Moving averages are more than the study of a sequence of numbers in successive order. Early practitioners of time series analysis were actually more concerned with individual time series numbers than they were with the interpolation of that data. Interpolation, in the form of probability theories and analysis, came much later, as patterns were developed and correlations discovered.

Once understood, various shaped curves and lines were drawn along the time series in an attempt to predict where the data points might go. These are now considered basic methods currently used by technical analysis traders. Charting analysis can be traced back to 18th Century Japan, yet how and when moving averages were first applied to market prices remains a mystery. It is generally understood that simple moving averages (SMA) were used long before exponential moving averages (EMA), because EMAs are built on SMA framework and the SMA continuum was more easily understood for plotting and tracking purposes. (Would you like a little background reading? Check out Moving Averages: What Are They?)

Simple Moving Average (SMA)
Simple moving averages became the preferred method for tracking market prices because they are quick to calculate and easy to understand. Early market practitioners operated without the use of the sophisticated chart metrics in use today, so they relied primarily on market prices as their sole guides. They calculated market prices by hand, and graphed those prices to denote trends and market direction. This process was quite tedious, but proved quite profitable with confirmation of further studies.

To calculate a 10-day simple moving average, simply add the closing prices of the last 10 days and divide by 10. The 20-day moving average is calculated by adding the closing prices over a 20-day period and divide by 20, and so on.

This formula is not only based on closing prices, but the product is a mean of prices - a subset. Moving averages are termed "moving" because the group of prices used in the calculation move according to the point on the chart. This means old days are dropped in favor of new closing price days, so a new calculation is always needed corresponding to the time frame of the average employed. So, a 10-day average is recalculated by adding the new day and dropping the 10th day, and the ninth day is dropped on the second day. (For more on how charts are used in currency trading, check out our Chart Basics Walkthrough.)

Exponential Moving Average (EMA)
The exponential moving average has be refined and more commonly used since the 1960s, thanks to earlier practitioners' experiments with the computer. The new EMA would focus more on most recent prices rather than on a long series of data points, as the simple moving average required.

To Calculate an EMA

Current EMA= ((Price(current) - previous EMA)) X multiplier) + previous EMA.

The most important factor is the smoothing constant that = 2/(1+N) where N = the number of days.

A 10-day EMA = 2/( 10+1) = 18.8

This means a 10-period EMA weights the most recent price 18.8%, a 20-day EMA 9.52 % and 50-day EMA 3.92% weight on the most recent day. The EMA works by weighting the difference between the current period's price and the previous EMA, and adding the result to the previous EMA. The shorter the period, the more weight applied to the most recent price.

Fitting Lines
By these calculations, points are plotted, revealing a fitting line. Fitting lines above or below the market price signify that all moving averages are lagging indicators, and are used primarily for following trends. They don't work well with range markets and periods of congestion because the fitting lines fail to denote a trend due to a lack of evident higher highs or lower lows. Plus, fitting lines tend to remain constant without hint of direction. A rising fitting line below the market signifies a long, while a falling fitting line above the market signifies a short. (For a complete guide, read our Moving Average Tutorial.)

The purpose of employing a simple moving average is to spot and measure trends by smoothing the data using the means of several groups of prices. A trend is spotted and extrapolated into a forecast. The assumption is that prior trend movements will continue. For the simple moving average, a long-term trend can be found and followed much easier than an EMA, with reasonable assumption that the fitting line will hold stronger than an EMA line due to the longer focus on mean prices.

An EMA is used to capture shorter trend moves, due to the focus on most recent prices. By this method, an EMA supposed to reduce any lags in the simple moving average so the fitting line will hug prices closer than a simple moving average. The problem with the EMA is this: Its prone to price breaks, especially during fast markets and periods of volatility. The EMA works well until prices break the fitting line. During higher volatility markets, you could consider increasing the length of the moving average term. One can even switch from an EMA to an SMA, since the SMA smoothes out the data much better than an EMA due to its focus on longer-term means.

Trend-Following Indicators
As lagging indicators, moving averages serve well as support and resistance lines. If prices break below a 10-day fitting line in an upward trend, chances are good that the upward trend may be waning, or at least the market may be consolidating. If prices break above a 10-day moving average in a downtrend, the trend may be waning or consolidating. In these instances, employ a 10- and 20- day moving average together, and wait for the 10-day line to cross above or below the 20-day line. This determines the next short-term direction for prices.

For longer term periods, watch the 100- and 200-day moving averages for longer term direction. For example, using the 100- and 200-day moving averages, if the 100-day moving average crosses below the 200-day average, it's called the death cross, and is very bearish for prices. A 100-day moving average that crosses above a 200-day moving average is called the golden cross, and is very bullish for prices. It doesn't matter if an SMA or an EMA is used, because both are trend-following indicators. It's only in the short-term that the SMA has slight deviations from its counterpart, the EMA.

Conclusion
Moving averages are the basis of chart and time series analysis. Simple moving averages and the more complex exponential moving averages help visualize the trend by smoothing out price movements. Technical analysis is sometimes referred to as an art rather than a science, both of which take years to master. (Learn more in our Technical Analysis Tutorial.)

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