$3\mathrm{.}7$ The average annual U$.$S$.$ landed cost of Saudi Arabian Light Crude Oil $($in U$.$S$.$

dollars

per barrel$)$ for $1978-2015$ is provided in SA$\_$oil$\_$prices$\_2.$xIsx.

A$.$ Use the observed value for $1978$ as the starting value, and compute the one$-$

step$-$

ahead SES forecasts for subsequent years for each of $=0\mathrm{.}2,0\mathrm{.}5,$ and $0\mathrm{.}8$ in turn.

B$.$ With the same starting value, find the optimal level for $,$ using the data for

the period $1978-2007$ as the estimation sample. Use the ESM or other suitable

software.

C$.$ Generate the forecasts for $2008-2015.$

D$.$ Compute the out$-$of$-$sample RMSE, MAE, and MAPE for each case, and contrast

the results. Does using the median rather than the mean make any difference?

$3\mathrm{.}8$ Repeat the analysis in Exercise $3\mathrm{.}7,$ using linear exponential smoothing. $($Use

the

ESM or other suitable software.$)$ Compare the forecasting performance of the two

methods.

SOLVE THIS QUESTION ONLY:

Refer to Exercise $3\mathrm{.}8.$ What is the error of your one$-$step ahead forecast for $2015$ when

alpha is $0\mathrm{.}5,$ beta is $0\mathrm{.}49?$