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Dataset modeling for financial time series data.md

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Dataset modeling for Financial Time Series Data

This document aims to provide information on the research related to find the best format to represent financial time series data with certain data analysis for the usage of machine learning techniques

On the data provided - Overview

%matplotlib inline

import pandas as pd
import pandas_datareader as web
from IPython.core.display import display
import matplotlib.pylab as plt
from stockstats import StockDataFrame
import seaborn as sns
sns.set()

df = web.DataReader('BRL=X', 'yahoo')
data = pd.DataFrame(df)
data = StockDataFrame.retype(data)
display(data.head())
data.plot(figsize=(15,10))
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open high low close adj close volume
Date
2010-01-04 1.6930 1.7412 1.6723 1.7190 1.7190 0.0
2010-01-05 1.6713 1.7370 1.6713 1.7370 1.7370 0.0
2010-01-06 1.6798 1.7359 1.6798 1.7315 1.7315 0.0
2010-01-07 1.7242 1.7472 1.6805 1.7389 1.7389 0.0
2010-01-08 1.6954 1.7492 1.6954 1.7320 1.7320 0.0 
<matplotlib.axes._subplots.AxesSubplot at 0x10f4d7310>

png

On the indicators

%matplotlib inline

import pandas as pd
import pandas_datareader as web
from IPython.core.display import display
import matplotlib.pylab as plt
from stockstats import StockDataFrame
import seaborn as sns
sns.set()

data = pd.read_csv('USDBRL/all_indicators.csv')
data = StockDataFrame.retype(data)
copy = data.copy()
display(data.tail())
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open high low close adj close volume close_20_sma close_20_mstd boll boll_ub ... mdi_14 mdi dx_14 dx dx_6_ema adx adx_6_ema adxr trix trix_9_sma
date
2018-01-22 3.1912 3.2063 3.1828 3.1947 3.1947 0.0 3.25131 0.045347 3.25131 3.342003 ... 32.424464 32.424464 50.393826 50.393826 44.705562 44.705562 46.145262 46.145262 -0.104079 -0.070007
2018-01-23 3.2007 3.2364 3.1986 3.2007 3.2007 0.0 3.24457 0.042074 3.24457 3.328719 ... 27.456171 27.456171 12.093108 12.093108 35.387718 35.387718 43.071678 43.071678 -0.108291 -0.079818
2018-01-24 3.2337 3.2382 3.1757 3.2355 3.2355 0.0 3.24086 0.039202 3.24086 3.319265 ... 31.174430 31.174430 28.154808 28.154808 33.321172 33.321172 40.285819 40.285819 -0.107148 -0.087835
2018-01-25 3.1451 3.1484 3.1215 3.1451 3.1451 0.0 3.23245 0.040851 3.23245 3.314153 ... 41.194580 41.194580 52.070509 52.070509 38.678126 38.678126 39.826478 39.826478 -0.112533 -0.094800
2018-01-26 3.1454 3.1543 3.1312 3.1469 3.1469 0.0 3.22424 0.040712 3.22424 3.305665 ... 36.821796 36.821796 45.967524 45.967524 40.760811 40.760811 40.093430 40.093430 -0.120949 -0.101018

5 rows × 69 columns

Handling missing data (Data Cleaning)

#How much of the data is missing
counter_nan = data.isnull().sum().sort_values(ascending=False)
plt.figure(figsize=(15,10))
plt.scatter(counter_nan, counter_nan.values)
plt.show()

png

#how many columns does not have a single nan
counter_without_nan = counter_nan[counter_nan==0]
print " [+] Number of columns that does not have a nan: " + str(len(counter_without_nan))
print " [+] Number of total columns: " + str(len(data.columns))
 [+] Number of columns that does not have a nan: 24
 [+] Number of total columns: 69
Much of the encountered NaN are caused from the indicators necessity for previous data
display(data[counter_nan.keys()].head())
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cci_20 cci tr high_delta um low_delta dm close_-1_d cr-ma3 close_-1_s ... kdjk_9 close_10_sma macds close_50_sma dma pdm pdm_14_ema pdm_14 macdh macd
date
2010-01-04 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN ... 55.926463 1.719000 0.000000 1.719000 0.0 0.0000 0.000000 0.000000 0.000000 0.000000
2010-01-05 66.666667 66.666667 0.0657 -0.0042 0.0000 -0.0010 0.001 0.0180 NaN 1.7190 ... 68.614781 1.728000 0.000224 1.728000 0.0 0.0000 0.000000 0.000000 0.000359 0.000404
2010-01-06 60.363636 60.363636 0.0572 -0.0011 0.0000 0.0085 0.000 -0.0055 NaN 1.7370 ... 74.450865 1.729167 0.000273 1.729167 0.0 0.0000 0.000000 0.000000 0.000141 0.000344
2010-01-07 133.333333 133.333333 0.0667 0.0113 0.0113 0.0007 0.000 0.0074 NaN 1.7315 ... 79.322096 1.731600 0.000376 1.731600 0.0 0.0113 0.003457 0.003457 0.000400 0.000576
2010-01-08 106.533036 106.533036 0.0538 0.0020 0.0020 0.0149 0.000 -0.0069 NaN 1.7389 ... 78.854868 1.731680 0.000387 1.731680 0.0 0.0020 0.003077 0.003077 0.000055 0.000415

5 rows × 69 columns

Erasing equal or all zero columns
from pandas.util.testing import assert_series_equal
import numpy as np

