The business analyst for Video Sales, Inc. wants to forecast this year's demand for DVD decoders based on the following historical data: $$\begin{array} { | c | c | }
\hline \text { Year } & \text { Enrollments } \
\hline 5 \text { Years ago } & 900 \
\hline 4 \text { Years ago } & 700 \
\hline 3 \text { Years ago } & 600 \
\hline 2 \text { Years ago } & 500 \
\hline \text { Last Year } & 300 \
\hline
\end{array}$$
What is the forecast for this year using trend-adjusted (double) smoothing with alpha = .3 and beta = .2, if the forecast for last year was 310, the forecast for two years ago was 430, and the trend estimate for last year's forecast was -150?
A) 162.4
B) 180.3
C) 301.4
D) 403.2
E) 510

Question

The business analyst for Video Sales, Inc. wants to forecast this year's demand for DVD decoders based on the following historical data: $$\begin{array} { | c | c | } 
\hline \text { Year } & \text { Enrollments } \
\hline 5 \text { Years ago } & 900 \
\hline 4 \text { Years ago } & 700 \
\hline 3 \text { Years ago } & 600 \
\hline 2 \text { Years ago } & 500 \
\hline \text { Last Year } & 300 \
\hline
\end{array}$$
What is the forecast for this year using trend-adjusted (double) smoothing with alpha = .3 and beta = .2, if the forecast for last year was 310, the forecast for two years ago was 430, and the trend estimate for last year's forecast was -150?
A) 162.4
B) 180.3
C) 301.4
D) 403.2
E) 510

Quizplus · Accepted Answer

The trend-adjusted forecast is calculated using the formula: $ F_{t+1} = S_t + T_t $, where $ S_t $ is the smoothed forecast and $ T_t $ is the trend estimate. First, update the smoothed forecast and trend using: $ S_t = \alpha \times A_t + (1-\alpha) \times (S_{t-1} + T_{t-1}) $ and $ T_t = \beta \times (S_t - S_{t-1}) + (1-\beta) \times T_{t-1} $. Given $ \alpha = 0.3 $, $ \beta = 0.2 $, $ A_t = 300 $, $ S_{t-1} = 310 $, $ T_{t-1} = -150 $, calculate $ S_t $ and $ T_t $, then use them to find $ F_{t+1} $.

The Business Analyst for Video Sales, Inc What Is the Forecast for This Year Using Trend-Adjusted (Double)