Machine learning

Zorro can utilize included or external machine learning algorithms, for instance from R packages, for applying 'artificial intelligence' to algorithmic trading. Three internal algorithms for price prediction are available: a decision tree, a simple neural network, and a signal pattern learning system. They generate trading rules separately for any WFO cycle, asset, algo, and long or short trades. You can also provide your own function for training an individual model, or use functions from R or Python packages. An introduction into various machine learning methods can be found on Financial Hacker.

The advise functions are used to implement a machine learning algorithm just like a standard indicator:

adviseLong (int Method, var Objective, var Signal0, var Signal1, var Signal2, ..., var Signal19): var

adviseShort (int Method, var Objective, var Signal0, var Signal1, var Signal2, ... var Signal19): var

adviseLong (int Method, var Objective, var* Signals, int NumSignals): var

adviseShort (int Method, var Objective, var* Signals, int NumSignals): var

Call a machine learning algorithm for training or for prediction. In [Train] mode the function trains the algorithm to predict either a subsequent trade return or a training target (Objective). In [Test] or [Trade] mode the function calls the algorithm and returns the predicted value. Depending on algorithm, training can generate a binary model or a prediction function in C code that is stored in the Data folder. The only difference of the ..Long and ..Short variants is that they can train on the returns of long and short trades; otherwise they are identical. They can thus alternatively be used for generating two different models per algo/asset component.



SIGNALS - don't train, but only export Signals and Objective in [Train] mode to a Data\*.csv file.
NEURAL - train and predict with a user-supplied or external machine learning algorithm. See below.
- train and predict with a decision tree (20 signals max).
PERCEPTRON - train and predict with logistic regression (20 signals max).
PATTERN - train and predict with a signal pattern analyzer (20 signals max).
+FAST - fast pattern finding with large patterns (for PATTERN).
+FUZZY - fuzzy pattern finding for PATTERN; analog output for PERCEPTRON.
+2 .. +6 - number of pattern groups (for PATTERN).
+BALANCED - enforce similar numbers of positive and negative target values by replication (for SIGNALS, NEURAL, DTREE, PERCEPTRON).
+RETURNS - use the subsequent long or short trade for the training target, instead of the Objective parameter. The target is the profit or loss including trading costs of the immediately following trade with the same asset, algo, and matching long/short trade direction.
0 or omitted - use the method and signals of the last advise call. Only when signal parameters and trade returns are used.

Objective The training target. For instance an indicator value at the next bar, or a binary value like +1 / -1 for the sign of the next price change. The value should be in the same range as the signals. If persistent at 0, the next trade result is used, as if the RETURNS flag were set. The Objective parameter is only used in the training run and has no meaning in test or trade mode. Set the PEEK flag for accessing future prices in training.
... Signal19
3..20 parameters that are used as features to the machine learning algorithm for training or prediction (less than 3 signals would be interpreted as a Signals array). Use signals that carry information about the current market situation, for instance candle patterns, price differences, indicators, filters, or statistics functions. All signal values should be in the same range, for instance 0..1, -1..+1, or -100..+100, dependent on machine learning method (see remarks). Signals largely outside that range will generate a warning message. If the signals are omitted, the signals from the last advise call are used.
Signals Alternative input method, a var array of arbitrary length containing the features to the machine learning algorithm. Use this for less than 3 or more than 20 signals.
NumSignals Array length, the number of features in the Signals array.


[Train] mode: 100 when trade results are to be trained, i.e. the RETURNS flag is set or Objective is zero. Otherwise 0.
[Test], [Trade] mode: Prediction value returned from the trained algorithm. Can be used as a signal for entering, exiting, or filtering trades. The DTREE, PERCEPTRON, PATTERN algorithms normally return a value in the -100 .. +100 range.

DTREE (Decision Tree)

A decision tree is a tree-like graph of decisions by comparing signals with fixed values. The values and the tree structure are generated in the training run. For this the training process iterates through the sets of signals and finds the signal values with the lowest information entropy. These values are then used to split the data space in a profitable and a non profitable part, then the process continues with iterating through the parts. Details about the decision tree algorithm can be found in books about machine learning.