# Taking out columns that have all values as 0 or equal values
data = StockDataFrame.retype(data)
cols = data.select_dtypes([np.number]).columns
diff = data[cols].diff().sum()

data = data.drop(diff[diff==0].index, axis=1)
data = data.drop('adj close', 1)
display(data.tail())
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open high low close close_20_sma close_20_mstd boll boll_ub boll_lb close_-1_s ... mdi_14 mdi dx_14 dx dx_6_ema adx adx_6_ema adxr trix trix_9_sma
date
2018-01-22 3.1912 3.2063 3.1828 3.1947 3.25131 0.045347 3.25131 3.342003 3.160617 3.2051 ... 32.424464 32.424464 50.393826 50.393826 44.705562 44.705562 46.145262 46.145262 -0.104079 -0.070007
2018-01-23 3.2007 3.2364 3.1986 3.2007 3.24457 0.042074 3.24457 3.328719 3.160421 3.1947 ... 27.456171 27.456171 12.093108 12.093108 35.387718 35.387718 43.071678 43.071678 -0.108291 -0.079818
2018-01-24 3.2337 3.2382 3.1757 3.2355 3.24086 0.039202 3.24086 3.319265 3.162455 3.2007 ... 31.174430 31.174430 28.154808 28.154808 33.321172 33.321172 40.285819 40.285819 -0.107148 -0.087835
2018-01-25 3.1451 3.1484 3.1215 3.1451 3.23245 0.040851 3.23245 3.314153 3.150747 3.2355 ... 41.194580 41.194580 52.070509 52.070509 38.678126 38.678126 39.826478 39.826478 -0.112533 -0.094800
2018-01-26 3.1454 3.1543 3.1312 3.1469 3.22424 0.040712 3.22424 3.305665 3.142815 3.1451 ... 36.821796 36.821796 45.967524 45.967524 40.760811 40.760811 40.093430 40.093430 -0.120949 -0.101018

5 rows × 66 columns

Slicing the index gives us a pretty simple solution with minimum data miss for the indicator necessity on previous data
data = data[14:-14]
counter_nan = data.isnull().sum().sort_values(ascending=False)
display(data[counter_nan.keys()].head())
plt.figure(figsize=(15,10))
plt.scatter(counter_nan, counter_nan.values)
plt.show()
print " [+] Number of columns that does not have a nan: " + str(len(counter_nan))
print " [+] Number of total columns: " + str(len(data.columns))
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cci_20 cci low_delta um high_delta tr close_-1_d dm wr_6 open ... mdm_14 mdi_14 trix kdjj kdjj_9 kdjd kdjd_9 kdjk kdjk_9 trix_9_sma
date
2010-01-22 178.996300 176.807799 0.0130 0.0269 0.0269 0.0776 0.0180 0.0000 9.292763 1.7525 ... 0.001941 3.085113 0.143416 97.528377 97.528377 92.856768 92.856768 94.413971 94.413971 0.083942
2010-01-25 128.966672 124.296506 0.0130 0.0000 -0.0088 0.0558 -0.0353 0.0000 38.800999 1.8189 ... 0.001653 2.659399 0.155344 73.827148 73.827148 90.138251 90.138251 84.701217 84.701217 0.096051
2010-01-26 197.350586 184.521032 0.0474 0.0247 0.0247 0.0625 0.0501 0.0000 9.117647 1.8136 ... 0.001411 2.269388 0.172968 82.362163 82.362163 89.027382 89.027382 86.805642 86.805642 0.110112
2010-01-27 170.239369 148.954115 -0.0269 0.0203 0.0203 0.0803 0.0160 0.0269 11.533149 1.7860 ... 0.005090 7.953166 0.195355 85.874366 85.874366 88.576951 88.576951 87.676089 87.676089 0.125540
2010-01-28 166.319888 142.587103 0.0204 0.0049 0.0049 0.0648 0.0184 0.0000 2.429765 1.8064 ... 0.004363 6.809581 0.222101 94.516229 94.516229 89.425419 89.425419 91.122356 91.122356 0.142624

5 rows × 66 columns

png

 [+] Number of columns that does not have a nan: 66
 [+] Number of total columns: 66
After slicing we can backfill NaN values for holidays and exceptional days on the market
#Back filling for holidays and exceptional days on the market
data = data.fillna(method='bfill')
data = data[1:-1]
counter_without_nan = data.isnull().sum().sort_values(ascending=False)
print " [+] Number of columns that does not have a nan: " + str(len(counter_without_nan))
print " [+] Number of total columns: " + str(len(data.columns))
 [+] Number of columns that does not have a nan: 66
 [+] Number of total columns: 66

Data Exploring

def plot_histogram(x):
    plt.figure(figsize=(15,10))
    plt.hist(x,  alpha=0.5)
    plt.title("Histogram of '{var_name}'".format(var_name=x.name))
    plt.xlabel("Value")
    plt.ylabel("Frequency")
    plt.show()
plot_histogram(data['macdh'])
plot_histogram(data['cci'])

png

png

Exploring the distribution of percentage change in the close value
import matplotlib.mlab as mlab

mu = data['close_-1_r'].mean()
sigma = data['close_-1_r'].std()
x = data['close_-1_r']
num_bins = 50
fig, ax = plt.subplots(figsize=(15,10))
n, bins, patches = ax.hist(x, num_bins, normed=1)
y = mlab.normpdf(bins, mu, sigma)
ax.plot(bins, y, '--')
ax.set_title('Histogram of 1-day Change $\mu=' + str(mu) + '$, $\sigma=' + str(sigma) + '$')
plt.show()

png

Making our first label of 1 day future forecast for feature exploration
label_display = pd.DataFrame()
label_display['close'] = data['close']
label_display['from_yesterday_rate'] = data['close_-1_r']
y1 = data['close_-1_r'].shift(-1)
y1 = y1.apply(lambda x:1 if x>0.0000 else 0)
label_display['y'] = y1
label_display['c1'] = c1
display(label_display.head(7))
Exploring influence of feature on outcome target
def plot_histogram_dv(x,y):
    plt.figure(figsize=(15,10))
    plt.hist(list(x[y==0]), alpha=0.5, label='Bear')
    plt.hist(list(x[y==1]), alpha=0.5, label='Bull')
    plt.title("Histogram of '{var_name}' by Forecast Target".format(var_name=x.name))
    plt.xlabel("Value")
    plt.ylabel("Frequency")
    plt.legend(loc='upper right')
    plt.show()
plot_histogram_dv(data['macdh'], y1)
plot_histogram_dv(data['cci'], y1)
plot_histogram_dv(data['adx'], y1)
plot_histogram_dv(data['kdjk'], y1)

png

png

png

png

Feature Engineering

Normalizing and Standardizing distributions

Different techniques to represent a price movement can be used to select the one with best results

data.plot(x=data.index, y=['close_20_sma','adx', 'cci'], figsize=(15, 10))
<matplotlib.axes._subplots.AxesSubplot at 0x1a17408850>

png

As shown above, different indicators have different metrics, so we need to normalize in various ways and search for the best results

