Exercise $10-43$ Static $($Using R$)$

The accompanying data file contains annual population data $($in millions$)$ for Japan from $1960$ to $2019.$ For crossvalidation, let the training and the validation sets comprise the periods from $1960$ to $2005$ and $2006$ to $2019,$ respectively.

Click here for the Excel Data File

a$.$ Use the training set to implement the Holt exponential smoothing method with user$-$supplied $(a=0\mathrm{.}20$ and $=0\mathrm{.}15),$ as well as the computer$-$generated, smoothing parameters and compute the resulting performance measures for the validation set.

Note: Do not round intermediate calculations. Round final answers to $2$ decimal places.

$\backslash$table$[[$Parameters$,$MSE,MAD,MAPE $(\%)],[\backslash$table$[[$Comper$-$supplied$],[$generated$-]],,,]]$

b$-1.$ Determine the preferred smoothing parameters for making the forecast?

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b$-2.$ Reestimate the preferred model with the entire data set to forecast the population in Japan for $2020($in millions$).$ Note: Do not round intermediate calculations. Round final answers to $2$ decimal places.

Population $in$ Japan for

$2020$ :