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Fat Tails
Version 2.0 October 15, 2017
The Moving Median is a central tendency which is calculated over a sliding window of price bars or indicator values. The median is the numeric value separating the higher from the lower half of the data set built from the input series over the selected window.
The moving median is a non-linear FIR (finite impulse response) filter that can be used like a moving average. Compared to all standard moving averages, it is a more robust central tendency, because it is less sensitive to outliers.
The moving median over a lookback period N is calculated by writing the last N values of the input series to an array, sorting the array and selecting the middle value of that array.
Please download the new Supertrend U11 (Universal), which allows to calculate the stop line from median, mode and 27 other moving averages.
This is a new implementation of the TradeStation SuperTrend indicator for NinjaTrader 7. The SuperTrend indicator is an application of the concept of MAE (maximum adverse excursion), which was introduced by John Sweeney in the mid-nineties.
The SuperTrend M11 is particularly stable and has a few advantages over other SuperTrend indicators:
It uses a moving (statistical) median of the arithmetic mean (High + Low)/2 of the bars instead of a moving average. The (statistical) median is known to be more robust than any average.
It calculates both the Median and the ATR (average true range) 1 bar ago, whereas the original SuperTrend indicator takes the ATR and moving average of the current bar. If you use the current bar's ATR, the current bar's breakout is partly measured against its own range. This is particularly true, if the ATR period is short.
Accessing the trend: The indicator comes with a BoolSeries that holds the trend. This BoolSeries can be accessed by other indicators or automated strategies.
Reverse Intra-bar = false: This is the default setting of the indicator. A logical signal will be generated when the close of the signal bar has taken out the stop line. The position may be reversed at the open of the next bar. The paint bars will only change colors for the bar after the signal bar. The arrow will be also plotted for the entry bar.
Reverse Intra-bar = true: This is an unusual setting for the SuperTrend. The signal will be generated with the first tick that has plotted on the other side of the stop line. In this case the position may be reversed intra-bar for the signal bar. Paintbars and arrows will already plot for the signal bar.
Paintbars: The indicator has an option to display the current trend via paintbars. Downclose bars are filled, upclose bars are hollow. For the upclose bars an opacity can be selected for better visibility.
Arrows: The indicator has an option to display trend changes via an arrow.
Sound alerts: The indicator will alert to trend reversals and potential trend reversals. A potential trend reversal occurs when price touches the stop line intra-bar prior to the confirmation by a close on the other side of the stop line. The sound files are included with the indicator install file. Please unzip and copy them into the program files (x86)\ NinjaTrader 7\ sounds directory or whatever directory is used by NinjaTrader to store the sound files.
Comparison between SuperTrend M1 and SuperTrend M11:
The SuperTrend M11 calculates both the average true range and the median 1 bar ago. This results in a considerable saving in CPU load, if you use the indicators in CalculateOnBarClose = false mode. The SuperTrend M11 does the median calculation only once per bar, while the SuperTrend M1 recalculates it with every incoming tick. If you use the indicator with CalculateOnBarClose = true setting, you can also continue to use the SuperTrend M1. There will be no significant difference in performance.
Changed formula: The Supertrend M11 will give slightly different results, when compared with the Supertrend M1. If you want to reproduce the settings of your Supertrend M1, you should use the same value for the ATR period and the ATR multiplier, but reduce the value for the median period by 1. The result will still not be identical. Also for both indicators a minimum size for the ATR values has been imposed, the ATR may not be smaller than the ticksize. This is only important for lower timeframes during low volatility and prevents the SuperTrend from changing the trend too often.
SuperTrend M1: The indicator package contains an updated version of the SuperTrend M1. However, I recommend to switch to SuperTrend M11.
Update August 10, 2011 : Visual design improved. The new indicator version can also be called by other indicators and strategies.
Update May 23, 2012: Entirely recoded version, which uses Median and ATR 1 bar ago to avoid recalculation with every tick. Sound alerts added that trigger intra-bar and which can be used on replay. Smaller improvements added.
Update May 24, 2012: Bug removed, upclose candles were not plotting properly.
Update June 30, 2012: New SuperTrend U11 "Universal" released, this is a new indicator - see link for more information
Update October 2, 2012: Indicator simplified. Trend state can no longer change intra-bar.
Update October 3, 2012: Indicator now allows for displacement. BoolSeries modified for accessing the trend. Trend change intra-bar is possible with option reverse intra-bar and COBC = false.
Update March 5, 2013: Arrows now plotting one bar earlier for the option Reverse intra-bar = true.
This is a new implementation of the TradeStation SuperTrend indicator for NinjaTrader 7. The SuperTrend indicator is an application of the concept of MAE (maximum adverse excursion), which was introduced by John Sweeney in the mid-nineties. The SuperTrend can be viewed as a trailing stop and changes direction, when the trailing stop is taken out.
The SuperTrend U11 calculates both the baseline and the offset 1 bar ago, as did the SuperTrend M11. This is to reduce CPU load and avoid feedback loops.