First let's explore the behavior of each target label
#Labeling the different window frames
##Signaling the difference between a feature datapoint and the previous/next one
       
def labelwf(dataframe, wf):
    for i in wf:
        swf = str(i)
        dataframe['label' + swf] = \
        (dataframe['close'] - dataframe['close'].shift(i))/dataframe['close'].shift(i)
        dataframe['label' + swf] = dataframe['label' + swf].apply(lambda x:1 if x>0.0 else 0)
    return dataframe
    
#Negative for looking future datapoints
#Positive for looking backwards
window_frames = [-1, -2, -15, 1, 2, 15]
labeled_data = labelwf(data.copy(), window_frames)
index = list(range(len(data)))
index = index[-250:-15]
label1 = labeled_data['label-1'].values
label1 = label1[-250:-15]
label15 = labeled_data['label-15'].values
label15 = label15[-250:-15]
c1 = copy['close_1_r'].apply(lambda x:0 if x>0.000 else 1)
c15 = copy['close_15_r'].apply(lambda x:0 if x>0.000 else 1)
y_5 = copy['close_5_r'].apply(lambda x:0 if x>0.000 else 1)
y_10 = copy['close_10_r'].apply(lambda x:0 if x>0.000 else 1)
y_30 = copy['close_30_r'].applu(lambda x:0 if x>0.000 else 1)
index = list(range(len(c1)))
index = index[-250:-15]

fig, ax = plt.subplots(figsize=(15, 8), sharey=True)
ax.plot(index, c1[-250:-15], label='1d forward', color='r')
ax.scatter(index, c15[-250:-15], label='15d forward', color='g')
ax.legend()


labeled_data['index'] = list(range(len(data)))
data.plot(y='close', figsize=(15, 8))
for r in labeled_data.iterrows():
    if r[1]['label1'] == 1:
        plt.axvline(x=r[1]['index'], linewidth=0.3, alpha=0.3, color='g')
    else:
        plt.axvline(x=r[1]['index'], linewidth=0.3, alpha=0.3, color='r')
    
plt.show()

png

png

Percentage change of each indicator : (xn - xn-1)/xn-1 where n = [n, n+y, n+2y] and y = Time Frame Window selected
#Normalizing the features datapoints 
#Accordingly to its window frame

#Each datapoint to the change percentage of timeframe
def percent_change(dataframe, wf):
    new = pd.DataFrame()
    swf = str(wf)
    for feature in dataframe:
        if 'label' in str(dataframe[feature].name):
            pass
        elif 'change_' in str(dataframe[feature].name):
            pass
        else:
            dataframe['change_' + str(dataframe[feature].name)] = \
            (dataframe[feature] - dataframe[feature].shift(wf))/dataframe[feature].shift(wf)
            new['change_' + str(dataframe[feature].name)] = \
            (dataframe[feature] - dataframe[feature].shift(wf))/dataframe[feature].shift(wf)
    return dataframe, new

raw_data = data.copy()
data, percent_change_data = percent_change(data, 1)
data = data.drop('change_pdm', 1)
data = data.drop('change_um', 1)
data = data.drop('change_dm', 1)
percent_change_data = percent_change_data.drop('change_pdm', 1)
percent_change_data = percent_change_data.drop('change_um', 1)
percent_change_data = percent_change_data.drop('change_dm', 1)
percent_change_data = percent_change_data.replace([np.inf, -np.inf], np.nan)
percent_change_data = percent_change_data.fillna(method='bfill')
data = data.replace([np.inf, -np.inf], np.nan)
data = data.fillna(method='bfill')
data.plot(x=data.index, y='change_close_20_sma', figsize=(15,10))
data.plot(x=data.index, y=['change_kdjk','change_adx', 'change_close_20_sma'], figsize=(15,10))
                          
display(data.tail())
display(percent_change_data.tail())
plot_histogram_dv(data['change_macdh'], y1)
plot_histogram_dv(data['change_macdh'], c15)
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open high low close close_20_sma close_20_mstd boll boll_ub boll_lb close_-1_s ... change_mdi_14 change_mdi change_dx_14 change_dx change_dx_6_ema change_adx change_adx_6_ema change_adxr change_trix change_trix_9_sma
date
2018-01-01 3.3075 3.3117 3.3075 3.3076 3.296855 0.029485 3.296855 3.355825 3.237885 3.3111 ... -0.073114 -0.073114 -6.225712e-16 -6.225712e-16 0.047143 0.047143 -0.009660 -0.009660 -0.034542 0.016791
2018-01-02 3.3108 3.3127 3.2585 3.3110 3.300275 0.026696 3.300275 3.353666 3.246884 3.3076 ... 0.695512 0.695512 1.310292e+00 1.310292e+00 0.448662 0.448662 0.118096 0.118096 -0.044511 0.007815
2018-01-03 3.2574 3.2638 3.2410 3.2578 3.301150 0.024849 3.301150 3.350849 3.251451 3.3110 ... -0.015868 -0.015868 1.234280e-01 1.234280e-01 0.283790 0.283790 0.177938 0.177938 -0.126147 -0.007375
2018-01-04 3.2356 3.2410 3.2214 3.2355 3.301210 0.024680 3.301210 3.350571 3.251849 3.2578 ... 0.066333 0.066333 1.039332e-01 1.039332e-01 0.204003 0.204003 0.188197 0.188197 -0.228872 -0.030493
2018-01-05 3.2328 3.2479 3.2256 3.2331 3.298505 0.028901 3.298505 3.356306 3.240704 3.2355 ... -0.105324 -0.105324 -1.462284e-01 -1.462284e-01 0.061550 0.061550 0.137684 0.137684 -0.352545 -0.063682

