Category: Fractal adaptive moving average formula

Fractal adaptive moving average formula

Moving Average MA is one of the most popular technical indicators in the Forex market. Our purpose is to consider various MAs as well as to compare them within trading under equal conditions of entering and exiting of the market.

Moving Average is one of the most widespread technical indicators. It depicts the average value of symbol price for a given period of time. There are different variants of MA indicator:.

fractal adaptive moving average formula

Let us consider displays of different variants of Moving Average indicator at a price chart. Figure 1 demonstrates variants of Moving Average indicator with the period of 12, as calculated by Close prices. Variants of Moving Average indicator. As the figure shows, Simple Moving Average in flat slightly fluctuates and this can yield false trade signals. Smoothed Moving Average, as it follows from its name, looks more smoothed. The main advantage is absence of false signals at the moments when the price moves in zigzag fashion.

It sustains position maintenance during the period of a strong trend and reduces signal lag as compared to ordinary EMA. The indicator is applied instead of traditional moving averages as well for smoothing a price chart and values of other indicators.

It measures a ratio between totals of positive and negative increments for a given period CMO period. In trend, almost all the indicators behave equally. Let us compare the above considered technical indicators on the trading strategy with equal conditions of entering and exiting the market. To test the indicator, a simple strategy with obvious conditions of entering and exiting the market was chosen.

A similar trading strategy is realised in Moving Average Expert Adviser which can be found in MetaTrader 5 terminal navigator. We will check conditions of entering and exiting the market only at a new bar instead of each tick. At first, availability of an open position is checked for this purpose, SelectPosition function is provided in the EA. If there are no such positions we check the entry condition CheckForOpen functionif available - we check the exit one CheckForClose function.

Checkup of entry conditions is realized in CheckForOpen function as follows:. TakeProfit — 80 points, StopLoss — 50 points, volume of trade lot is 0. For each indicator, there were optimised the period variation range - 5 - 50, pace 1 and parameter Growth factor variation range 0.

For Nick Rypock Moving Average, the Fact parameter was optimized which determines the period of the indicator calculation. The indicator values are calculated on the basis of Close price without horizontal and vertical shift.

Some indicators have additional parameters:. For a more vivid comparison of testing results, let us normalize the indices of Total net profit, Profit factor, Sharpe ratio, Recovery factor, Balance and Equity drawdowns maximal by the following formula:. Outcomes are represented in the table the best results are in yellow, the worst one is in red color :.

In the last column of the table, when summing up indicators, the values of Balance and Equity drawdowns maximal are taken with the negative sign the less the drawdown, the best the strategy. Balance equity chart for Triple Exponential Moving Average. Report for Triple Exponential Moving Average.

Balance equity chart for Nick Rypock Moving Average.

fractal adaptive moving average formula

Report for Nick Rypock Moving Average. At the balance equity chart of NRMA, we observe a spike in profit for the last 3 months of trading, at DEMA chart profit growth with a slight drawdown starts from December Normalized results are represented in the table the best results are in yellow, the worst one is in red color :.

Adaptive Moving Average demonstrates the best indicators of Profit factor, Recovery factor and Sharpe ratio, as well it has the least balance and equity drawdowns. Variable Index Dynamic Average has the biggest total net profit, however, other indicators are not the highest.

SMA and VIDYA have the highest profit for the account of a bigger quantity of trades, whereas the number of profitable trades exceeds those loss.Moving averages are a favorite tool of active traders. However, when markets consolidate, this indicator leads to numerous whipsaw trades, resulting in a frustrating series of small wins and losses.

fractal adaptive moving average formula

Analysts have spent decades trying to improve the simple moving average. In this article, we look at these efforts and find that their search has led to useful trading tools. Pros and Cons of Moving Averages The advantages and disadvantages of moving averages were summed up by Robert Edwards and John Magee in the first edition of Technical Analysis of Stock Trendswhen they said "and, it was back in that we delightedly made the discovery though many others had made it before that by averaging the data for a stated number of days…one could derive a sort of automated trendline which would definitely interpret the changes of trend…It seemed almost too good to be true.

As a matter of fact, it was too good to be true. With the disadvantages outweighing the advantages, Edwards and Magee quickly abandoned their dream of trading from a beach bungalow. But 60 years after they wrote those words, others persist in trying to find a simple tool that would effortlessly deliver the riches of the markets. Simple Moving Averages To calculate a simple moving averageadd the prices for the desired time period and divide by the number of periods selected. This trend-defining property makes it possible for moving averages to generate trading signals.

In its simplest application, traders buy when prices move above the moving average and sell when prices cross below that line.

An approach such as this is guaranteed to put the trader on the right side of every significant trade. Unfortunately, while smoothing the data, moving averages will lag behind the market action and the trader will almost always give back a large part of their profits on even the biggest winning trades.

Exponential Moving Averages Analysts seem to like the idea of the moving average and have spent years trying to reduce the problems associated with this lag. One of these innovations is the exponential moving average EMA. This approach assigns a relatively higher weighting to recent data, and as a result it stays closer to the price action than a simple moving average. The formula to calculate an exponential moving average is:.

A common weighting value is 0. Another is 0. Although it reduces the lag, the exponential moving average fails to address another problem with moving averages, which is that their use for trading signals will lead to a large number of losing trades.

To address this problem, several analysts have suggested varying the weighting factor of the EMA calculation. For more, see How are moving averages used in trading?

