Boosting Strategies with MMI

We will now repeat our experiment with the 900 trend trading strategies, but this time with trades filtered by the Market Meanness Index. In our first experiment we found many profitable strategies, some even with high profit factors, but none of them passed White’s Reality Check. So they all would probably fail in real trading in spite of their great results in the backtest. This time we hope that the MMI improves most systems by filtering out trades in non-trending market situations.

900 systems experiment revisited

I have been informed by readers that I committed two mistakes, or at least inaccuracies, in the previous experiment. First, I didn’t detrend the price data. Second, I used the equity curves instead of balance curves for determining the profit factor. I didn’t detrend the prices because the systems traded long/short in a symmetric way, and I supposed that this would eliminate any trend bias. But even if this was true back then, it is now not true anymore: filtering trades by MMI or other means can introduce asymmetry. Also, calculating the profit factor from the balance curve makes indeed more sense because you’re interested in the end profit of the trades, not in their interim behavior. Therefore and for the sake of comparable results I will now and in the future use detrended trade returns and balance curves for such experiments.

The original test, repeated with the modifications, produced a wider profit factor distribution due to eliminating intermediate returns. But the outcome of the experiment was the same. The statistic (including trade costs) did not change much, however the profit factor distribution (without trade costs) did. This is the new WRC histogram of the original 900 systems (best system vs. bootstrap-randomized returns of all systems):  

900 trend systems (no MMI)

Although the best system (black bar, a system using ALMA) is at the right side of the distribution, still 11% of random systems were better. The system does not pass the WRC at the required 95% confidence level. This turned out very different when filtering trades with the MMI.

The MMI experiment

This is our script TrendMMI.c for the new experiment:

// helper function: remove systems that exceed the 4 months lookback period
int checkLookBack(int Period) 
  if(Period >= LookBack/TimeFrame) {
    StepNext = 0;	// abort optimization
    return LookBack/TimeFrame; // reduce the period
  } else
    return Period;

// calculate profit factor and remove systems with not enough trades 
var objective() 
  if(NumWinTotal < 30 || NumLossTotal < 30) { 
    StepNext = 0;     // abort optimization
    return 0;         // don't store this system
  } else
      return WinTotal/LossTotal; // Profit factor

var filter(var* Data,int Period);

void run()
  Curves = "DailyBalance.bin";
  StartDate = 2010;
  BarPeriod = 15;
  LookBack = 80*4*24; // ~ 4 months
  Detrend = TRADES;   // detrend trade results
    TimeFrame = 1;
    if(Algo == "MH1")
      TimeFrame = 1*4;
    else if(Algo == "MH4")
      TimeFrame = 4*4;	

// no trade costs
    Spread = Commission = RollLong = RollShort = Slippage = 0;

    int Periods[10] = { 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000 };
    int Period = Periods[round(optimize(1,1,10,1),1)-1];
    var *Price = series(price());
    var *Smoothed = series(filter(Price,Period));

    bool DoTrade = true;
    int MMIPeriod = optimize(0,200,500,100);
    if(MMIPeriod) {
      MMIPeriod = checkLookBack(MMIPeriod);
      var *MMI_Raw = series(MMI(Price,MMIPeriod));
      var *MMI_Smooth = series(LowPass(MMI_Raw,MMIPeriod));
      DoTrade = falling(MMI_Smooth);

    if(DoTrade) {
      else if(peak(Smoothed))

The 10 trend trading scripts with the 10 different indicators remain unchanged, aside from now including TrendMMI.c instead of Trend.c. Trading is now dependent on a boolean variable DoTrade. The length of the MMI range is varied between 200, 300, 400, and 500 bars. As most parameters in a strategy, the MMI range is a compromise: It should be no less than 200 bars for getting any accuracy, but it should not be too long for preventing that different market regimes fall in the same MMI range. At the default range of 0, no MMI is applied and trading is not filtered. This way we’re including all the previous systems in the test. This is required for properly detecting Data Mining Bias, which must consider all systems that were discarded based on their result.

