The following table shows the production figures (x_{i}) of cars of a company over a time period

Question:

The following table shows the production figures $x_{i}$ of cars of a company over a time period of 12 years (in $10^{3}$ ).

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(1) Draw a time series plot. Is the underlying trend function linear?
(2) Smooth the time series $\left\{x_{i}\right\}$ by the Epanechnikov kernel with bandwidth $[-2,+2]$.
(3) Smooth the time series $\left\{x_{i}\right\}$ by exponential smoothing with parameter $\lambda=0.6$ and predict the output for year 13 by the recursive equation (6.31).

Data from 6.31