Adapting Moving Averages to Market Action One method of addressing the disadvantages of moving averages is to multiply the weighting factor by a volatility ratio. Doing this would mean that the moving average would be further from the current price in volatile markets. This would allow winners to run. As a trend comes to an end and prices consolidatethe moving average would move closer to the current market action and, in theory, allow the trader to keep most of the gains captured during the trend.

It is calculated with a simple formula:. Consider a stock that has a five-point range each day, and at the end of five days has gained a total of 15 points.

This would result in an ER of 0. Had this stock declined 15 points, the ER would be For more trading advice from Perry Kaufman, read Losing To Winwhich outlines strategies for coping with trading losses.It takes the importance of price changes into account and follows price closely with significant moves while remaining flat if price ranges. The FRAMA takes advantage of the fact that markets are fractal and dynamically adjusts the lookback period based on this fractal geometry.

The actual calculation is very elaborate and complicated. Just read on below links to understand more about this super useful moving average: etfhq.

Credit goes to Shizaru for the original calculation. I made just a few fixes, so that the calculation is really that of Ehlers. Fixed H2 and L2 period, fixed w natural logarithm. The basic strategy is simple: long if the price crosses up the line, short or exit if vice versa. It's quite reactive, but its major strength resides in its ability to filter the noise during lateral price movements, avoiding some false signal provided by more common I've updated it to Pine Script 4 and added Bands Extension.

This indicator is constructed based on the algorithm of the Exponential Moving Averagein which the smoothing factor is calculated based on Indicators and Strategies All Scripts.

All Scripts. Indicators Only. Strategies Only. Open Sources Only. Fractal Adaptive Moving Average real one. Fractal Adaptive Moving Average.This indicator is constructed based on the algorithm of the Exponential Moving Averagein which the smoothing factor is calculated based on the current fractal dimension of the price series. The advantage of FRAMA is the possibility to follow strong trend movements and to sufficiently slow down at the moments of price consolidation.

All types of analysis used for Moving Averages can be applied to this indicator. Exponential smoothing factor is calculated according to the below formula:. D i — current fractal dimension; EXP — mathematical function of exponent. Fractal dimension of a straight line is equal to one. Thus if price changes in straight lines, exponential smoothing is not used, because in such a case the formula looks like this The fractal dimension of a plane is equal to two.

Such a small value of the exponential smoothing factor is obtained at moments when price makes a strong saw-toothed movement. Such a strong slow-down corresponds to approximately period simple moving average. It is calculated based on the additional formula:. HighestPrice i — current maximal value for Length periods; LowestPrice i — current minimal value for Length periods.

Values N1, N2 and N3 are respectively equal to:. Legal Information. MetaQuotes is a software development company and does not provide investment or brokerage services.

For any trader-related query — please visit www. Registered company name. Registration number. Business activity type. Company Registration Certificate. Attach file.

fractal adaptive moving average formula

Physical address. Country of registration. Phone number. An error occurred.KAMA will closely follow prices when the price swings are relatively small and the noise is low. KAMA will adjust when the price swings widen and follow prices from a greater distance. This trend-following indicator can be used to identify the overall trend, time turning points and filter price movements. There are several steps required to calculate Kaufman's Adaptive Moving Average.

Breaking down the formula into bite-size nuggets makes it easier to understand the methodology behind the indicator. In statistical terms, the Efficiency Ratio tells us the fractal efficiency of price changes. ER fluctuates between 1 and 0, but these extremes are the exception, not the norm. ER would be 1 if prices moved up 10 consecutive periods or down 10 consecutive periods. ER would be zero if price is unchanged over the 10 periods.

The smoothing constant uses the ER and two smoothing constants based on an exponential moving average. As you may have noticed, the Smoothing Constant is using the smoothing constants for an exponential moving average in its formula.

Since we need an initial value to start the calculation, the first KAMA is just a simple moving average.

Tutorial: Kaufman's Adaptive Moving Average (KAMA)

The following calculations are based on the formula below. Click here to download this spreadsheet example. Chartists can use KAMA like any other trend following indicator, such as a moving average. Chartists can look for price crosses, directional changes and filtered signals.

First, a cross above or below KAMA indicates directional changes in prices.

Kaufman's Adaptive Moving Average (KAMA)

As with any moving average, a simple crossover system will generate lots of signals and lots of whipsaws. Chartists can reduce whipsaws by applying a price or time filter to the crossovers.

One might require price to hold the cross for a set number of days or require the cross to exceed KAMA by a set percentage. Second, chartists can use the direction of KAMA to define the overall trend for a security.

This may require a parameter adjustment to smooth the indicator further. The trend is down as long as KAMA is falling and forging lower lows. The trend is up as long as KAMA is rising and forging higher highs. Finally, chartists can combine signals and techniques. For example, KAMA 10,5,30 could be used as a trend filter and be deemed bullish when rising.

Once bullish, chartists could then look for bullish crosses when price moves above KAMA 10,2, The default settings will automatically appear in the parameter box once it is selected and chartists can change these parameters to suit their analytical needs. The first parameter is for the Efficiency Ratio and chartists should refrain from increasing this number. Instead, chartists can decrease it to increase sensitivity. Chartists looking to smooth KAMA for longer-term trend analysis can increase the middle parameter incrementally.

Click here for a live version of the chart. This scan starts with stocks that averageshares daily volume and have an average closing price above An uptrend is present when trading above the longer-term KAMA 10,5, A buy signal materializes when price moves above the shorter-term KAMA 10,2, A downtrend is present when trading below the longer-term KAMA 10,5, A sell signal materializes when price moves below the shorter-term KAMA 10,2, In order to use StockCharts.

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Fractal Adaptive Moving Average

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Comparing different types of moving averages in trading

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