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

question 6

Short Answer

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 = 0.25 if the exponentially smooth value for the $10 ^ { \mathrm { th } }$ and $11 ^ { \text {th } }$ month are 9,477.7776 and 9,411.8332, respectively?

---

Definitions:

Free Markets

An economic system in which prices are determined by unrestricted competition between privately owned businesses, without government intervention.

Efficiency

The optimal allocation of resources to produce the maximum amount of goods and services, with the least waste of resources.

Pareto Optimality

Pareto Optimality is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.

Income Distribution

Income Distribution refers to the way in which total income is shared among the members of a society.