Please solve using RStudio. #Run the library first

library$($fpp$3)1\mathrm{.}1.$Create the data set $$us$\_$manu$\_$emp$$ from the data set $$us$\_$employment$$ that covers the period from January $1990$ to the end of the time series.

$1\mathrm{.}2.$Create a tsibble for us$\_$manu$\_$emp, print the first $10$ rows, and attach them here. Use font courier new and size $8.1\mathrm{.}3.$Compute the autocorrelation coefficients for US manufacturing employment up to lag $10.$ Explain the autocorrelations. Attach the autocorrelation tsibble here. Use font $$courier new$$ and size $8$ to format the table. $1\mathrm{.}4.$Create a plot of the ACF for US manufacturing employment. Explain the ACF. $2\mathrm{.}1.$Create the data set $$us$\_$private$\_$emp$$ from the data set $$us$\_$employment$$ that covers the period from January $1990$ to the end of the time series.

$2\mathrm{.}1$ Do an STL decomposition for US private employment. Use a trend$($window $=7)$ and season $($window $=$periodic$).$ Attach the plot here.

$2\mathrm{.}2$Print the dable that shows the STL components and attach it here. Use font $$courier new$$ and size $8$ to format the table. $3\mathrm{.}1.$Compute the mean of the original US private employment series that you created in problem $2.$ Attach it here. Use font $$courier new$$ and size $8.$

$3\mathrm{.}2.$Compute the minimum, the maximum, and the quartiles for US private employment. Attach it here. Use font $$courier new$$ and size $8.$

$3\mathrm{.}3.$Compute the ACF features and describe them. Attach them here. Use font $$courier new$$ and size $8$

Compute the STL features. Attach them here. Use font $$courier new$$ and size $8.4\mathrm{.}1.$Use the data $$us$\_$private$\_$emp$$ you created in problem $2$ above and create the data set $$us$\_$private$\_$emp$\_$train$$ that covers the period from January $1990$ to December $2015.$

$4\mathrm{.}2.$Fit the models Mean, Na$$ve$,$ Seasonal Na$$ve$,$ and Drift to the original US private employment series.

$4\mathrm{.}3.$Generate forecasts for the period January $2016-$ September $2019.$

$4\mathrm{.}4.$Generate a plot of the forecasts and the actual data. Attach the plot here.

$4\mathrm{.}5.$Generate accuracy measures and identify the best forecasting model. Paste the accuracy measures here. Use font courier new and size $8.$

$4\mathrm{.}6.$Generate a plot of the residual diagnostics. Explain the residual diagnostics. Attach the plot here.

$4\mathrm{.}7.$Do the Box$-$Pierce and Ljung$-$Box correlation tests of the residuals. Explain the results. Attach the results here. Use font courier new and size $8.$ Provide the answers with necessary codes.