We’re running the MMI return value through a lowpass filter that uses the same period as the MMI range. This gives us a smooth MMI value that does not jump around. This value is now used for trade filtering: trades are opened and closed only when the smoothed MMI is falling, meaning that the market has entered trending mode within the last 200 to 500 bars. The MMI is only applied to one of the systems resulting from the prior period variation (the optimize function automatically selects the parameter of the “most robust” system before optimizing the next parameter). So now we’re testing in fact not 900, but 1260 systems: 900 without MMI and each 90 with MMI ranges of 200, 300, 400, and 500 bars. The systems with not enough trades or a too-long lookback period are again removed from the pool, so the real number of tested systems is about 1100.

Depending on the speed of your PC, Zorro will need about 1 hour to test all systems. At the end of every system test, Zorro produces the parameter histograms. We have now two parameters. The histogram of the first one, the price smoothing filter period, looks as before because MMI was switched off during optimization. The second histogram displays the MMI range in combination with the best value from the first histogram. “Best” is here not the highest bar from the previous histogram, but the value that Zorro deems the most robust and least sensitive to market changes. A typical MMI histograms look like this:

The first bar, marked “100”, is the best system without MMI. We can see that it is unprofitable: The profit factor (left scale) is only about 0.8. Using the MMI with a range of 200 and 300 makes the system in fact worse, and reduces the profit factor t0 0.7. However the last two MMI ranges, 400 and 500, shift the system into the profit zone. This was just a random example, but how does the MMI affect all the other systems? Here are the statistics from the MMI experiment:

Asset, Period, Indicator Success Rate Winning Losing
EUR/USD 46% (+8%) 154 185
S&P 500 4% (+3%) 15 318
Silver 27% (+7%) 87 240
15 Minutes 18% (+7%) 71 322
1 Hour 27% (+9%) 92 251
4 Hours 35% (+2%) 93 170
ALMA 22% (+6)% 22 79
Decycle 21% (+8%) 23 89
EMA 23% (+5%) 24 79
HMA 34% (+9%) 33 66
Laguerre 33% (+3%) 20 38
LinearReg 29% (+6%) 31 77
Lowpass 24% (+5%) 26 82
SMA 26% (+5%)  27  76
Smooth 26% (+7%) 23 67
ZMA 22% (+8)% 27 90

The Rate column shows the percentage of successful systems, and in parentheses the difference to the percentage without MMI. We can see that the MMI increased the number of successful systems in all markets, time frames, and indicators. However the numbers are not really representative: the MMI only affected a quarter of the tested systems, but the upper quarter, so some increase in the number of profitable systems was to be expected anyway. A more meaningful measure is the WRC. We’re using the same Bootstrap.c script as in the previous experiment, we only need to increase the CURVES number to 1260. This is the WRC histogram of systems with MMI (again, best system vs. bootstrapped returns of all systems):

900 trend systems (with MMI)

The MMI filter now shifted the best system (black) far to the right side of the histogram. It got a p-value of 0.02, meaning that it is better than 98% of the best randomized systems, and thus well above the 95% significance level. Using the MMI for filtering trades, the method of trading on curve peaks and valleys passed White’s Reality Check. In fact two of the 1260 systems got p-values above the significance level.

The best systems of the experiment had some things in common: They traded with silver and used either the ALMA or the lowpass filter. This is a surprising result, because neither silver nor ALMA and  lowpass had the highest number of profitable systems. From the above table, one would assume that EUR/USD and the HMA or Laguerre filter are the most promising. They indeed produced many apparently good systems with profit factors above 2 (without trade costs), but none of them passed the WRC.


  • The MMI improves trend following systems with all tested markets, time frames, and indicators.
  • Trend following systems using the MMI can pass White’s Reality Check.
  • From the 10 tested smoothing indicators, ALMA produced the best results, although within a relatively small parameter range.
  • To do: Test more trend filters, f.i. the Hurst Exponent or Ehlers’ Trend/ Cycle decomposition.
  • To do: Create a real trading system by combining the best trend systems and adding the usual system components such as stop loss, trailing algorithm, profit lock, money management, and so on.

I’ve added the scripts to the 2015 scripts collection. Please note that you’ll again need Zorro 1.36 or above for reproducing the experiment.

15 thoughts on “Boosting Strategies with MMI”

  1. Hi,

    All looks so good but:

    if(DoTrade) {
    else if(peak(Smoothed))

    if valley or peak have a future leak you will get better, biased results. So can you show the code of
    valley/peak ??