5 rows × 129 columns

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change_open change_high change_low change_close change_close_20_sma change_close_20_mstd change_boll change_boll_ub change_boll_lb change_close_-1_s ... change_mdi_14 change_mdi change_dx_14 change_dx change_dx_6_ema change_adx change_adx_6_ema change_adxr change_trix change_trix_9_sma
date
2018-01-01 -0.001057 -0.000151 0.007770 -0.001057 0.000762 -0.037582 0.000762 0.000062 0.001489 -0.000664 ... -0.073114 -0.073114 -6.225712e-16 -6.225712e-16 0.047143 0.047143 -0.009660 -0.009660 -0.034542 0.016791
2018-01-02 0.000998 0.000302 -0.014815 0.001028 0.001037 -0.094602 0.001037 -0.000643 0.002779 -0.001057 ... 0.695512 0.695512 1.310292e+00 1.310292e+00 0.448662 0.448662 0.118096 0.118096 -0.044511 0.007815
2018-01-03 -0.016129 -0.014761 -0.005371 -0.016068 0.000265 -0.069161 0.000265 -0.000840 0.001407 0.001028 ... -0.015868 -0.015868 1.234280e-01 1.234280e-01 0.283790 0.283790 0.177938 0.177938 -0.126147 -0.007375
2018-01-04 -0.006692 -0.006986 -0.006048 -0.006845 0.000018 -0.006802 0.000018 -0.000083 0.000122 -0.016068 ... 0.066333 0.066333 1.039332e-01 1.039332e-01 0.204003 0.204003 0.188197 0.188197 -0.228872 -0.030493
2018-01-05 -0.000865 0.002129 0.001304 -0.000742 -0.000819 0.170995 -0.000819 0.001712 -0.003427 -0.006845 ... -0.105324 -0.105324 -1.462284e-01 -1.462284e-01 0.061550 0.061550 0.137684 0.137684 -0.352545 -0.063682

5 rows × 63 columns

png

png

png

We see in the above picture that even with the percent change ratio we cant diferentiate on how much that change was significant by some orders of magnitude

Standardized change range : ((xn - xn-1)/xn-1) / (xMax - xMin)
#How abnormal was the change compared to the feature range
def normalized_range(dataframe, wf):
    swf = str(wf)
    new = pd.DataFrame()
    for feature in dataframe:
        if 'label' in str(dataframe[feature].name):
            pass
        elif 'change_' in str(dataframe[feature].name):
            pass
        elif 'rchange_' in str(dataframe[feature].name):
            pass
        else:
            try:
                range = dataframe['change_' + str(dataframe[feature].name)].max() - \
                                              dataframe['change_' + str(dataframe[feature].name)].min()
                dataframe['rchange_' + str(dataframe[feature].name)] = \
                                              dataframe['change_' + str(dataframe[feature].name)] / range
                new['rchange_' + str(dataframe[feature].name)] = \
                                              dataframe['change_' + str(dataframe[feature].name)] / range
            except:
                pass
    return dataframe, new
                                              

change_data = data.copy()
data, normalized_range_data = normalized_range(data, 1)
data.plot(x=data.index, y=['rchange_close_20_sma','rchange_adx', 'rchange_close'], figsize=(15,10))
data = data.replace([np.inf, -np.inf], np.nan)
data = data.fillna(method='bfill')
normalized_range_data = normalized_range_data.replace([np.inf, -np.inf], np.nan)
normalized_range_data = normalized_range_data.fillna(method='bfill')


display(data.tail())
display(normalized_range_data.tail())
plot_histogram_dv(normalized_range_data['rchange_rsi_6'], y1)    
plot_histogram_dv(normalized_range_data['rchange_rsi_6'], c15)
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open high low close close_20_sma close_20_mstd boll boll_ub boll_lb close_-1_s ... rchange_mdi_14 rchange_mdi rchange_dx_14 rchange_dx rchange_dx_6_ema rchange_adx rchange_adx_6_ema rchange_adxr rchange_trix rchange_trix_9_sma
date
2018-01-01 3.3075 3.3117 3.3075 3.3076 3.296855 0.029485 3.296855 3.355825 3.237885 3.3111 ... -0.010609 -0.010609 -2.072037e-19 -2.072037e-19 0.012496 0.012496 -0.015652 -0.015652 -0.000204 0.000091
2018-01-02 3.3108 3.3127 3.2585 3.3110 3.300275 0.026696 3.300275 3.353666 3.246884 3.3076 ... 0.100917 0.100917 4.360903e-04 4.360903e-04 0.118926 0.118926 0.191346 0.191346 -0.000263 0.000042
2018-01-03 3.2574 3.2638 3.2410 3.2578 3.301150 0.024849 3.301150 3.350849 3.251451 3.3110 ... -0.002302 -0.002302 4.107921e-05 4.107921e-05 0.075224 0.075224 0.288305 0.288305 -0.000745 -0.000040
2018-01-04 3.2356 3.2410 3.2214 3.2355 3.301210 0.024680 3.301210 3.350571 3.251849 3.2578 ... 0.009625 0.009625 3.459096e-05 3.459096e-05 0.054075 0.054075 0.304928 0.304928 -0.001352 -0.000165
2018-01-05 3.2328 3.2479 3.2256 3.2331 3.298505 0.028901 3.298505 3.356306 3.240704 3.2355 ... -0.015282 -0.015282 -4.866762e-05 -4.866762e-05 0.016315 0.016315 0.223084 0.223084 -0.002083 -0.000345

