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Predict Stock-Market Behavior with Markov Chains and Python

Image(filename='predicting-stock-market-with-markov/markov.png')

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Predicting the Stock Market with Markov Chains and Python

Hello Friends

Let's apply Markov Chains to predict the stock market. I am basing this off a post from Pranab Gosh in his blog titled 'Customer Conversion Prediction with Markov Chain Classifier' (https://pkghosh.wordpress.com/2015/07/06/customer-conversion-prediction-with-markov-chain-classifier/)

He is applying it obviously to customer conversion data but that data isn't as easy to get a stock market data. Also, this is just my interpretation of his pseudo code as there are many ways of slicing and dicing this. But what i like about his approach is that his cleaver way of doing binary classification with by creating two transition matrices - a positive one and a negative one (I also did an R version in the past - find it here). Let's dig in.

Markov Chains

A Markov Chain offers a probabilistic approach in predicting the likelihood of an event based on prior behavior.

First-Order Transition Matrix

A transition matrix is the probability matrix from the Markov Chain. In its simplest form, you read it by choosing the current event on the y axis and look for the probability of the next event off the x axis. In the below image from Wikipedia, you see that the highest probability for the next note after A is C#.

In our case, we will analyze each event pair in a sequence and catalog the market behavior. We then tally all the matching moves and create two data sets for volume action, one for up moves and another for down moves. New stock market events are then broken down into sequential pairs and tallied for both positive and negative outcomes - biggest moves win (there is a little more to this in the code, but that’s it in a nutshell).

Image(filename='predicting-stock-market-with-markov/transition-matrix.png')

Cataloging Patterns Using S&P 500 Market Data

Get market data at Yahoo Fiance and download historical data for symbol ^GSPC

In its raw form, 10 years of S&P 500 index data represents only one sequence of many events leading to the last quoted price. In order to get more sequences and, more importantly, get a better understanding of the market’s behavior, we need to break up the data into many samples of sequences leading to different price patterns. This way we can build a fairly rich catalog of market behaviors and attempt to match them with future patterns to predict future outcomes. For example, below are three sets of consecutive S&P 500 price closes. They represent different periods and contain varying amounts of prices. Think of each of these sequences as a pattern leading to a final price expression. Let’s look at some examples:

2012-10-18 to 2012-11-21

1417.26 –> 1428.39 –> 1394.53 –> 1377.51 –> Next Day Volume Up

2016-08-12 to 2016-08-22

2184.05 –> 2190.15 –> 2178.15 –> 2182.22 –> 2187.02 –> Next Day Volume Up

2014-04-04 to 2014-04-10

1865.09 –> 1845.04 –> Next Day Volume Down

Take the last example, imagine that past three days of the current market match historical behaviors of day 1, 2 and 3. You now have a pattern that matches current market conditions and can use the future price (day 4) as an indicator for tomorrow’s market direction (i.e. market going down). This obviously isn’t using any of Markov’s ideas and is just predicting future behavior on the basis of an up-down-up market pattern.

If you collect thousands and thousands of these sequences, you can build a rich catalog of S&P 500 market behavior. We won’t just compare the closing prices, we’ll also compare the day’s open versus the day’s close, the previous day’s high to the current high, the previous day’s low to the current low, the previous day’s volume to the current one, etc (this will become clearer as we work through the code).

Binning Values Into 3 Buckets

An important twist in Pranab Ghosh’s approach is to simplify each event within a sequence into a single feature. He splits the value into 3 groups - Low, Medium, High. The simplification of the event into three bins will facilitate the subsequent matching between other sequence events and, hopefully, capture the story so it can be used to predict future behavior.

To better generalize stock market data, for example, we can collect the percent difference between one day’s price and the previous day’s. Once we have collected all of them, we can bin them into three groups of equal frequency using the InfoTheo package. The small group is assigned ‘L’, the medium group, ‘M’ and the large, ‘H’.