  2. Hi, i’ve traied TrendMMI script but after compiling in zorro platform received an error

    TrendMMI compiling….
    Undefined function called!
    Train: TrendMMI 2010..2017
    Loop[1][1]p1 step 1: 1.00 => 0.00 0/0

    and so on.
    any output/report be generated

    could help me?
    thanks a lot

  3. If I remember right, TrendMMI was an #include script, not intended to be executed. You must execute one of the 10 scripts with the 10 indicators.

  4. I don’t think that you can get a useful result this way. Check if you can classify your trades in trend-following, trend-neutral, and counter-trend trades. MMI is for detecting trend regime, so you can not use it to just filter a bunch of trades. On pattern, cycle, or mean reversion trades it would probably even have an adverse effect. Filter the trend-following trades out of your database and then check if MMI has an effect on them. I’m interested if you get a better or worse result than the 5% advantage for simple trend systems.

    Also, smoothing the MMI with the SMA is ineffective since the SMA is slow and adds an additional delay on the already slow MMI. Better use a lowpass filter. Here’s the basic code:

    double LowPass(double* Buffer,double Val,double a)
    double* Data = Buffer+3; // static buffer for interim results
    double* LP = Buffer;
    double a2 = a*a;
    LP[2] = LP[1], LP[1] = LP[0]; // shift
    LP[0] = (a-0.25*a2)*Val
    + 0.5*a2*Data[0]
    - (a-0.75*a2)*Data[1]
    + 2*(1.-a)*LP[1]
    - (1.-a)*(1.-a)*LP[2];
    Data[1] = Data[0], Data[0] = Val; // shift
    return LP[0];

  5. General question. What is an out of sample period for 900 systems test ??? Or you just make a back test on entire data just changing the parameters and and assets ??


  6. Yes, a backtest with all parameter and asset combinations. Since the systems are not optimized, there is no in sample and therefore no out of sample period.

    – Another idea: I understood that your database of trades has been generated with machine learning or data mining methods. The MMI is not suited for filtering those trades, but other functions possibly are, for instance the Shannon entropy.

  7. Well I believe i know whats going on here. First SMA – its a low pass filter with lag (N-1)/2 and passband 2*N. Your low pass filter perhaps has a different characteristics but if the lag is a problem here i made another experiment.


    so I just changed the smooth to 5 to decrease the SMA lag than decreasing the Lenght to decrease lag from difference between current price and median and you can see that PF is rock solid around 1.19 reference value from full set of trades so lag is not a problem here…..

    so there are two possibilities here:

    1) MMI just generates the random filtering signal
    2) MMI detects trend mode but somehow profit distribution within my trade file is uniform i.e. whatever you sub-sample them regardless of market conditions they show the same profit factor. This sounds very unlikely….

    regarding your experiment. You created 900 systems by sending to a few systems different parameter values (MMI affected just quarter of them)

    than according to your description

    “The MMI is only applied to one of the systems resulting from the prior period variation (the optimize function automatically selects the parameter of the “most robust” system before optimizing the next parameter). So now we’re testing in fact not 900, but 1260 systems:
    900 without MMI and each 90 with MMI ranges of 200, 300, 400, and 500 bars.The systems with not enough trades or a too-long lookback period are again removed from the pool, so the real number of tested systems is about 1100.”

    so i have a feeling that you introduced selection bias here by not testing exact the same systems (900) with MMI and making final results based on this. Additionally you didn’t make any out of sample test to verify this.

    Anyway, can you make out of sample test on unseen data (2016-) from your best performing systems with and without MMI and post results ??


  8. You can check if 1) or 2) is true by not applying the MMI to a collection of random trades, but to trend following trades. Either use simple systems as here, or filter them out of your database by testing the trend prior to the trade.

    In this experiment there’s no selection bias because there is no selection. All tested systems were included in the WRC, including those without MMI. So it is irrelevant on how many systems the MMI was applied. This had only relevance, if any, on the statistics table with the per-asset results. There’s also some misunderstanding with ‘seen’ and ‘unseen’ data. There is no seen data since we do not optimize the systems.

    The used data was from 2010-2015, and the result is thus of course only valid for this time period, not for 2016. You can not repeat it with 2016 data since you would not get a statistically relevant number of trades from only one year. What you could do is repeating the experiment with 2004-2009 data. Or wait until 2021 and then repeat it with data from 2016-2021.

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