7.4. EWMA Exponential Weighted Moving Average

• Exercise with the airline dataset

Formula $y(t)=\frac{{\sum }_{i=0}^t{w}_{i}x(t-i)}{{\sum }_{i=0}^t{w}_i},$ where $x(t)$ is the input value, $w_i$ is the applied weight and $y(t)$ is the output

How to decide on the values of $w_i$?

Adjust (from pandas) calculates the weights using two different formulae whether or not adjust is true ot not. The weights are parametrized by a value $\alpha$

Pandas sets $\alpha$ in three ways: * Span: corresponds to $N-day$ exponential moving average. This parametrizes $\alpha$ by a value $s\ge 1$ * Center of mass: has a more physical interpretation. This parametrizes $\alpha$ by a value $c=(s-1)/2$ * Half-life: period of time for the exponential weight to reduct to one half. This parametrizes $\alpha$ by a value $h$.