The following table gives monthly data for four years in million tons of consumption of ice cream in a country. Plot the series and comment on the visible seasonality and trend. Estimate the centered moving averages for this monthly series. Plot CMA and comment. Next, estimate the S$,$I component which only includes seasonal and irregular movements of the series. Then find the seasonal indexes for the twelve months removing the irregular component. Find the de$-$seasonalized levels for the series. Plot De$-$seasonalized Y and comment. Then estimate the trend values for the four sample years and the $12$ months of the year $2021$ using linear regression. Finally, make the forecast for the $12$ months of $2021$ using the Ratio$-$to$-$Moving Average method to capture the Trend and Seasonal patterns, using Excel. Plot the forecasted values for the $60$ periods including $12$ months of the year $2021.$ Plot the errors for in$-$sample periods and calculate RMSE. Comment on the error plot with respect to the existence of pattern or lack of visible pattern.

Month$/$Year $2017201820192020$

Jan $100115135155$

Feb $105118140160$

Mar $110120145165$

Apr $115132150175$

May $125145160190$

Jun $135160170205$

Jul $140170180215$

Aug $135160175205$

Sep $130155170200$

Oct $125150160190$

Nov $115140150170$

Dec $110130145165$