The signals should be normalized roughly to the -100..100 range for best precision. They should be carefully selected so that the displayed prediction accuracy is well above 60% in all WFO cycles. Decision trees work best with signals that are independent of each other. They do not work very well when the prediction depends on a linear combination of the signals. In order to reduce overfitting, the resulting trees are pruned by removing non-predictive signals. The output of the tree is a number between -100 .. +100 dependent on the predictive quality of the current signal combination.

The decision tree functions are stored in C source code in the \Data\*.c file. The functions are automatically included in the strategy script and used by the advise function in test and trade mode. They can also be exported for using them in strategy scripts or expert advisors of other platforms.The example below is a typical Zorro-generated decision tree:

int EURUSD_S(var* sig)
if(sig[1] <= 12.938) {
if(sig[3] <= 0.953) return -70;
else {
if(sig[2] <= 43) return 25;
else {
if(sig[3] <= 0.962) return -67;
else return 15;
else {
if(sig[3] <= 0.732) return -71;
else {
if(sig[1] > 30.61) return 27;
else {
if(sig[2] > 46) return 80;
else return -62;

The advise() call used 5 signals, of which the first and the last one - sig[0] and sig[4] - had no predictive power, and thus were pruned and do not appear in the tree. Unpredictive signals are displayed in the message window.

Example of a script for generating a decision tree:

void run()
  BarPeriod = 60;
  LookBack = 150;
  TradesPerBar = 2;
  if(Train) Hedge = 2;
// generate price series
  vars H = series(priceHigh()), 
    L = series(priceLow()),
    C = series(priceClose());

// generate some signals from H,L,C in the -100..100 range
  var Signals[2]; 
  Signals[0] = (LowPass(H,1000)-LowPass(L,1000))/PIP;
  Signals[1] = 100*FisherN(C,100);

// train and trade the signals 
  Stop = 4*ATR(100); 
  TakeProfit = 4*ATR(100);
  if(adviseLong(DTREE,0,Signals,2) > 0)
  if(adviseShort(DTREE,0,Signals,2) > 0)


A perceptron, also called a logistic regression function, is a simple neural net consisting of one neuron with one output and up to 20 signal inputs. It calculates its predictions from a linear combination of weighted signals. It has some similarity to the polyfit algorithm, but with arbitrary variables instead of powers of a single variable, and with a binary output. A short preceptron algorithm description can be found on the machine learning overview. The signal weights are generated in the training run for producing the best possible prediction.

The perceptron algorithm works best when the weighted sum of the signals has predictive power. It does not work well when the prediction requires a nonlinear signal combination, i.e. when trade successes and failures are not separated by a straight plane in the signal space. A classical example of a function that a perceptron can not emulate is a logical XOR. Often a perceptron can be used where a decision tree fails, and vice versa.

The perceptron learning algorithm generates prediction functions in C source code in the \Data\*.c file. The functions are automatically included in the strategy script and used by the advise function in test and trade mode. They can also be exported for using them in strategy scripts or expert advisors of other platforms. The output is >0 for a positive or <0 for a negative prediction. The output magnitude is the probability associated with the prediction, in percent, f.i. 70 for 70% estimated probability. A generated perceptron function with 3 signals and binary output looks like this:

int EURUSD_S(var* sig)
if(-27.99*sig[0]+1.24*sig[1]-3.54*sig[2] > -21.50)
return 70;
return -70;

In FUZZY mode the output magnitude is equivalent to the prediction strength, thus allowing to ignore signals below a threshold. The scaling factor, 2.50 in the example below, is calculated so that the average perceptron return value of the training set has a magnitude of 50. Example of a fuzzy perceptron:

int EURUSD_S(var* sig)
return (-27.99*sig[0]+1.24*sig[1]-3.54*sig[2]-21.50)*2.50;
Signals that do not contain predictive market information get a weight of 0.

PATTERN (Pattern Analyzer)

The pattern analyzer is an intelligent version of classic candle pattern indicators. It does not use predefined patterns, but learns them from historical price data. It's normally fed with up to 20 open, close, high or low prices of a number of candles. It compares every signal with every other signal, and uses the comparison results - greater, smaller, or equal - for classifying the pattern.

The signals can be divided into groups with the PATTERN+2 .. PATTERN+6 methods. They divide the signals into up to six pattern groups and only compare signals within the same group. This is useful when, for instance, only the first two candles and the last two candles of a 3-candle pattern should be compared with each other, but not the first candle with the third candle. PATTERN+2 requires an even number of signals, of which the first half belongs to the first and and the second half to the second group. PATTERN+3 likewise requires a number of signals that is divisible by 3, and so on. Pattern groups can share signals - for instance, the open, high, low, and close of the middle candle can appear in the first as well as in the second group - as long as the total number of signals does not exceed 20.

