Forecast the series in three ways: $($i$)$ simple exponential smoothing $($ $=0\mathrm{.}35),($ii$)$ Holt's method $($ $=0\mathrm{.}5,$ $=0\mathrm{.}1),$ and $($iii$)$ simple exponential smoothing $($ $=0\mathrm{.}3)$ on trend$-$adjusted data, that is$,$ the residuals from regressing linearly versus time. $($These smoothing constants are close to optimal.$)$ For each of these, list the MAE, the RMSE, and the forecast for next year. $($Round your answers to three decimal places.$)$

Exponential smoothing methodMAERMSEForecastSimple forecast $($ $=0\mathrm{.}35)$ Holt's forecast $($ $=0\mathrm{.}5,$ $=0\mathrm{.}1)$ Simple forecast on trend$-$adjusted data $($ $=0\mathrm{.}3)$

Comment on any "problems" with forecast errors from any of these three approaches. Finally, compare the qualitative features of the three forecasting methods. For example, how do their short$-$run or longer$-$run forecasts differ? Is any one of the methods clearly superior to the others?

The Selectsimple forecastHolt's forecastsimple forecast on trend$-$adjusted dataItem $16$ appears to be the most believable because it does the best job at projecting the SelectdownwardstationaryupwardItem $17$ trend we have seen in recent years.

d$.$Do the data indicate convincingly that global warming has been occurring?

SelectYesNoItem $18$