\hat{y}_t = \hat{T}_t \times \hat{C}_t \times \hat{S}_t \times \hat{R}_t$. Substituting the given values, $\hat{y}_t = 125 \times 1.03 \times 1.02 \times 0.97 = 127.385.$

The Time-Series Multiplicative Model Is Used for Forecasting, Where Tt,Ct,St,T _ { t } , C _ { t } , S _ { t },Tt​,Ct​,St​,

The Time-Series Multiplicative Model Is Used for Forecasting, Where $T _ { t } , C _ { t } , S _ { t },$