5 rows × 192 columns

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rchange_open rchange_high rchange_low rchange_close rchange_close_20_sma rchange_close_20_mstd rchange_boll rchange_boll_ub rchange_boll_lb rchange_close_-1_s ... rchange_mdi_14 rchange_mdi rchange_dx_14 rchange_dx rchange_dx_6_ema rchange_adx rchange_adx_6_ema rchange_adxr rchange_trix rchange_trix_9_sma
date
2018-01-01 -0.006705 -0.000915 0.065792 -0.007716 0.055369 -0.022755 0.055369 0.001321 0.041792 -0.004847 ... -0.010609 -0.010609 -2.072037e-19 -2.072037e-19 0.012496 0.012496 -0.015652 -0.015652 -0.000204 0.000091
2018-01-02 0.006329 0.001830 -0.125450 0.007503 0.075386 -0.057278 0.075386 -0.013763 0.078024 -0.007716 ... 0.100917 0.100917 4.360903e-04 4.360903e-04 0.118926 0.118926 0.191346 0.191346 -0.000263 0.000042
2018-01-03 -0.102309 -0.089450 -0.045477 -0.117284 0.019267 -0.041874 0.019267 -0.017975 0.039494 0.007503 ... -0.002302 -0.002302 4.107921e-05 4.107921e-05 0.075224 0.075224 0.288305 0.288305 -0.000745 -0.000040
2018-01-04 -0.042451 -0.042332 -0.051209 -0.049965 0.001321 -0.004119 0.001321 -0.001775 0.003437 -0.117284 ... 0.009625 0.009625 3.459096e-05 3.459096e-05 0.054075 0.054075 0.304928 0.304928 -0.001352 -0.000165
2018-01-05 -0.005489 0.012901 0.011040 -0.005414 -0.059547 0.103531 -0.059547 0.036623 -0.096222 -0.049965 ... -0.015282 -0.015282 -4.866762e-05 -4.866762e-05 0.016315 0.016315 0.223084 0.223084 -0.002083 -0.000345

5 rows × 63 columns

png

png

png

As we can see, the datapoints are now expressing in a much more intuiteve manner their movements with a same axis of change

Normalized change rate : ( ( (xn - xn-1)/xn-1 ) - (Σxi / n) ) / ( √( (Σxi - (Σxi / n)ˆ2 ) / n ) ) = (Change - Mean) / Standard Deviation
#How abnormal was this change percentage ratio in comparison to the others
def normalized_change(dataframe, wf):
    swf = str(wf)
    new = pd.DataFrame()
    for feature in dataframe:
        if 'label' in str(dataframe[feature].name):
            pass
        elif 'change_' in str(dataframe[feature].name):
            pass
        elif 'rchange_' in str(dataframe[feature].name):
            pass
        elif 'nchange_' in str(dataframe[feature].name):
            pass
        else:
            try:
                std = dataframe['change_' + str(dataframe[feature].name)].std()
                mean = dataframe['change_' + str(dataframe[feature].name)].mean()
                dataframe['nchange_' + str(dataframe[feature].name)] = \
                (dataframe['change_' + str(dataframe[feature].name)] - mean)/std
                new['nchange_' + str(dataframe[feature].name)] = \
                (dataframe['change_' + str(dataframe[feature].name)] - mean)/std
            except:
                pass
            
    return dataframe, new

rchange_data = data.copy()
data, normalized_change_data = normalized_change(data, 1)
data = data.replace([np.inf, -np.inf], np.nan)
data = data.fillna(method='bfill')
normalized_change_data = normalized_change_data.replace([np.inf, -np.inf], np.nan)
normalized_change_data = normalized_change_data.fillna(method='bfill')
data.plot(x=data.index, y=['nchange_close_20_sma','nchange_adx', 'nchange_close'], figsize=(15, 10))
                          
display(data.tail())
display(normalized_change_data.tail())

plot_histogram_dv(normalized_change_data['nchange_rsi_6'], y1)    
plot_histogram_dv(normalized_change_data['nchange_rsi_6'], c15)
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open high low close close_20_sma close_20_mstd boll boll_ub boll_lb close_-1_s ... nchange_mdi_14 nchange_mdi nchange_dx_14 nchange_dx nchange_dx_6_ema nchange_adx nchange_adx_6_ema nchange_adxr nchange_trix nchange_trix_9_sma
date
2018-01-01 3.3075 3.3117 3.3075 3.3076 3.296855 0.029485 3.296855 3.355825 3.237885 3.3111 ... -0.277020 -0.277020 -0.045644 -0.045644 0.134691 0.134691 -0.148862 -0.148862 0.007774 0.020925
2018-01-02 3.3108 3.3127 3.2585 3.3110 3.300275 0.026696 3.300275 3.353666 3.246884 3.3076 ... 1.612389 1.612389 -0.026412 -0.026412 2.033934 2.033934 1.249729 1.249729 0.004729 0.018454
2018-01-03 3.2574 3.2638 3.2410 3.2578 3.301150 0.024849 3.301150 3.350849 3.251451 3.3110 ... -0.136300 -0.136300 -0.043832 -0.043832 1.254066 1.254066 1.904840 1.904840 -0.020209 0.014271
2018-01-04 3.2356 3.2410 3.2214 3.2355 3.301210 0.024680 3.301210 3.350571 3.251849 3.2578 ... 0.065763 0.065763 -0.044118 -0.044118 0.876665 0.876665 2.017157 2.017157 -0.051589 0.007907
2018-01-05 3.2328 3.2479 3.2256 3.2331 3.298505 0.028901 3.298505 3.356306 3.240704 3.2355 ... -0.356199 -0.356199 -0.047790 -0.047790 0.202839 0.202839 1.464168 1.464168 -0.089369 -0.001231

