Simple Exponential Smoothing with a Tuned Alpha

Simple exponential smoothing keeps a level $\ell_t = \alpha y_t + (1-\alpha)\ell_{t-1}$, starting from $\ell_0 = y_0$; the one-step-ahead forecast for $y_{t+1}$ is $\ell_t$.

Implement:

• ses(y, alpha) returning (levels, sse) where sse is the sum of squared one-step-ahead errors for $t = 1..n-1$
• fit_alpha(y, grid) returning the alpha in grid with the smallest SSE (first wins ties)