Here are 6 percentage differences between one close and the previous one:

-0.00061281019 -0.00285190466 0.00266118835 0.00232492640 0.00530862595 0.00512213970

Using equal-frequency binning we can translate the above numbers into:

"M" "L" "M" "M" "H" "H"

Combining Event Features into a Single Event Feature

You then paste all the features for a particular event into a single feature. If we are looking at the percentage difference between closes, opens, highs, lows, we’ll end up with a feature containing four letters. Each representing the bin for that particular feature:

"MLHL"

Then we string all the feature events for the sequence and end up with something like this along with the observed outcome:

"HMLL" "MHHL" "LLLH" "HMMM" "HHHL" "HHHH" --> Volume Up

Creating Two Markov Chains, One for Days with Volume Jumps, and another for Volume Drops

Another twist in Pranab Ghosh’s approach is to separate sequences of events into separate data sets based on the outcome. As we are predicting volume changes, one data set will contain sequences of volume increases and another, decreases. This enables each data set to offer a probability of a directional volume move and the largest probability, wins.

%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
import io, base64, os, json, re 
import pandas as pd
import numpy as np
import datetime
from random import randint

# load market data from Yahoo Finance (https://finance.yahoo.com/quote/%5EGSPC/history?p=%5EGSPC)

gspc_df = pd.read_csv('^GSPC.csv')
gspc_df['Date'] = pd.to_datetime(gspc_df['Date'])

cut_off_date = '2010-01-01' 
gspc_df = gspc_df[gspc_df['Date'] >= cut_off_date]


gspc_df.head()

	Date	Open	High	Low	Close	Adj Close	Volume
15097	2010-01-04	1116.560059	1133.869995	1116.560059	1132.989990	1132.989990	3991400000
15098	2010-01-05	1132.660034	1136.630005	1129.660034	1136.520020	1136.520020	2491020000
15099	2010-01-06	1135.709961	1139.189941	1133.949951	1137.140015	1137.140015	4972660000
15100	2010-01-07	1136.270020	1142.459961	1131.319946	1141.689941	1141.689941	5270680000
15101	2010-01-08	1140.520020	1145.390015	1136.219971	1144.979980	1144.979980	4389590000

# take random sets of sequential rows 
new_set = []
for row_set in range(0, 100000):
    if row_set%2000==0: print(row_set)
    row_quant = randint(10, 30)
    row_start = randint(0, len(gspc_df)-row_quant)
    market_subset = gspc_df.iloc[row_start:row_start+row_quant]

    Close_Date = max(market_subset['Date'])
    if row_set%2000==0: print(Close_Date)
    
    # Close_Gap = (market_subset['Close'] - market_subset['Close'].shift(1)) / market_subset['Close'].shift(1)
    Close_Gap = market_subset['Close'].pct_change()
    High_Gap = market_subset['High'].pct_change()
    Low_Gap = market_subset['Low'].pct_change() 
    Volume_Gap = market_subset['Volume'].pct_change() 
    Daily_Change = (market_subset['Close'] - market_subset['Open']) / market_subset['Open']
    Outcome_Next_Day_Direction = (market_subset['Volume'].shift(-1) - market_subset['Volume'])
    
    new_set.append(pd.DataFrame({'Sequence_ID':[row_set]*len(market_subset),
                            'Close_Date':[Close_Date]*len(market_subset),
                           'Close_Gap':Close_Gap,
                           'High_Gap':High_Gap,
                           'Low_Gap':Low_Gap,
                           'Volume_Gap':Volume_Gap,
                           'Daily_Change':Daily_Change,
                           'Outcome_Next_Day_Direction':Outcome_Next_Day_Direction}))

 

0
2014-09-25 00:00:00
2000
2017-05-01 00:00:00
4000
2014-10-31 00:00:00
6000
2013-08-01 00:00:00
8000
2013-02-19 00:00:00
10000
2013-05-13 00:00:00
12000
2018-12-06 00:00:00
14000
2017-06-15 00:00:00
16000
2018-12-31 00:00:00
18000
2012-12-07 00:00:00
20000
2018-02-21 00:00:00
22000
2012-03-02 00:00:00
24000
2010-02-22 00:00:00
26000
2013-04-25 00:00:00
28000
2017-03-03 00:00:00
30000
2014-05-28 00:00:00
32000
2014-05-16 00:00:00
34000
2016-01-21 00:00:00
36000
2017-12-11 00:00:00
38000
2014-12-22 00:00:00
40000
2018-02-13 00:00:00
42000
2010-09-02 00:00:00
44000
2018-12-28 00:00:00
46000
2015-01-30 00:00:00
48000
2014-10-28 00:00:00
50000
2014-03-14 00:00:00
52000
2013-09-09 00:00:00
54000
2011-10-04 00:00:00
56000
2018-12-24 00:00:00
58000
2013-11-27 00:00:00
60000
2015-03-10 00:00:00
62000
2016-12-20 00:00:00
64000
2016-08-23 00:00:00
66000
2014-11-03 00:00:00
68000
2014-03-19 00:00:00
70000
2011-08-04 00:00:00
72000
2010-03-08 00:00:00
74000
2017-05-10 00:00:00
76000
2010-04-29 00:00:00
78000
2015-09-08 00:00:00
80000
2018-05-03 00:00:00
82000
2016-10-03 00:00:00
84000
2018-02-12 00:00:00
86000
2017-11-22 00:00:00
88000
2017-04-07 00:00:00
90000
2018-08-30 00:00:00
92000
2017-10-10 00:00:00
94000
2015-03-27 00:00:00
96000
2015-03-04 00:00:00
98000
2016-02-18 00:00:00

