fix(models): improve the SES implementation

[christophertitchen]

Summary

• Amend README.md to note support for in-sample fitted values for SimpleExponentialSmoothing, SimpleExponentialSmoothingOptimized, SeasonalExponentialSmoothing, and SeasonalExponentialSmoothingOptimized.
• Set the first in-sample fitted value in _ses_fcst_mse to the first observation, rather than np.nan, to make it explicitly clear that the initial state is the first observation.
• Improve the efficiency and performance of _ses_fcst_mse by, for example, pre-calculating the smoothing complement, $1 - \alpha$, and removing the unnecessary $n - 1$ copies of fitted values before assignment.
• Improve the performance of _optimized_ses_forecast by changing from scipy.optimize.minimize to scipy.optimize.minimize_scalar. This uses Brent's method which is derivative-free and optimised for local one-dimensional optimisation problems like this, with guaranteed convergence within a reasonable number of evaluations. The convergence will also be superlinear for our strictly convex $C^2$ objective function when the minimum is at an interior point of the interval for $\alpha$, which will be the case particularly in SimpleExponentialSmoothingOptimized and SeasonalExponentialSmoothingOptimized, where $0 \lt \alpha \lt 1$. It should also be quite a bit faster even for the $0.1 \lt \alpha \lt 0.3$ bounds of ADIDA, Croston, and IMAPA. It also does not have the initialisation sensitivity that L-BFGS-B has (the initialisation of $\alpha$ was also out-of-bounds before for some reason).
• Add a temporary benchmark to test_efficiency.py for CodSpeed.

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CodSpeed Performance Report

Merging #973 will not alter performance

_{Comparing christophertitchen:fix/ses-fitted (099d906) with main (fea7193)}

Summary

✅ 6 untouched benchmarks

[jmoralez]

Thanks. Can you just elaborate on the following?

Set the first in-sample fitted value in _ses_fcst_mse to the first observation, rather than np.nan, to make it explicitly clear that the initial state is the first observation.

The fitted values are supposed to be the one-step ahead forecasts with an expanding training set, so the first value should be NaN.