SCENARIO 16-13
Given Below Is the Monthly Time Series Data

SCENARIO 16-13
Given below is the monthly time series data for U.S. retail sales of building materials over a
specific year. $$\begin{array} { | c | c | } \hline \text { Month } & \text { Retail Sales } \\\hline 1 & 6,594 \\\hline 2 & 6,610 \\\hline 3 & 8,174 \\\hline 4 & 9,513 \\\hline 5 & 10,595 \\\hline 6 & 10,415 \\\hline 7 & 9,949 \\\hline 8 & 9,810 \\\hline 9 & 9,637 \\\hline 10 & 9,732 \\\hline 11 & 9,214 \\\hline 12 & 9,201 \\\hline\end{array}$$ The results of the linear trend, quadratic trend, exponential trend, first-order autoregressive,
second-order autoregressive and third-order autoregressive model are presented below in which
the coded month for the 1st month is 0: $\text { Linear trend model: }$
$\begin{array}{lrrrr} & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } \\\hline \text { Intercept } & 7950.7564 & 617.6342 & 12.8729 & 0.0000 \\\text { Coded Month } & 212.6503 & 95.1145 & 2.2357 & 0.0494\end{array}$

$\text { Quadratic trend model: }$


$\text { Exponential trend model: }$
$\begin{array}{lrrrr}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } \\\hline \text { Intercept } & 3.8912 & 0.0315 & 123.3674 & 0.0000 \\\text { Coded Month } & 0.0116 & 0.0049 & 2.3957 & 0.0376\end{array}$


$\text { First-order autoregressive: }$
$\begin{array}{lrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & {\text { P-value }} \\\hline \text { Intercept } & 3132.0951 & 1287.2899 & 2.4331 & 0.0378 \\\text { YLag1 } & 0.6823 & 0.1398 & 4.8812 & 0.0009 \\\hline\end{array}$


-Referring to Scenario 16-13, what is the exponentially smoothed value for the $12 ^ { \text {th } }$ month
using a smoothing coefficient of W = 0.5 if the exponentially smooth value for the $10 ^ { \text {th } }$ and
11th month are 9,746.3672 and 9,480.1836, respectively?