[Editor’s note: Just getting started with moving averages? Read this beginner’s article first.]

Moving averages are one of the most widely used indicators in technical analysis studies. What started with the simple moving average and then towards exponential moving average has with the passage of time and advent of computer programmed software’s have made technicians to experiment and come up with new types of data calculation.

DEFINITION

Mean reversion suggests that the asset prices will eventually reverse towards its mean or average before trend resumption or trend reversal, it can be that the prices will return towards the average or consolidate for a while up to the time it comes closer to the average, this is a process on which many trading systems are based on where action is taken when the recent performance has differed from their historical averages.

MODERN MOVING AVERAGES

Simple moving averages are still used by many but with time and a requirement to measure price differently made way for new thoughts and new averages. In this article I will explain newer moving averages which have evolved with time and need.

DOUBLE EXPONENTIAL (DEMA) AND TRIPLE (TEMA)

A moving average is a smooth curving line which provides the visual confirmation of the longer term trend of an average, they are lagging indicators where faster moving averages are choppy and longer term averages are smoother, to decrease the time lag these modified exponential averages were thought of. They are used for providing signals in crossover or trend determination earlier than other moving averages.

DOING THE MATH

Double Exponential MA Formula:

DEMA = 2*EMA – EMA(EMA)

Triple Exponential MA Formula:

TEMA = (3*EMA – 3*EMA(EMA)) + EMA(EMA(EMA))

Where:

EMA = EMA(1) + ? * (Close – EMA(1))

? = 2 / (N + 1)

N = The smoothing period.

Dua10412Fig1.png

Chart 1 has moving average crossover, it clearly shows that TEMA gives signal the earliest followed by DEMA and then Simple Moving average. So the lag is reduced and we can enter the trend earlier.

DISPLACED MOVING AVERAGE (DispMA)

A DispMA is a moving average which can be adjusted forward or backward by a specific time interval. Shifting the Moving Average Backward to stay in the long term trend, it will create a lagging effect shifting the moving average forward to make a timely exit when the counter trend develops, it will create a leading effect.

The aim of the DisMA is to avoid sudden whipsaws which usually come in the matured trend or news related events, the displacement will cause less number of false signals. The usual displacement levels are 3 days to 5 days forward or back. It can be used for finding support and resistances or as a crossover signal and also quite useful in cyclical studies.

Dua10412Fig2.png

Chart 2 shows that the longer moving average placed forward keeps us in the trend while the shorter moving average which is placed backward helps us get a timely exit.

WEIGHTED MOVING AVERAGE (WMA)

Let’s take a look at another type of moving average. The aim of WMA is to take away the lag and increase the sensitivity factor towards the price. The Weighted moving average is weighted average of the last n prices, where the weighting decreases by 1 with each previous price.

MORE MATH

Calculation: ((n * Pn) + ((n – 1) * Pn-1) + ((n – 2) * Pn-2) + … ((n – (n – 1)) * Pn-(n-1)) / (n + (n – 1) + … + (n – (n – 1)))

WMA reacts more quickly to price changes because it places more importance on the recent price moves , that way it shows the trend faster as compared to the simple moving average.

LEAST SQUARES MOVING AVERAGE

This moving average sometimes also called as an End Point Moving Average. It is based on linear regression but takes it one step forward by estimating that what would have happened if the regression line continued, making it more responsive to trends and spotting the trends earlier as compared to other moving averages.

ITS USES

Used mainly as a crossover signal with itself or with other moving average or can be used with the price moving above or below it as a buy or sell signal.

Dua10412Fig3.png

In Chart 3 we plot three moving averages in one chart; the first one is Least Square Moving average (green) also called as End point moving average. The Red Circles show the price rise above the average showing change in trend or end point of trend up and down helping to exit the position or take the opposite trade.

The other two are WMA (thick violet) and EMA (dashed Red), calculation of both the averages is nearly same but in WMA more weight is given to the current price so it shows that WMA is closer to price as compared to EMA

WILDERS MOVING AVERAGE

As the name suggests this was created by Welles Wilder the great technician whose works include Relative Strength Index (RSI), Average Directional Index (ADX), Parabolic Sar and Average True Range (ATR). This is sometimes called as the modified moving average; the aim is to smooth the price movements to identify price trends.

Wilder EMA = price today * K + EMA yesterday (1-k)

Where k = 1/N, N = Number of Periods

The formula is similar to EMA which has 2 parameters, a time series and a look back period and it returns a smooth line. Price staying and closing above the average is termed as an uptrend and below it as a downtrend.

Dua10412Fig4.png

Chart 4 shows two averages under Wilders calculation. The longer moving average can be used for trend determination and shorter for trading for buying on dip and sell on rise. Crossover provides trading signals but with a lag.

RISING EQUITY CRUVE

Almost everyone uses moving averages in trading price trends, these newer moving averages will help traders capture trend in a better way and build a finer trading system towards understanding market trends better yielding a rising equity curve.

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