len(market_subset)

26

new_set_df = pd.concat(new_set)
print(new_set_df.shape)
new_set_df = new_set_df.dropna(how='any') 
print(new_set_df.shape)
new_set_df.tail(20)

(1999567, 8)
(1799567, 8)

	Close_Date	Close_Gap	Daily_Change	High_Gap	Low_Gap	Outcome_Next_Day_Direction	Sequence_ID	Volume_Gap
16638	2016-03-17	-0.004666	-0.005053	-0.000352	0.008579	-2.936400e+08	99999	-0.114745
16639	2016-03-17	-0.000026	0.000543	-0.005813	-0.006746	-8.814000e+07	99999	-0.066187
16640	2016-03-17	0.014454	0.010943	0.014551	0.011708	-1.640600e+08	99999	-0.021275
16641	2016-03-17	-0.012454	-0.010868	-0.002219	-0.002598	4.266000e+08	99999	-0.040462
16642	2016-03-17	0.004440	0.006383	-0.005303	-0.014817	-1.990400e+08	99999	0.109647
16643	2016-03-17	0.011348	0.010265	0.010222	0.018197	2.303000e+08	99999	-0.046103
16644	2016-03-17	-0.001870	-0.003529	0.005702	0.010580	2.396700e+08	99999	0.055922
16645	2016-03-17	-0.008121	-0.007652	-0.002389	-0.007180	2.315700e+08	99999	0.055115
16646	2016-03-17	0.023869	0.021300	0.010254	0.002733	-1.531400e+08	99999	0.050471
16647	2016-03-17	0.004094	0.004983	0.004125	0.016370	4.150900e+08	99999	-0.031773
16648	2016-03-17	0.003499	0.003928	0.003614	0.004353	9.682300e+08	99999	0.088949
16649	2016-03-17	0.003306	0.002999	0.007744	0.004754	-1.081750e+09	99999	0.190533
16650	2016-03-17	0.000885	0.002831	-0.001498	0.001314	-3.265300e+08	99999	-0.178804
16651	2016-03-17	-0.011240	-0.008824	-0.004606	-0.006007	-6.035300e+08	99999	-0.065724
16652	2016-03-17	0.005052	0.003947	-0.002098	0.001219	3.386700e+08	99999	-0.130025
16653	2016-03-17	0.000156	-0.000703	0.006218	-0.005349	-2.981700e+08	99999	0.083868
16654	2016-03-17	0.016396	0.013776	0.008623	0.012929	-5.907700e+08	99999	-0.068125
16655	2016-03-17	-0.001261	0.000183	0.001088	0.008693	7.243000e+07	99999	-0.144846
16656	2016-03-17	-0.001837	0.000328	-0.004263	-0.003390	4.967400e+08	99999	0.020766
16657	2016-03-17	0.005600	0.006444	0.007976	0.002399	4.734600e+08	99999	0.139523

new_set_df.head()

	Close_Date	Close_Gap	Daily_Change	High_Gap	Low_Gap	Outcome_Next_Day_Direction	Sequence_ID	Volume_Gap
16263	2014-09-25	0.002950	0.002793	0.003113	0.004622	-337060000.0	0	0.023012
16264	2014-09-25	-0.001993	-0.002108	-0.000612	-0.001037	-67980000.0	0	-0.127726
16265	2014-09-25	0.004788	0.003103	0.004219	0.003517	218070000.0	0	-0.029533
16266	2014-09-25	0.001051	0.000716	0.001544	0.003439	-107600000.0	0	0.097619
16267	2014-09-25	0.000050	-0.000210	-0.001446	-0.001196	-61950000.0	0	-0.043883

# confirm sequence
# new_set_df[new_set_df['Close_Date'] == '1973-06-27'] {HLH, HLH, HHH, HHH, LLL, LML, LML, LLL, LHL, ...	