Aside from the grouping, Zorro makes no assumptions of the signals and their relations. Therefore the pattern analyzer can be also used for other signals than candle prices. All signals within a pattern group should have the same unit for being comparable, but different groups can have different units. For candle patterns, usually the high, low, and close of the last 3 bars is used for the signals - the open is not needed as it's normally identical with the close of the previous candle. More signals, such as the moving average of the price, can be added for improving the prediction (but in most cases won't).

For simple patterns with few signals, the pattern analyzer can generate direct pattern finding functions in plain C source code in the \Data\*.c file. These functions are automatically included in the strategy script and used by the advise function in test and trade mode. They can also be exported to other platforms. They find all patterns that occurred 4 or more times in the training data set and had a positive profit expectancy. They return the pattern's information ratio - the ratio of profit mean to standard deviation - multiplied with 100. The better the information ratio, the more predictive is the pattern. A typical pattern finding function with 12 signals looks like this:

int EURUSD_S(float* sig)
  if(sig[1]<sig[2] && eqF(sig[2]-sig[4]) && sig[4]<sig[0] && sig[0]<sig[5] && sig[5]<sig[3]
    && sig[10]<sig[11] && sig[11]<sig[7] && sig[7]<sig[8] && sig[8]<sig[9] && sig[9]<sig[6])
      return 19;
  if(sig[4]<sig[1] && sig[1]<sig[2] && sig[2]<sig[5] && sig[5]<sig[3] && sig[3]<sig[0] && sig[7]<sig[8]
    && eqF(sig[8]-sig[10]) && sig[10]<sig[6] && sig[6]<sig[11] && sig[11]<sig[9])
      return 170;
  if(sig[1]<sig[4] && eqF(sig[4]-sig[5]) && sig[5]<sig[2] && sig[2]<sig[3] && sig[3]<sig[0]
    && sig[10]<sig[7] && eqF(sig[7]-sig[8]) && sig[8]<sig[6] && sig[6]<sig[11] && sig[11]<sig[9])
      return 74;
  if(sig[1]<sig[4] && sig[4]<sig[5] && sig[5]<sig[2] && sig[2]<sig[0] && sig[0]<sig[3] && sig[7]<sig[8]
    && eqF(sig[8]-sig[10]) && sig[10]<sig[11] && sig[11]<sig[9] && sig[9]<sig[6])
      return 143;
  if(sig[1]<sig[2] && eqF(sig[2]-sig[4]) && sig[4]<sig[5] && sig[5]<sig[3] && sig[3]<sig[0]
    && sig[10]<sig[7] && sig[7]<sig[8] && sig[8]<sig[6] && sig[6]<sig[11] && sig[11]<sig[9])
      return 168;
  return 0;

The eqF function in the code above checks if two signals are equal. Signals that differ less than the FuzzyRange are considered equal.

There are two additional special methods for the pattern analyzer. The FUZZY method generates a pattern finding function that also finds patterns that can slightly deviate from the profitable patterns in the training data set. It gives patterns a higher score when they 'match better'. The deviation can be set up with FuzzyRange. A typical fuzzy pattern finding function looks like this:

int EURUSD_S(float* sig)
  double result = 0.;
  result += belowF(sig[1],sig[4]) * belowF(sig[4],sig[2]) * belowF(sig[2],sig[5]) * belowF(sig[5],sig[3]) * belowF(sig[3],sig[0])
    * equF(sig[10],sig[11]) * belowF(sig[11],sig[7]) * belowF(sig[7],sig[8]) * belowF(sig[8],sig[9]) * belowF(sig[9],sig[6]) * 19;
  result += belowF(sig[4],sig[5]) * belowF(sig[5],sig[1]) * belowF(sig[1],sig[2]) * belowF(sig[2],sig[3]) * belowF(sig[3],sig[0])
    * belowF(sig[10],sig[7]) * belowF(sig[7],sig[11]) * belowF(sig[11],sig[8]) * belowF(sig[8],sig[9]) * belowF(sig[9],sig[6]) * 66;
  result += belowF(sig[4],sig[1]) * belowF(sig[1],sig[2]) * belowF(sig[2],sig[0]) * belowF(sig[0],sig[5]) * belowF(sig[5],sig[3])
    * belowF(sig[10],sig[11]) * belowF(sig[11],sig[7]) * belowF(sig[7],sig[8]) * belowF(sig[8],sig[6]) * belowF(sig[6],sig[9]) * 30;
  result += belowF(sig[1],sig[4]) * belowF(sig[4],sig[2]) * belowF(sig[2],sig[5]) * belowF(sig[5],sig[3]) * belowF(sig[3],sig[0])
    * belowF(sig[7],sig[10]) * belowF(sig[10],sig[11]) * belowF(sig[11],sig[8]) * belowF(sig[8],sig[6]) * belowF(sig[6],sig[9]) * 70;
  result += belowF(sig[4],sig[5]) * belowF(sig[5],sig[1]) * belowF(sig[1],sig[2]) * belowF(sig[2],sig[3]) * belowF(sig[3],sig[0])
    * belowF(sig[7],sig[10]) * belowF(sig[10],sig[8]) * belowF(sig[8],sig[11]) * belowF(sig[11],sig[9]) * belowF(sig[9],sig[6]) * 108;
  return result;

The belowF function is described on the Fuzzy Logic page.

The FAST method does not generate C code; instead it generates a list of patterns that are classified with alphanumeric names. For finding a pattern, it is classified and its name compared with the pattern list. This is about 4 times faster than the pattern finding function in C code, and can also handle bigger and more complex patterns with up to 20 signals. It can make a remarkable difference in backtest time or when additional parameters have to be trained. A pattern name list looks like this (the numbers behind the name are the information ratios):

/* Pattern list for EURUSD_S
HEICBFGDA 108 ...*/

The FAST method can not be used in combination with FUZZY or with FuzzyRange. But the FAST as well as the FUZZY method can be combined with pattern groups (f.i. PATTERN+FAST+2).

The find rate of the pattern analyzer can be adjusted with two variables:


The minimum number of occurrences of the found patterns in the analyzed price curve; default = 4.


The minimum win rate of the found patterns, in percent; default = 50.

An example of a pattern trading script can be found in Workshop 7.

NEURAL (General Machine Learning)

The NEURAL method uses an external machine learning library, for instance a support vector machine, random forest, or a deep learning neural network for predicting the next price or next trade return in an algo trading system. Many machine learning libraries are available in R packages; therefore the NEURAL method will often call R functions for training and prediction. Alternatively, any DLL-based machine learning library can be used (look here for accessing DLL classes and functions). The algorithm is implemented with a single user-provided function:

neural (int Status, ínt Model, int NumSignals, void* Data): var

This function is automatically called several times during the training, test, or trade process. It has access to all global and predefined variables. Its behavior depends on Status:

Status Parameters Called Description
NEURAL_INIT --- After the INITRUN Initialize the machine learning library (f.i. by calling Rstart); return 0 if the initialization failed, otherwise 1. The script is aborted if the system can not be initialized.
NEURAL_EXIT --- After the EXITRUN Release the machine learning library if required.
NEURAL_TRAIN Model, NumSignals, Data After any WFOCycle in train mode

Batch training. Train the model with the given Model index with all data samples collected in the previous training run or WFO training cycle. The Model index is incremented for any asset, algo, and long/short combination. The list of samples is given in CSV format in the Data string. The columns of the CSV table are the signals, the last column is the Objective parameter or the trade result. The prediction accuracy in percent can be optionally returned by the neural function; otherwise return 1 if no accuracy is calculated, or 0 for aborting the script when the training failed.

NEURAL_PREDICT Model, NumSignals, Data By any advise call in test/trade mode Return the value predicted by the model with the given Model index, using the signals contained in the Data double array.
NEURAL_SAVE Data After any WFOCycle in train mode Save all models trained in the previous training run or WFO training cycle to the file with the name given by the string Data.
NEURAL_LOAD Data Before any WFOCycle in test mode, at session begin in trade mode.  Prepare the prediction by loading all trained models from the file with the name given by the string Data. Also called in trade mode whenever the model file was updated by re-training.