5 rows × 255 columns

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nchange_open nchange_high nchange_low nchange_close nchange_close_20_sma nchange_close_20_mstd nchange_boll nchange_boll_ub nchange_boll_lb nchange_close_-1_s ... nchange_mdi_14 nchange_mdi nchange_dx_14 nchange_dx nchange_dx_6_ema nchange_adx nchange_adx_6_ema nchange_adxr nchange_trix nchange_trix_9_sma
date
2018-01-01 -0.128347 -0.050057 0.821339 -0.127259 0.229905 -0.441805 0.229905 -0.071889 0.362274 -0.089153 ... -0.277020 -0.277020 -0.045644 -0.045644 0.134691 0.134691 -0.148862 -0.148862 0.007774 0.020925
2018-01-02 0.061175 -0.003072 -1.676715 0.059701 0.368936 -1.041422 0.368936 -0.279976 0.760588 -0.124398 ... 1.612389 1.612389 -0.026412 -0.026412 2.033934 2.033934 1.249729 1.249729 0.004729 0.018454
2018-01-03 -1.518482 -1.565728 -0.632093 -1.473256 -0.020851 -0.773884 -0.020851 -0.338086 0.337015 0.062559 ... -0.136300 -0.136300 -0.043832 -0.043832 1.254066 1.254066 1.904840 1.904840 -0.020209 0.014271
2018-01-04 -0.648116 -0.759089 -0.706970 -0.646273 -0.145504 -0.118126 -0.145504 -0.114609 -0.059371 -1.470369 ... 0.065763 0.065763 -0.044118 -0.044118 0.876665 0.876665 2.017157 2.017157 -0.051589 0.007907
2018-01-05 -0.110665 0.186461 0.106153 -0.098988 -0.568277 1.751577 -0.568277 0.415113 -1.154962 -0.643402 ... -0.356199 -0.356199 -0.047790 -0.047790 0.202839 0.202839 1.464168 1.464168 -0.089369 -0.001231

5 rows × 63 columns

png

png

png

And now, we can evaluate the order of the anomaly of a certain datapoint without losing information on the feature
Normalizing the raw features instead of the change rate
#How abnormal is the position that the datapoint is located at
#We substitute the original feature value for this one
def distance(dataframe):
    new = pd.DataFrame()
    for feature in dataframe:
        if 'label' in str(dataframe[feature].name):
            pass
        elif 'change_' in str(dataframe[feature].name):
            pass
        elif 'nchange_' in str(dataframe[feature].name):
            pass
        elif 'rchange_' in str(dataframe[feature].name):
            pass
        elif 'distance_' in str(dataframe[feature].name):
            pass
        else:
            std = dataframe[feature].std()
            mean = dataframe[feature].mean()
            dataframe['distance_' + str(dataframe[feature].name)] = (dataframe[feature] - mean)/std 
            new['distance_' + str(dataframe[feature].name)] = (dataframe[feature] - mean)/std 
    return dataframe, new

nchange = data.copy()
data, distance_data = distance(data)
data = data.replace([np.inf, -np.inf], np.nan)
data = data.fillna(method='bfill')
distance_data = distance_data.replace([np.inf, -np.inf], np.nan)
distance_data = distance_data.fillna(method='bfill')
data.plot(x=data.index, y=['distance_close_20_sma','distance_adx', 'close_20_sma'], figsize=(15,10))


display(data.tail())
display(distance_data.tail())

plot_histogram_dv(distance_data['distance_macdh'], y1)
plot_histogram_dv(data['macdh'], y1)    
plot_histogram_dv(distance_data['distance_macdh'], c15)
plot_histogram_dv(data['macdh'], c15)
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open high low close close_20_sma close_20_mstd boll boll_ub boll_lb close_-1_s ... distance_mdi_14 distance_mdi distance_dx_14 distance_dx distance_dx_6_ema distance_adx distance_adx_6_ema distance_adxr distance_trix distance_trix_9_sma
date
2018-01-01 3.3075 3.3117 3.3075 3.3076 3.296855 0.029485 3.296855 3.355825 3.237885 3.3111 ... 0.488966 0.488966 -0.348806 -0.348806 -0.616822 -0.616822 -0.665492 -0.665492 0.338169 0.335080
2018-01-02 3.3108 3.3127 3.2585 3.3110 3.300275 0.026696 3.300275 3.353666 3.246884 3.3076 ... 2.302947 2.302947 1.064375 1.064375 -0.031028 -0.031028 -0.485673 -0.485673 0.314458 0.339260
2018-01-03 3.2574 3.2638 3.2410 3.2578 3.301150 0.024849 3.301150 3.350849 3.251451 3.3110 ... 2.232778 2.232778 1.371921 1.371921 0.505743 0.505743 -0.182739 -0.182739 0.250250 0.335284
2018-01-04 3.2356 3.2410 3.2214 3.2355 3.301210 0.024680 3.301210 3.350571 3.251849 3.2578 ... 2.521454 2.521454 1.662856 1.662856 1.001106 1.001106 0.194673 0.194673 0.148451 0.318967
2018-01-05 3.2328 3.2479 3.2256 3.2331 3.298505 0.028901 3.298505 3.356306 3.240704 3.2355 ... 2.032685 2.032685 1.210983 1.210983 1.181051 1.181051 0.522749 0.522749 0.027533 0.285929

5 rows × 321 columns

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distance_open distance_high distance_low distance_close distance_close_20_sma distance_close_20_mstd distance_boll distance_boll_ub distance_boll_lb distance_close_-1_s ... distance_mdi_14 distance_mdi distance_dx_14 distance_dx distance_dx_6_ema distance_adx distance_adx_6_ema distance_adxr distance_trix distance_trix_9_sma
date
2018-01-01 1.129346 1.105120 1.161948 1.130977 1.128932 -0.326446 1.128932 1.056927 1.203622 1.136831 ... 0.488966 0.488966 -0.348806 -0.348806 -0.616822 -0.616822 -0.665492 -0.665492 0.338169 0.335080
2018-01-02 1.133888 1.106495 1.093890 1.135696 1.133691 -0.433323 1.133691 1.054054 1.216700 1.131972 ... 2.302947 2.302947 1.064375 1.064375 -0.031028 -0.031028 -0.485673 -0.485673 0.314458 0.339260
2018-01-03 1.060385 1.039224 1.069584 1.061854 1.134909 -0.504066 1.134909 1.050304 1.223338 1.136692 ... 2.232778 2.232778 1.371921 1.371921 0.505743 0.505743 -0.182739 -0.182739 0.250250 0.335284
2018-01-04 1.030377 1.007858 1.042361 1.030902 1.134993 -0.510543 1.134993 1.049934 1.223916 1.062847 ... 2.521454 2.521454 1.662856 1.662856 1.001106 1.001106 0.194673 0.194673 0.148451 0.318967
2018-01-05 1.026523 1.017350 1.048194 1.027570 1.131228 -0.348840 1.131228 1.057567 1.207719 1.031893 ... 2.032685 2.032685 1.210983 1.210983 1.181051 1.181051 0.522749 0.522749 0.027533 0.285929