# create sequences
# simplify the data by binning values into three groups
 
# Close_Gap
new_set_df['Close_Gap_LMH'] = pd.qcut(new_set_df['Close_Gap'], 3, labels=["L", "M", "H"])

# High_Gap - not used in this example
new_set_df['High_Gap_LMH'] = pd.qcut(new_set_df['High_Gap'], 3, labels=["L", "M", "H"])

# Low_Gap - not used in this example
new_set_df['Low_Gap_LMH'] = pd.qcut(new_set_df['Low_Gap'], 3, labels=["L", "M", "H"])

# Volume_Gap
new_set_df['Volume_Gap_LMH'] = pd.qcut(new_set_df['Volume_Gap'], 3, labels=["L", "M", "H"])
 
# Daily_Change
new_set_df['Daily_Change_LMH'] = pd.qcut(new_set_df['Daily_Change'], 3, labels=["L", "M", "H"])

# new set
new_set_df = new_set_df[["Sequence_ID", 
                         "Close_Date", 
                         "Close_Gap_LMH", 
                         "Volume_Gap_LMH", 
                         "Daily_Change_LMH", 
                         "Outcome_Next_Day_Direction"]]

new_set_df['Event_Pattern'] = new_set_df['Close_Gap_LMH'].astype(str) + new_set_df['Volume_Gap_LMH'].astype(str) + new_set_df['Daily_Change_LMH'].astype(str)
 

new_set_df.tail(10)

	Sequence_ID	Close_Date	Close_Gap_LMH	Volume_Gap_LMH	Daily_Change_LMH	Outcome_Next_Day_Direction	Event_Pattern
16648	99999	2016-03-17	H	H	H	9.682300e+08	HHH
16649	99999	2016-03-17	H	H	H	-1.081750e+09	HHH
16650	99999	2016-03-17	M	L	M	-3.265300e+08	MLM
16651	99999	2016-03-17	L	L	L	-6.035300e+08	LLL
16652	99999	2016-03-17	H	L	H	3.386700e+08	HLH
16653	99999	2016-03-17	M	H	M	-2.981700e+08	MHM
16654	99999	2016-03-17	H	L	H	-5.907700e+08	HLH
16655	99999	2016-03-17	M	L	M	7.243000e+07	MLM
16656	99999	2016-03-17	L	M	M	4.967400e+08	LMM
16657	99999	2016-03-17	H	H	H	4.734600e+08	HHH

new_set_df['Outcome_Next_Day_Direction'].describe()

count    1.799567e+06
mean    -6.390038e+05
std      6.867248e+08
min     -4.995080e+09
25%     -2.985100e+08
50%     -7.380000e+06
75%      3.103400e+08
max      4.299510e+09
Name: Outcome_Next_Day_Direction, dtype: float64

# reduce the set
compressed_set = new_set_df.groupby(['Sequence_ID', 
                                     'Close_Date'])['Event_Pattern'].apply(lambda x: "{%s}" % ', '.join(x)).reset_index()

print(compressed_set.shape)
compressed_set.head() 
    
    

(100000, 3)

	Sequence_ID	Close_Date	Event_Pattern
0	0	2014-09-25	{MMM, LLL, HMH, MHM, MMM, LMM, HMM, MHM, MMM, ...
1	1	2016-08-15	{HLM, HHH, MLM, HMM, MLM, MMM, MMM, HHH, LHL, ...
2	2	2014-08-21	{LLL, HHH, MMM, MHM, LLL, MHM, LHL, MHM, LHL, ...
3	3	2018-02-20	{HLH, LML, LHL, MHL, MLM, LHL, LHL, HHH, LLL, ...
4	4	2014-04-11	{HLH, HMH, LHL, HMH, LHL, LLL, HLH, LHL, LHL, ...

