(Monte Carlo) Using a computer, generate an artificial data set of 21 observations as follows:

(a) Set $w_n = \frac{20}{21}(n-1)$ for $n = 1, \dots, 21$.

(b) Set $y_n = w_n^2 + \epsilon_n$ where $\epsilon_n \sim \mathcal{N}(0, \frac{1}{100})$.

Using this data set, compute OLS fitted values for each of the following specifications:

Compare the fitted values. Also compute and compare out-of-sample forecasts for y for values of w from −2 to 3.

Elyw] B+ B Elyw] B+B Elynw] B+ Be En B+B cos(w)