Accessing the trend: The indicator comes with a BoolSeries that holds the trend. This BoolSeries can be accessed by other indicators or automated strategies.
Reverse Intra-bar = false: This is the default setting of the indicator. A logical signal will be generated when the close of the signal bar has taken out the stop line. The position may be reversed at the open of the next bar. The paint bars will only change colors for the bar after the signal bar. The arrow will be also plotted for the entry bar.
Reverse Intra-bar = true: This is an unusual setting for the SuperTrend. The signal will be generated with the first tick that has plotted on the other side of the stop line. In this case the position may be reversed intra-bar for the signal bar. Paintbars and arrows will already plot for the signal bar.
Paintbars: The indicator has an option to display the current trend via paintbars. Downclose bars are filled, upclose bars are hollow. For the upclose bars an opacity can be selected for better visibility.
Arrows: The indicator has an option to display trend changes via an arrow.
Sound alerts: The indicator will alert to trend reversals and potential trend reversals. A potential trend reversal occurs when price touches the stop line intra-bar prior to the confirmation by a close on the other side of the stop line. The sound files are included with the indicator install file. Please unzip and copy them into the program files (x86)\ NinjaTrader 7\ sounds directory or whatever directory is used by NinjaTrader to store the sound files.
Comparing Supertrend U11 to Supertrend M11:
The SuperTrend U11 is a generalization of the SuperTrend M11.
-> The SuperTrend M11 uses the moving median of the arithmetic mean (High + Low)/2 one bar ago and adds/subtracts a multiple of the average true range one bar ago.
-> The SuperTrend U11 allows you to use the median as above , but instead you can also calculate the baseline from a selection of other indicators. These are the options available for the baseline
- a moving median
- a moving mode
- an ADXVMA
- a 2-pole Butterworth filter
- a 3-pole Butterworth filter
- a DEMA (double exponential MA)
- a DSMA (double simple MA)
- a DTMA (double triangular MA)
- a DWMA (double weighted MA)
- an Ehlers filter
- an EMA
- a 2-pole Gauss filter
- a 3-pole Gauss filter
- a 4-pole Gauss filter
- a HMA (Hull MA)
- a Holt EMA
- a Linear Regression indicator
- a LLMA (phase set to 0)
- a SMA
- a 2-pole Supersmoother
- a 3-pole Supersmoother
- a TEMA (triple exponential MA)
- a TMA (triangular MA)
- a TSMA (triple simple MA)
- a TWMA (triple weighted MA)
- a VWMA(volume weighted MA)
- a WMA (weighted MA)
- a ZeroLagHATEMA
- a ZeroLagTEMA
- a ZLEMA
While the SuperTrend M11 uses the average true range as an offset, the offset for the SuperTrend U11, can be selected as
- a moving average (or median, mode) of the simple range
- a moving average (or median, mode) of the true range
- the standard deviation
The added options will not slow down the indicator, as the selection becomes effective, when the indicator is added.
You can reproduce the SuperTrend M11 with the SuperTrend U11, if you apply it to the arithmetic mean (Median in NinjaSpeak) and select "Median" for the baseline, "EMA" for offset smoothing and "True Range" for offset type. However you need to take into account that the ATR uses Wilder's exponential smoothing (smoothing constant k = 1/n) which is different from the EMA (smoothing constant k = 2/(n+1)). For example an offset period of 8 for the SuperTrend M11 will produce a smoothing factor of 1/8 and translate to an offset period of 15 for the SuperTrend U11.
Update July 3, 2012: ADXVMA option for baseline added.
Update July 5, 2012: Bug removed - Butterworth, Gauss and Supersmoother Fillter did not use the specified baseline period.
Update August 17, 2012: Old version of ADXVMA replaced with new version.
Update August 31, 2012: Ehlers filter updated.
Update October 2, 2012: Indicator simplified. Trend state can no longer change intra-bar. Gaussian and Ehlers filters updated. Mode removed from options.
Update October 3, 2012: Indicator now allows for displacement. BoolSeries modified for accessing the trend. Trend change intra-bar is possible with option reverse intra-bar and COBC = false.
Update March 5, 2013: Arrows now plotting one bar earlier for the option Reverse intra-bar = true.
For the last three updates you also need to update Bollinger Universal & Keltner Universal, if you have them installed. Please remove old versions of those indicators first.
Besides the average there are other statistical measures to describe the behavior of a sample of n values. One of these measures the median, which is the numeric value separating the higher half of the sample from the lower half of the sample. In case that the number n of the values of the sample is even, the median is defined as the mean of the two middle values.
The median is statistically more robust than any average, as it does not take into account outliers or black swans. A moving average can be replaced with the moving median for many purposes.
This indicator calculates the moving median by writing the last n values to an array, sorting the array and selecting the middle value - or in case that n is even, the two middle values of the sample.
The NinjaScript method GetMedian() is not used, because it is flawed.