$3\mathrm{.}7$ The average annual U$.$S$.$ landed cost of Saudi Arabian Light Crude Oil $($in U$.$S$.$Only solve the question in the pictureRefer to Exercise $3\mathrm{.}8.$ What is the error of your one$-$step ahead forecast for $2014$ when alpha

is $0\mathrm{.}8,$ beta is $0\mathrm{.}44?$ edollars

per barrel$)$ for $19782015$ is provided in SA$\_$oil$\_$prices$\_2.$xlsx$.$

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 $\backslash$alpha $=0\mathrm{.}2,0\mathrm{.}5,$ and $0\mathrm{.}8$ in turn.

b$.$ With the same starting value, find the optimal level for $\backslash$alpha $,$ using the data for

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

software.

c$.$ Generate the forecasts for $20082015.$

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.

Refer to Exercise $3\mathrm{.}8.$ What is the error of your one$-$step ahead forecast for $2014$ when alpha is $0\mathrm{.}5,$ beta is $0\mathrm{.}49?$