## Predicting Stock Exchange Prices with Machine Learning

This article will describe how to get an average 75% prediction accuracy in next day’s average price change. The target magnitude is the 2-day simple moving average. The reason is that if we do not apply smoothing to daily prices, the forecasts are much harder to get. The minimum possible smoothing is two days, and that will be the target: altering actual prices as little as possible.

I have selected randomly a company from the New York Stock Exchange, it was «CNH Industrial NV». No reason for that, it has been a completely random choice among a couple thousand files I have generated extracted from either Yahoo! or Google finance, I do not remember the source. The files are uploaded here: https://drive.google.com/open?id=18DkJeCqpibKdR8ezwk9hGjdHYSGwovWH.

The method is valid for any financial data as long as it has the same structure. I have also tested it with Forex data getting similar accuracy levels with currencies such as EURUSD, GBPUSD or USDJPY. The interesting point of forecasting those quotes is that by examining where it fails, I think you will improve your price action trading skills and your understanding of the market and what matters.

## Data Collection and Variable Configuration

There are millions of possible variable candidates that may seem valid to be analyzed. And which will be the target value we will try to aim? I like thinking that price is like any other object subject to physical laws. It reacts to market forces, it has an inertia, velocity, acceleration, etc.

The forces may be volume, it may have a potential energy depending if it is very high or very low, the rate of change may be important and so on. There are other many factors we could analyze such as gaps, breakouts, technical patterns, candlestick analysis or price distribution within space just to mention a few. For this example we will only be focused on price action and volume.

I have the files saved in csv format to be used with Excel, so let’s start loading the csv file into a DataFrame object using Python.

```# Importing all the libraries that we will use.

import pandas as pd
import matplotlib.pyplot as plt
import xgboost as xgb
from sklearn.metrics import accuracy_score

#Load the data from a csv file.
CNHI = {"stock_name":"CNH Industrial NV", "data": pd.read_csv("./data/CNHI_excel.csv",sep="\t",header=0,decimal=',')}

CNHI["data"]=CNHI["data"].drop("Adj Close",1).set_index("Date")```

The previous code will, after extracting, remove a column that won’t be used («Adj Close») and creating an index using the «Date» column. The date is not a variable we may use for forecasting, so there is no need to keep it as a column of the dataset.

The data now has the typical structure of the financial data: Date, Open, High, Low and Close. The first three rows are shown in the next table:

 Date Open High Low Close Volume 2013-09-30 2.75 13.08 12.5 12.5 352800 2013-10-01 12.76 13.16 12.75 12.92 1477900 2013-10-02 13.02 13.08 12.87 12.9 1631900

### Predictors

We are going to omit High, Low and Open, using only Open and Volume for the study. Let’s start preparing the data for the analysis. The predictors (X variables) to be used to predict the target magnitued (y variable) will be the following ones:

• Two day simple moving average (SMA2). The formula is (Ct – Ct-1)/2, being Ct equal to current day’s open price and Ct-1 to previous day’s open price. This formula is applied to each row of the data set.
`Predictors = pd.DataFrame({"sma2":CNHI["data"].Open.rolling(window=2).mean()})`
• 1 day window SMA2. The previous day’s SMA2 value.
`Predictors["sma2_1"] = Predictors.sma2.shift(1)`

And the other predictors will be:

• Current day SMA2 increment. (SMA2t – SMA2t-1).
• 1 day window SMA2 increment. (SMA2t-1 – SMA2t-2).
• Current day volume increment. (Volt – Volt-1).
• Current day volume rate of change. (Volt – Volt-1)/Volt
• 1 day window open price. (Ct-1)
• Current day open price increment. Ct – Ct-1
• Current day open price. Ct.
```Predictors["sma2_increment"] = Predictors.sma2.diff()

Predictors["sma2_1_increment"] = Predictors.sma2_1.diff()

Predictors["vol_increment"] = CNHI["data"].Volume.diff()

Predictors["vol_rel_increment"] = CNHI["data"].Volume.diff() / CNHI["data"].Volume

Predictors["open_1"] = CNHI["data"].Open.shift(1)

Predictors["open_incr"] = CNHI["data"].Open - CNHI["data"].Open.shift(1)

Predictors["open"] = CNHI["data"].Open

# The rows with nulls generated by rolling values will be removed.
Predictors = Predictors.dropna()```

A sample of the first 5 rows:

 Date sma2 sma2_1 sma2_increment sma2_1_increment vol_increment vol_rel_increment open_1 open_incr open 2013-10-03 12.895 12.89 0.005 0.135 -495500 -0.436026047 13.02 -0.25 12.77 2013-10-04 12.765 12.895 -0.13 0.005 -21800 -0.019558586 12.77 -0.01 12.76 2013-10-07 12.59 12.765 -0.175 -0.13 -400 -0.000359002 12.76 -0.34 12.42 2013-10-08 12.42 12.59 -0.17 -0.175 104600 0.08582212 12.42 0 12.42 2013-10-09 12.5 12.42 0.08 -0.17 -232400 -0.235604217 12.42 0.16 12.58

### Target Variable

This will be a classification variable, if the average price will go either up or down the next day.  The target will be forecasting the difference between today’s price and tomorrow’s price (which is unkonwn).

`target = pd.DataFrame({"value":Predictors.sma2.shift(-1) - Predictors.sma2}).dropna()`

After calculating the data to predict, the three first rows look like this:

 Date value 2013-10-03 -0.13 2013-10-04 -0.175 2013-10-07 -0.17

Finally we will match predictors and target values by date and remove those rows without counterpart in the other table.

```X = pd.merge(Predictors, target,left_index=True,right_index=True)[Predictors.columns]
y = pd.merge(Predictors, target,left_index=True,right_index=True)[target.columns]```

X now contains the predictors and y the target values. The table contains 1,059 records at this moment.

### Extreme Gradient Boosting prediction

The extreme gradient boosting is an exceptional machine learning technique for many reasons. It is based on decision trees and it has nice features such as residuals analysis, non-linear regression, feature selection tools, overfitting avoidance and many other more. Other machine learning alternative techniques commonly used for this type of analysis are Support Vector Machines, Neural Networks and Random Forest. I have used all of those for predicting market prices and the Extreme Gradient Boosting is always my first choice.

We will setup the regression model using the 65% of the data and with that model, the next 35% of the data will be used to predict future values. This simulates the actual scenario in which we have past data to train our model and we want to predict how a future datum will be with the data we currently have on hand. The data will be split in two sets: the training set to preconfigure the model and the testing set that won’t be used to build the model, but only to test if it works as expected with new data.

```train_samples = int(X.shape * 0.65)

X_train = X.iloc[:train_samples]
X_test = X.iloc[train_samples:]

y_train = y.iloc[:train_samples]
y_test = y.iloc[train_samples:]```

After applying the data splitting, the test data set contains:

• Train records: 688.
• Test records: 371.

The target variables will be transformed for binary classification. A positive change in the value of prices will be classified as 1 and a non-positive change as 0.

```def getBinary(val):
if val>0:
return 1
else:
return 0

# and the transformation is applied on the test data for later use.
# The train data will be transformed while it is being fit.
y_test_binary = pd.DataFrame(y_test["value"].apply(getBinary)```

And next, the model is trained and the test data predicted to verify the accuracy of the system:

```regressor = xgb.XGBRegressor(gamma=0.0,n_estimators=150,base_score=0.7,colsample_bytree=1,learning_rate=0.01)

xgbModel = regressor.fit(X_train,y_train.value.apply(getBinary))

y_predicted = xgbModel.predict(X_test)
y_predicted_binary = [1 if yp >=0.5 else 0 for yp in y_predicted]

print (accuracy_score(y_test_binary,y_predicted_binary))

Out: 0.76010781671159033```

So, the initial accuracy without optimizing the model is 76% predicting the daily average price change for each of the the next 371 trading days.

The model can be optimized, I have just used a few parameters to avoid overfitting with the training data and adjusting the learning rate.

The features used should also be analyzed to avoid using redundant variables and to discard those with no correlation. New features should be added to try improved approaches and, to sum up, there is a lot of work that could be done around this basic model.

XGBOOST has also ways to study features. Let’s take a look at their importance:

```fig = plt.figure(figsize=(8,8))
plt.xticks(rotation='vertical')
plt.bar([i for i in range(len(xgbModel.feature_importances_))], xgbModel.feature_importances_.tolist(), tick_label=X_test.columns, color="chocolate")
plt.show()``` It is obvious that the field extension is huge and especially interesting.