5 rows × 66 columns

png

png

png

png

png

And evaluate the distance of the datapoint address in comparison to the others of its kind

Creating new features via interactions between them
from itertools import combinations
from sklearn.preprocessing import PolynomialFeatures

def add_interactions(df):
    # Get feature names
    combos = list(combinations(list(df.columns), 2))
    colnames = list(df.columns) + ['_'.join(x) for x in combos]
    
    # Find interactions
    poly = PolynomialFeatures(interaction_only=True, include_bias=False)
    df = poly.fit_transform(df)
    df = pd.DataFrame(df)
    df.columns = colnames
    
    # Remove interaction terms with all 0 values            
    noint_indicies = [i for i, x in enumerate(list((df == 0).all())) if x]
    df = df.drop(df.columns[noint_indicies], axis=1)
    
    return df
teste = add_interactions(data.copy())
print (teste.head(5))
     open    high     low   close  close_20_sma  close_20_mstd      boll  \
0  1.8189  1.8213  1.7655  1.7835      1.758200       0.028923  1.758200   
1  1.8136  1.8460  1.8129  1.8336      1.762635       0.033447  1.762635   
2  1.7860  1.8663  1.7860  1.8496      1.767467       0.038380  1.767467   
3  1.8064  1.8712  1.8064  1.8680      1.772758       0.043854  1.772758   
4  1.8200  1.8729  1.8200  1.8729      1.777765       0.048201  1.777765   

    boll_ub   boll_lb  close_-1_s                ...                  \
0  1.816046  1.700354      1.8188                ...                   
1  1.829528  1.695742      1.7835                ...                   
2  1.844227  1.690707      1.8336                ...                   
3  1.860465  1.685051      1.8496                ...                   
4  1.874167  1.681363      1.8680                ...                   

   distance_adx_distance_adx_6_ema  distance_adx_distance_adxr  \
0                         2.155962                    2.155962   
1                         3.204561                    3.204561   
2                         2.238586                    2.238586   
3                         1.551822                    1.551822   
4                         1.090493                    1.090493   

   distance_adx_distance_trix  distance_adx_distance_trix_9_sma  \
0                    1.237139                          0.663483   
1                    1.774381                          1.013457   
2                    1.445436                          0.852129   
3                    1.260181                          0.754362   
4                    1.133128                          0.694455   

   distance_adx_6_ema_distance_adxr  distance_adx_6_ema_distance_trix  \
0                          1.881588                          1.079697   
1                          2.633112                          1.457967   
2                          2.594067                          1.674967   
3                          2.216411                          1.799871   
4                          1.767651                          1.836761   

   distance_adx_6_ema_distance_trix_9_sma  distance_adxr_distance_trix  \
0                                0.579046                     1.079697   
1                                0.832734                     1.457967   
2                                0.987445                     1.674967   
3                                1.077429                     1.799871   
4                                1.125687                     1.836761   

   distance_adxr_distance_trix_9_sma  distance_trix_distance_trix_9_sma  
0                           0.579046                           0.332270  
1                           0.832734                           0.461089  
2                           0.987445                           0.637585  
3                           1.077429                           0.874942  
4                           1.125687                           1.169698  

[5 rows x 51681 columns]

Feature Selection

The methods based on F-test estimate the degree of linear dependency between two random variables. On the other hand, mutual information methods can capture any kind of statistical dependency, but being nonparametric, they require more samples for accurate estimation.
import numpy as np
from sklearn.feature_selection import f_classif, mutual_info_classif

y_15 = c15[15:-15]
y_1 = c1[15:-15]
y_5 = y_5[15:-15]
y_30 = y_30[15:-15]
mi = mutual_info_regression(distance_data, y_15, discrete_features='auto')
#print test.columns
mi /= np.max(mi)
result = distance_data.columns[mi > 0.1]
miresult = result
mi = mi[mi > 0.1]
print len(result)
display(result)
mi_df = pd.DataFrame(index=result, columns=['value'])
mi_df['value'] = mi
mi_df.plot(figsize=(15,10))
display(mi_df.head())
print mi_df

print "\n"

ftest, _ = f_regression(distance_data, y_15)
ftest /= np.max(ftest)
_[np.isnan(_)] = 0.0
f = _[~np.isnan(_)]
result = distance_data.columns[f > 0.1]
f = f[f > 0.1]
#print f.max()
#print result.max()
print len(result)
print result

f_df = pd.DataFrame(index=result, columns=['value'])
f_df['value'] = f
f_df.plot(figsize=(15,10))
display(f_df.head())
print f_df

equal = []

for i in miresult.values:
    if i in result.values:
        equal.append(i)
    
print "\n"
display(equal)

29



Index([u'distance_open', u'distance_high', u'distance_low', u'distance_close',
       u'distance_close_20_sma', u'distance_close_20_mstd', u'distance_boll',
       u'distance_boll_ub', u'distance_boll_lb', u'distance_close_-1_s',
       u'distance_close_26_ema', u'distance_macd', u'distance_middle',
       u'distance_cr-ma1', u'distance_cr-ma3', u'distance_open_2_sma',
       u'distance_middle_14_sma', u'distance_middle_20_sma', u'distance_atr',
       u'distance_close_10_sma', u'distance_close_50_sma', u'distance_dma',
       u'distance_atr_14', u'distance_dx_14', u'distance_dx',
       u'distance_dx_6_ema', u'distance_adx', u'distance_trix',
       u'distance_trix_9_sma'],
      dtype='object')
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value
distance_open 0.440642
distance_high 0.443556
distance_low 0.505598
distance_close 0.468534
distance_close_20_sma 0.491667 
                           value
distance_open           0.440642
distance_high           0.443556
distance_low            0.505598
distance_close          0.468534
distance_close_20_sma   0.491667
distance_close_20_mstd  0.217032
distance_boll           0.494343
distance_boll_ub        0.829823
distance_boll_lb        0.555011
distance_close_-1_s     0.442161
distance_close_26_ema   0.729244
distance_macd           0.168234
distance_middle         0.637619
distance_cr-ma1         0.207764
distance_cr-ma3         0.198476
distance_open_2_sma     0.450697
distance_middle_14_sma  0.642620
distance_middle_20_sma  0.506292
distance_atr            0.241409
distance_close_10_sma   0.624836
distance_close_50_sma   1.000000
distance_dma            0.172680
distance_atr_14         0.246042
distance_dx_14          0.185833
distance_dx             0.173521
distance_dx_6_ema       0.113376
distance_adx            0.113376
distance_trix           0.319277
distance_trix_9_sma     0.260197


