Exponential moving average

The exponential moving average, which we will refer to as the EMA, is the single most well-known and widely used technical analysis indicator for time series data. 

The EMA is similar to the simple moving average, but, instead of weighing all prices in the history equally, it places more weight on the most recent price observation and less weight on the older price observations. This is endeavoring to capture the intuitive idea that the new price observation has more up-to-date information than prices in the past. It is also possible to place more weight on older price observations and less weight on the newer price observations. This would try to capture the idea that longer-term trends have more information than short-term volatile price movements.

The weighting depends on the selected time period of the EMA; the shorter the time period, the more reactive the EMA is to new price observations; in other words, the EMA converges to new price observations faster and forgets older observations faster, also referred to as Fast EMA. The longer the time period, the less reactive the EMA is to new price observations; that is, EMA converges to new price observations slower and forgets older observations slower, also referred to as Slow EMA.

Based on the description of EMA, it is formulated as a weight factor, , applied to new price observations and a weight factor applied to the current value of EMA to get the new value of EMA. Since the sum of the weights should be 1 to keep the EMA units the same as price units, that is, $s, the weight factor applied to EMA values turns out to be . Hence, we get the following two formulations of new EMA values based on old EMA values and new price observations, which are the same definitions, written in two different forms:

Alternatively, we have the following:

Here, the following applies:

: Current price of the instrument

: EMA value prior to the current price observation

: Smoothing constant, most commonly set to 

: Number of time periods (similar to what we used in the simple moving average)

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset
3.230.162.238