In statistics, a moving average is a calculation to analyze data points by creating series of averages of different subsets of the full data set. It is also called a moving mean or rolling mean and is a type of finite impulse response filter. Variations include: simple, and cumulative, or weighted forms.

Moving averages are a type of indicators which, over a period of time, identifies the average values of a security’s price.

Exponential moving averages are one of the types of moving averages. It is similar to moving averages in characteristics, but, EMA gives more weight to the current or latest price data. Therefore, they react quicker to any recent changes in price than a simple moving average. EMA’s are popularly used for the 12 and 26 day averages for short term.

The concept of EMA is mostly used by traders and investors as more attention is given to the recent price changes.

To calculate EMA's for any security trading, the following three steps are used:

- First, calculate the SMA (simple moving average). This could be for the last 5 days, 10 days, 15 days, etc.
- Once, the SMA are calculated, figure out the weighting multiplier as per the number of days for which the EMA will be calculated. Always remember that the number of periods will fundamentally affect your weighing multiplier as it plays an important role in determining the current action of the price.
- Lastly, after calculating the SMA and WM (weight multiplier) values, the EMA calculations will become an easy task. The following formula is used for calculations:

(Closing Price – EMA (Previous day) X multiplier + ema (Previous Day)

- The easiest way is to use study the price chart using two different periods. Then, wait for the faster period to move above or higher or lower than the other (slower period). If the EMA of the faster period is above the slower period EMA, this would indicate that the market is going through ‘bullish momentum’. However, if the case is vice versa, then the market is in the ‘bearish momentum’
- Another way to use EMA crosses would be through using them as a ‘dynamic pivot zone’. Under this, the EMA periods, that are huge, such as 200 or 50 day period EMAs display a resistance zone.

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arxiv.org [PDF]

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www.sciencedirect.com [PDF]

… ratio (ShR), Sortino ratio (SoR), maximum drawdown (MDD) and average drawdown (ADD … hand, when fund managers estimate expected returns in practice, moving averages (MAs) of asset returns are often used, and in particular exponential moving averages (EMAs) are …

www.tandfonline.com [PDF]

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ieeexplore.ieee.org [PDF]

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