Model is the number of the trained model, for instance a set of decision rules, or a set of weights of a neural network, starting with 0. When several models are trained for long and short predictions and for different assets or algos, the index selects the suited model. The number of models is therefore normally equal to the number of advise calls per run cycle. All trained models are saved to a *.ml file at the end of every WFO cycle. In R, the models are normally stored in a list of lists and accessed through their index (f.i. Models[[model+1]]). Any aditional parameter set generated in the training process - for instance, a set of normalization factors, or selection masks for the signals - can be saved as part of the model.

The NumSignals parameter is the number of signals passed to the advise function. It is normally identical to the number of trained features.

The Data parameter provides data to the function. The data can be of different type. For NEURAL_LEARN/NEURAL_PREDICT it's a pointer to a double array of length NumSignals+1, containing the signal values plus the prediction objective or trade result at the end. Note that a plain data array has no "dim names" or other R gimmicks - if they are needed in the R training or predicting function, add them there. For NEURAL_TRAIN the Data parameter is a text string containing all samples in CSV format. The string can be stored in a temporary CSV file and then read by the machine learning algorithm for training the model. For NEURAL_SAVE/NEURAL_LOAD the Data parameter is the suggested file name for saving or loading all trained models of the current WFO cycle in the Data folder. Use the slash(string) function for converting backslashes to slashes when required for R file paths.

The code below is the default neural function in the r.h file for using a R machine learning algorithm. If required for special purposes, the default neural function can be replaced by a user-supplied function.

var neural(int Status, int model, int NumSignals, void* Data)
if(!wait(0)) return 0;
// open an R script with the same name as the stratefy script
if(Status == NEURAL_INIT) {
if(!Rstart(strf("%s.r",Script),2)) return 0;
return 1;
// export batch training samples and call the R training function
if(Status == NEURAL_TRAIN) {
string name = strf("Data\\signals%i.csv",Core);
Rx(strf("XY <- read.csv('%s%s',header = F)",slash(ZorroFolder),slash(name)));
return 0;
return 1;
// predict the target with the R predict function
if(Status == NEURAL_PREDICT) {
Rx(strf("Y <- neural.predict(%i,X)",model+1));
return Rd("Y[1]");
// save all trained models
if(Status == NEURAL_SAVE) {
print(TO_ANY,"\nStore %s",strrchr(Data,'\\')+1);
return Rx(strf("'%s')",slash(Data)),2);
// load all trained models
if(Status == NEURAL_LOAD) {
printf("\nLoad %s",strrchr(Data,'\\')+1);
return Rx(strf("load('%s')",slash(Data)),2);
return 1;

The default neural function requires an R script with same name as the strategy script, but extension .r instead of .c. This script must contain the following 4 functions:

neural.init()  initializes the machine learning package, defines a model list, sets the initial seed, number of cores, GPU/CPU context, etc.

neural.train(Model, XY)  trains the the algorithm and stores the trained model in the model list. XY is a data frame with signals in the first NumSignals columns and the objective in the last (NumSignals+1) column. The samples are the rows of the data frame. Model is the number in the model list where the trained model is to be stored. The model can be any R object combined from the machine learning model and any additional data, f.i. a set of normalization factors.  stores all models from the model list to a file with the given name and path. This function is called once per WFO cycle.

neural.load(FileName)  loads back the previously stored model list for the current WFO cycle. If this optional function is missing, the model list is loaded with the R load() function. Otherwise make sure to load the list into the global R environment so that it is accessible to neural.predict, f.i. with load(FileName, envir=.GlobalEnv).

neural.predict(Model, X)  predicts the objective from the signals. X is a vector of size NumSignals, containing the signal values for a single prediction. Model is the number of the model in the model list. The neural.predict return value is returned by the advise function. The neural.predict function should also support batch predictions where X is a data frame with several samples and a vector Y is returned. Batch predictions are not used by Zorro, but useful for calibrating the algorithm with a training/test data set generated in SIGNALS mode.

 An example of such a deep learning system can be found on Financial Hacker. A simple machine learning strategy DeepLearn.c is included, together with R scripts for running it with the Deepnet, H2O, MxNet, or Keras deep learning packages. The neural function is compatible with all Zorro trading, test, and training methods, including walk forward analysis, multi-core parallel training, and multiple assets and algorithms. A short description of installation and usage of four popular deep learning packages can be found here.


See also:

optimize, frechet, polyfit, predict, Workshop 7, R Bridge, deep learning

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