#compressed_outcomes = new_set_df[['Sequence_ID', 'Close_Date', 'Outcome_Next_Day_Direction']].groupby(['Sequence_ID', 'Close_Date']).agg()

compressed_outcomes = new_set_df.groupby(['Sequence_ID', 'Close_Date'])['Outcome_Next_Day_Direction'].mean()
compressed_outcomes = compressed_outcomes.to_frame().reset_index()
print(compressed_outcomes.shape)
compressed_outcomes.describe()

(100000, 3)

	Sequence_ID	Outcome_Next_Day_Direction
count	100000.000000	1.000000e+05
mean	49999.500000	-7.349918e+05
std	28867.657797	6.505046e+07
min	0.000000	-5.558712e+08
25%	24999.750000	-2.837385e+07
50%	49999.500000	-9.864706e+05
75%	74999.250000	2.641400e+07
max	99999.000000	6.212562e+08

 
compressed_set = pd.merge(compressed_set, compressed_outcomes, on= ['Sequence_ID', 'Close_Date'], how='inner')
print(compressed_set.shape)
compressed_set.head()
    

(100000, 4)

	Sequence_ID	Close_Date	Event_Pattern	Outcome_Next_Day_Direction
0	0	2014-09-25	{MMM, LLL, HMH, MHM, MMM, LMM, HMM, MHM, MMM, ...	2.642208e+07
1	1	2016-08-15	{HLM, HHH, MLM, HMM, MLM, MMM, MMM, HHH, LHL, ...	-6.992400e+06
2	2	2014-08-21	{LLL, HHH, MMM, MHM, LLL, MHM, LHL, MHM, LHL, ...	1.206957e+06
3	3	2018-02-20	{HLH, LML, LHL, MHL, MLM, LHL, LHL, HHH, LLL, ...	1.152375e+07
4	4	2014-04-11	{HLH, HMH, LHL, HMH, LHL, LLL, HLH, LHL, LHL, ...	4.647211e+07

# # reduce set 

# compressed_set = new_set_df.groupby(['Sequence_ID', 'Close_Date','Outcome_Next_Day_Direction'])['Event_Pattern'].apply(lambda x: "{%s}" % ', '.join(x)).reset_index()

compressed_set['Event_Pattern'] = [''.join(e.split()).replace('{','')
                                   .replace('}','') for e in compressed_set['Event_Pattern'].values]
compressed_set.head()

	Sequence_ID	Close_Date	Event_Pattern	Outcome_Next_Day_Direction
0	0	2014-09-25	MMM,LLL,HMH,MHM,MMM,LMM,HMM,MHM,MMM,MHL,HLH,LM...	2.642208e+07
1	1	2016-08-15	HLM,HHH,MLM,HMM,MLM,MMM,MMM,HHH,LHL,HLH,LML,MH...	-6.992400e+06
2	2	2014-08-21	LLL,HHH,MMM,MHM,LLL,MHM,LHL,MHM,LHL,LLL,HLH,LH...	1.206957e+06
3	3	2018-02-20	HLH,LML,LHL,MHL,MLM,LHL,LHL,HHH,LLL,LHL,HHH,HL...	1.152375e+07
4	4	2014-04-11	HLH,HMH,LHL,HMH,LHL,LLL,HLH,LHL,LHL,HLH,HHH,HM...	4.647211e+07

# use last x days of data for validation
compressed_set_validation = compressed_set[compressed_set['Close_Date'] >= datetime.datetime.now() 
                                           - datetime.timedelta(days=90)] # Sys.Date()-90 

compressed_set_validation.shape

(2110, 4)

compressed_set = compressed_set[compressed_set['Close_Date'] < datetime.datetime.now() 
                                           - datetime.timedelta(days=90)]  
compressed_set.shape

(97890, 4)

list(compressed_set)

['Sequence_ID', 'Close_Date', 'Event_Pattern', 'Outcome_Next_Day_Direction']

# drop date field
compressed_set = compressed_set[['Sequence_ID', 'Event_Pattern','Outcome_Next_Day_Direction']]
compressed_set_validation = compressed_set_validation[['Sequence_ID', 'Event_Pattern','Outcome_Next_Day_Direction']]

Keep big moves only and build outcome variable

compressed_set['Outcome_Next_Day_Direction'].describe()

count    9.789000e+04
mean    -6.352854e+05
std      6.498712e+07
min     -5.558712e+08
25%     -2.835400e+07
50%     -7.670000e+05
75%      2.663667e+07
max      6.212562e+08
Name: Outcome_Next_Day_Direction, dtype: float64

print(len(compressed_set['Outcome_Next_Day_Direction']))
len(compressed_set[abs(compressed_set['Outcome_Next_Day_Direction']) > 10000000])

