The Moving Average Indicator shows the mean value of an instrument for a particular period. When one calculates the moving average, one averages out the asset price for this period.

### History

Moving Average is the most popular indicator in all ranges of technical analyses. The words “Moving Average” are traceable to the articles about statistical studies of the data back to the beginning of 19th century (G. U. Yule, *Journal of the Royal Statistical Society*, 72, 721-730 (1909); W. I. King’s *Elements of Statistical Method* (1912)). Needless to say, that there are many references to the usage of MA in all kinds of modern books about trading and technical analysis. Historically, the Moving Average method was developed by Robert Goodell Brown and Charles Holt. Brown worked for the US Navy during World War II, where his was developing a tracking system for fire-control information to compute the location of submarines. Later, he applied this technique to the forecasting of demand for spare parts(an inventory control problem). Brown described those ideas in his 1959 book on inventory control. Holt’s research was sponsored by the Office of Naval Research; independently, he developed exponential smoothing models for constant processes, processes with linear trends, and for seasonal data. Naturally, in modern science, Moving Averages concepts underlie many of the forecasting methods. Nonetheless, there are a lot of trading strategies and concepts based on MA’s.

### Calculations

There are several traditional techniques for calculation of Moving Average:

Simple Moving Average (SMA), Exponential Moving Average (EMA), Smoothed Moving Average (SMMA), Linear Weighted Moving Average (LWMA)

###### Simple Moving Average (SMA)

SMA is calculated by summing up the prices of asset closure over a certain number of single periods (for instance, 4 hours). Then this value divided by the number of this periods.

SMA = SUM(CLOSE, N)/N

N — is the number of calculation periods.

###### Exponential Moving Average (EMA)

Exponential moving average solves the problem of SMA lag for the last price movements. EMA calculated by adding the moving average of a certain share of the current closing price to the previous value. In conclusion, exponentially smoothed moving average has more weight for the latest price.

EMA = (CLOSE(i)*P)+(EMA(i-1)*(1-P))

CLOSE(i) — the price of the current period closure;

EMA(i-1) — Exponentially Moving Average of the previous period closure;

P — the factor last value weight.

###### Smoothed Moving Average (SMMA)

Unlike higher sensitivity of EMA for recent quotes, SMMA solves the problem of high sensitivity for the large price spikes. The first value of this smoothed moving average is calculated as the SMA.

(SMA):SUM1 = SUM(CLOSE, N)

SMMA1 = SUM1/N

The second and succeeding moving averages are calculated according to this formula:

PREVSUM = SMMA(i-1) *N

SMMA(i) = (PREVSUM-SMMA(i-1)+CLOSE(i))/N

SUM1 — is the total sum of closing prices for N periods;

PREVSUM — is the smoothed sum of the previous bar;

SMMA1 — is the smoothed moving average of the first bar;

SMMA(i) — is the smoothed moving average of the current bar (except for the first one);

CLOSE(i) — is the current closing price;

N — is the smoothing period.

###### Linear Weighted Moving Average (LWMA)

LWMA has common principles with EMA, but slightly different approach. In the case of weighted moving average, the latest data has the bigger weight than more early data. Firstly Weighted moving average is calculated by multiplying each one of the closing prices of the considered series, by a certain weight coefficient. Then we use SMA formula for the result.

LWMA = SUM(Close(i)*i, N)/SUM(i, N)

SUM(i, N) — is the total sum of weight coefficients.

## How to use it

A moving average can help cut down the amount of “noise” on a price chart. Also the direction of the moving average useful to get a basic idea of the price direction. MA angled up, and the price is moving up (or was recent) overall, angled down and the price is moving down overall, moving sideways, and the price is likely in range.

A moving average can also act as support or resistance. Mostly used periods for support/resistant MA’s are 50-day, 100-day or 200-day periods. Such levels have a significant impact on market behavior, so the price bounces off this levels or struggles to cross them. To conclude, the more subconscious meaning MA period has – the stronger impact it will have.

In general, if the price is above a moving average – we consider the trend is up. If the price is below a moving average – the trend is down. Though Moving Averages can have different lengths (periods), though, so one may indicate an uptrend while another indicates a downtrend.

## Trading strategies

To illustrate basic principles of using Moving averages in trading let’s look at two simple strategies based on Moving Averages crossovers.

### Crossovers

Crossovers are one of the simplest strategies with the moving average. Different variations of time frames and MA periods suitable for this strategy. Yet the most popular periods for 1day timeframe are 5, 14, 25, 50, 100, 200. The rules are straightly simple: Price crossing MA upwards are considered as BUY signal, price crossing MA downwards – SELL signal.

Let’s see how this signals looks on the live chart.

As we see, in many cases price noises cause false signals. Therefore this strategy needs some filter for this false crossings.

### Golden Cross

One good way to improve the accuracy of the “Crossovers” strategy is to use the second, shorter period, MA. Consequently, the rules stay similar to the first strategy, but instead of the price crossing, we will use the shorter MA crossing longer MA signals.

Undoubtedly, as we see, this approach eliminates a lot of false signals. Thus, such technique does not guarantee 100 % win rate and has it’s own drawbacks. Meanwhile, the Crossovers strategy gives a lot of false signals; the Golden Cross strategy has a lag for the good signals.