Exponentially weighted average is a technique frequently used for time-series data. By taking the average sum of previous data, you could smooth your data series and get an approximate trend of it.

Consider you have a series of data points $\theta_0,...,\theta_n$, $\left\{ \begin{array}{ll}v_t = \theta_t & t=0 v_t = \beta v_{t-1} +(1-\beta)\theta_t & otherwise \end{array}\right.$ If we expand the second formula, $v_t = \beta v_{t-1}+(1-\beta)\theta_t$ $= (1-\beta)\theta_t+\beta(\beta v_{t-2}+(1-\beta)\theta_{t-1})$ $= (1-\beta)\theta_t + (1-\beta)\beta\theta_{t-1}+ (1-\beta)\beta^2\theta_{t-2}+...$ To get a sense of how the weighted term changes as $\beta$ gets closer to 1, $(1 - \epsilon)^{1 / \epsilon}\approx \frac{1}{\epsilon} \Rightarrow \beta^{1/(1-\beta)}\approx \frac{1}{\epsilon}$ If we denote $w_i$ be the weight we assign to $\theta_i$, then $w_{t-1/(1-\beta)}=\frac{1}{\epsilon}w_t$ Therefore, we are approximately average over $1/(1-\beta)days when calculatingv_t$.