97890

77769

# keep only keep big/interesting moves 
print('all moves:', len(compressed_set))
compressed_set = compressed_set[abs(compressed_set['Outcome_Next_Day_Direction']) > 10000000]
compressed_set['Outcome_Next_Day_Direction'] = np.where((compressed_set['Outcome_Next_Day_Direction'] > 0), 1, 0)
compressed_set_validation['Outcome_Next_Day_Direction'] = np.where((compressed_set_validation['Outcome_Next_Day_Direction'] > 0), 1, 0)
print('big moves only:', len(compressed_set))            

all moves: 97890
big moves only: 77769

compressed_set.head()

	Sequence_ID	Event_Pattern	Outcome_Next_Day_Direction
0	0	MMM,LLL,HMH,MHM,MMM,LMM,HMM,MHM,MMM,MHL,HLH,LM...	1
3	3	HLH,LML,LHL,MHL,MLM,LHL,LHL,HHH,LLL,LHL,HHH,HL...	1
4	4	HLH,HMH,LHL,HMH,LHL,LLL,HLH,LHL,LHL,HLH,HHH,HM...	1
5	5	MMM,MHM,MMM,LML,HHH,MHM,MHM,HHH,HLH,LLL,MHH,MM...	1
7	7	HLH,MLM,LHL,HHH,LLL,MMM,HLH,HMH,HMH,MHM,HMH,MM...	1

# create two data sets - won/not won
compressed_set_pos = compressed_set[compressed_set['Outcome_Next_Day_Direction']==1][['Sequence_ID', 'Event_Pattern']]
print(compressed_set_pos.shape)
compressed_set_neg = compressed_set[compressed_set['Outcome_Next_Day_Direction']==0][['Sequence_ID', 'Event_Pattern']]
print(compressed_set_neg.shape)

(38077, 2)
(39692, 2)

flat_list = [item.split(',') for item in compressed_set['Event_Pattern'].values ]
unique_patterns = ','.join(str(r) for v in flat_list for r in v)
unique_patterns = list(set(unique_patterns.split(',')))
len(unique_patterns)

24

 
compressed_set['Outcome_Next_Day_Direction'].head()       
    

0    1
3    1
4    1
5    1
7    1
Name: Outcome_Next_Day_Direction, dtype: int64

Build the markov transition grid

# build the markov transition grid
def build_transition_grid(compressed_grid, unique_patterns):
    # build the markov transition grid

    patterns = []
    counts = []
    for from_event in unique_patterns:

        # how many times 
        for to_event in unique_patterns:
            pattern = from_event + ',' + to_event # MMM,MlM

            ids_matches = compressed_grid[compressed_grid['Event_Pattern'].str.contains(pattern)]
            found = 0
            if len(ids_matches) > 0:
                Event_Pattern = '---'.join(ids_matches['Event_Pattern'].values)
                found = Event_Pattern.count(pattern)
            patterns.append(pattern)
            counts.append(found)

    # create to/from grid
    grid_Df = pd.DataFrame({'pairs':patterns, 'counts': counts})

    grid_Df['x'], grid_Df['y'] = grid_Df['pairs'].str.split(',', 1).str
    grid_Df.head()

    grid_Df = grid_Df.pivot(index='x', columns='y', values='counts')

    grid_Df.columns= [col for col in grid_Df.columns]
    del grid_Df.index.name

    # replace all NaN with zeros
    grid_Df.fillna(0, inplace=True)
    grid_Df.head()

    #grid_Df.rowSums(transition_dataframe) 
    grid_Df = grid_Df / grid_Df.sum(1)
    return (grid_Df)
 

grid_pos = build_transition_grid(compressed_set_pos, unique_patterns) 
grid_neg = build_transition_grid(compressed_set_neg, unique_patterns) 

grid_neg.head()

