# How to use exponential smoothing for trading?

I was wondering if there's a rule of thumb regarding the value of alpha used when performing exponential smoothing. I plan to use this technique to preprocess my data before feeding them into my machine learning algorithm.

Here is the answer given by Wikipedia:

The time constant of an exponential moving average is the amount of time for the smoothed response of a unit set function to reach $1-1/e\approx 63.2\,\%$ of the original signal. The relationship between this time constant, $\tau }$ , and the smoothing factor, $> \alpha$, is given by the formula:

$\alpha =1-e^{-\Delta T \over \tau }$

Where $\Delta T$ is the sampling time interval of the discrete time implementation. If the sampling time is fast compared to the time constant then $\alpha \ \approx {\frac{\Delta T}{\tau} }$.

This canonical approach is fine, but I find it fairly inefficient because:

• taking the double and triple EMAs is redundant; it is essentially equal to using a lower alpha value;
• The weights of terms only converge to one; i.e., $\sum w \ne 1$; and
• Estimating initial parameters requires significant amount of recursion.

I therefore propose the following method: Is there a non-recursive way of calculating the exponential moving average?