24
Index([u'distance_open', u'distance_high', u'distance_low', u'distance_close',
       u'distance_boll_lb', u'distance_close_-1_s', u'distance_close_-1_d',
       u'distance_close_-1_r', u'distance_middle', u'distance_cr-ma3',
       u'distance_rsv_9', u'distance_kdjk_9', u'distance_kdjk',
       u'distance_kdjj_9', u'distance_kdjj', u'distance_open_2_sma',
       u'distance_wr_10', u'distance_middle_14_sma', u'distance_close_10_sma',
       u'distance_pdm_14_ema', u'distance_pdm_14', u'distance_adx_6_ema',
       u'distance_adxr', u'distance_trix_9_sma'],
      dtype='object')
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value
distance_open 0.191533
distance_high 0.181462
distance_low 0.210108
distance_close 0.138125
distance_boll_lb 0.141074 
                           value
distance_open           0.191533
distance_high           0.181462
distance_low            0.210108
distance_close          0.138125
distance_boll_lb        0.141074
distance_close_-1_s     0.141206
distance_close_-1_d     0.740016
distance_close_-1_r     0.530851
distance_middle         0.174595
distance_cr-ma3         0.211435
distance_rsv_9          0.249812
distance_kdjk_9         0.276445
distance_kdjk           0.276445
distance_kdjj_9         0.714550
distance_kdjj           0.714550
distance_open_2_sma     0.184072
distance_wr_10          0.488122
distance_middle_14_sma  0.110842
distance_close_10_sma   0.116276
distance_pdm_14_ema     0.299721
distance_pdm_14         0.299721
distance_adx_6_ema      0.506360
distance_adxr           0.506360
distance_trix_9_sma     0.250674





['distance_open',
 'distance_high',
 'distance_low',
 'distance_close',
 'distance_boll_lb',
 'distance_close_-1_s',
 'distance_middle',
 'distance_cr-ma3',
 'distance_open_2_sma',
 'distance_middle_14_sma',
 'distance_close_10_sma',
 'distance_trix_9_sma']

png

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from sklearn.decomposition import PCA



pca = PCA(n_components=2)
data_pca = pd.DataFrame(pca.fit_transform(distance_data))
#display(data_pca.head())
data_pca.plot(figsize=(15,10))

datatest = pca.fit_transform(distance_data)
plt.figure(num=None, figsize=(18, 11), dpi=80, facecolor='w', edgecolor='k')
plt.scatter(datatest[:, 0], datatest[:, 1])
plt.show()

png

png

T - Distributed Stochastic Neighboor Embedding

Transforming the data into a Similarity Matrix for comparing the similarity of a certain datapoint with the rest

from sklearn.preprocessing import LabelEncoder
from sklearn.preprocessing import StandardScaler
from sklearn.cross_validation import train_test_split
from sklearn.metrics import accuracy_score

# t-distributed Stochastic Neighbor Embedding (t-SNE) visualization
from sklearn.manifold import TSNE
tsne = TSNE(n_components=2, random_state=0)
x_test_2d = tsne.fit_transform(distance_data)
#y_test = y_15

y_tsne = []
for key, i in np.ndenumerate(y_15):
    if i == 0:
        if y_1[key[0]] == 0:
            y_tsne.append(0)
        elif y_1[key[0]] == 1:
            y_tsne.append(1)
    if i == 1:
        if y_1[key[0]] == 0:
            y_tsne.append(2)
        elif y_1[key[0]] == 1:
            y_tsne.append(3)

y_test = np.array(y_tsne)
            

markers=('s', 'd', 'o', '^', 'v')
color_map = {0:'red', 1:'blue', 2:'lightgreen', 3:'purple'}
plt.figure(figsize=(15,10))
for idx, cl in enumerate(np.unique(y_test)):
    plt.scatter(x=x_test_2d[y_test==cl,0], y=x_test_2d[y_test==cl,1], c=color_map[idx], marker=markers[idx], label=cl, alpha=0.5)
plt.xlabel('X in t-SNE')
plt.ylabel('Y in t-SNE')
plt.legend(loc='upper left')
plt.title('t-SNE visualization of test data')
plt.show()

png

Facebook Time series forecasting

Prophet library
from fbprophet import Prophet
import numpy as np

test = data.copy()
test['ds'] = data.index
test['y'] = np.log(data['close'])
display(test.tail())
m = Prophet()
m.fit(test)
future = m.make_future_dataframe(periods=365)
forecast = m.predict(future)
forecast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']]
m.plot(forecast)
m.plot_components(forecast)
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open high low close adj close volume ds y
Date
2018-02-05 3.2169 3.2455 3.2138 3.2154 3.2154 0.0 2018-02-05 1.167952
2018-02-06 3.2611 3.2759 3.2175 3.2611 3.2611 0.0 2018-02-06 1.182065
2018-02-07 3.2333 3.2630 3.2314 3.2334 3.2334 0.0 2018-02-07 1.173534
2018-02-08 3.2696 3.2926 3.2562 3.2699 3.2699 0.0 2018-02-08 1.184759
2018-02-09 3.2844 3.3075 3.2708 3.2846 3.2846 0.0 2018-02-09 1.189245 
INFO:fbprophet.forecaster:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
/Library/Python/2.7/site-packages/pystan/misc.py:399: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.
  elif np.issubdtype(np.asarray(v).dtype, float):

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