	HHH	HHM	HLH	HLM	HMH	HML	HMM	LHH	LHL	LHM	...	LMM	MHH	MHL	MHM	MLH	MLL	MLM	MMH	MML	MMM
HHH	0.086754	0.001444	0.168020	0.011798	0.086131	0.0	0.007070	0.0	0.072858	0.002752	...	0.019035	0.005200	0.000000	0.039029	0.014794	0.002858	0.130618	0.002402	0.004135	0.092957
HHM	0.000000	0.000000	0.072331	0.000000	0.000000	0.0	0.000000	0.0	0.090356	0.000000	...	0.000000	0.000000	0.000000	0.000000	0.000000	0.082397	0.126404	0.000000	0.000000	0.000000
HLH	0.085635	0.006050	0.085052	0.000000	0.100106	0.0	0.007890	0.0	0.287597	0.005130	...	0.003640	0.005169	0.008343	0.064881	0.005726	0.000000	0.048971	0.000000	0.007216	0.057807
HLM	0.202015	0.000000	0.091971	0.000000	0.162668	0.0	0.000000	0.0	0.017914	0.000000	...	0.000000	0.000000	0.064139	0.000000	0.000000	0.000000	0.012636	0.137076	0.000000	0.198976
HMH	0.066143	0.021169	0.094028	0.006229	0.125219	0.0	0.012549	0.0	0.123513	0.014773	...	0.018260	0.006320	0.004599	0.068549	0.021900	0.005940	0.098567	0.004660	0.004554	0.093313

5 rows × 24 columns

grid_pos.head()

	HHH	HHM	HLH	HLM	HMH	HML	HMM	LHH	LHL	LHM	...	LMM	MHH	MHL	MHM	MLH	MLL	MLM	MMH	MML	MMM
HHH	0.086527	0.008394	0.136265	0.004255	0.092240	0.0	0.003328	0.0	0.075782	0.005944	...	0.010580	0.003924	0.000000	0.079954	0.013411	0.007384	0.156067	0.014107	0.005282	0.101313
HHM	0.000000	0.000000	0.061327	0.000000	0.000000	0.0	0.000000	0.0	0.177931	0.000000	...	0.000000	0.000000	0.000000	0.000000	0.000000	0.042970	0.114935	0.000000	0.000000	0.000000
HLH	0.090802	0.011281	0.058022	0.000000	0.060851	0.0	0.018867	0.0	0.303110	0.002207	...	0.003319	0.012605	0.019570	0.068420	0.003008	0.000000	0.041673	0.000000	0.010185	0.074649
HLM	0.142011	0.000000	0.090085	0.000000	0.083290	0.0	0.000000	0.0	0.088343	0.000000	...	0.000000	0.000000	0.052100	0.000000	0.000000	0.000000	0.081722	0.054016	0.000000	0.182610
HMH	0.096396	0.022888	0.110806	0.001934	0.098577	0.0	0.025136	0.0	0.133843	0.012312	...	0.007238	0.002793	0.014361	0.064088	0.005553	0.002545	0.070235	0.011386	0.014229	0.111831

5 rows × 24 columns

# compressed_set_validation[compressed_set_validation['Sequence_ID' == seq_id]]

def safe_log(x,y):
   try:
      lg = np.log(x/y)
   except:
      lg = 0
   return lg

# predict on out of sample data
actual = []
predicted = []
for seq_id in compressed_set_validation['Sequence_ID'].values:
    patterns = compressed_set_validation[compressed_set_validation['Sequence_ID'] == seq_id]['Event_Pattern'].values[0].split(',')
    pos = []
    neg = []
    log_odds = []
    
    for id in range(0, len(patterns)-1):
        # get log odds
        # logOdds = log(tp(i,j) / tn(i,j)
        if (patterns[id] in list(grid_pos) and patterns[id+1] in list(grid_pos) and patterns[id] in list(grid_neg) and patterns[id+1] in list(grid_neg)):
                
            numerator = grid_pos[patterns[id]][patterns[id+1]]
            denominator = grid_neg[patterns[id]][patterns[id+1]]
            if (numerator == 0 and denominator == 0):
                log_value =0
            elif (denominator == 0):
                log_value = np.log(numerator / 0.00001)
            elif (numerator == 0):
                log_value = np.log(0.00001 / denominator)
            else:
                log_value = np.log(numerator/denominator)
        else:
            log_value = 0
        
        log_odds.append(log_value)
        
        pos.append(numerator)
        neg.append(denominator)
      
    print('outcome:', compressed_set_validation[compressed_set_validation['Sequence_ID']==seq_id]['Outcome_Next_Day_Direction'].values[0])
    print(sum(pos)/sum(neg))
    print(sum(log_odds))

    actual.append(compressed_set_validation[compressed_set_validation['Sequence_ID']==seq_id]['Outcome_Next_Day_Direction'].values[0])
    predicted.append(sum(log_odds))

from sklearn.metrics import confusion_matrix

confusion_matrix(actual, [1 if p > 0 else 0 for p in predicted])

outcome: 0
1.3375874154820773
1.2984093918947566
outcome: 0
1.1591677885042169
1.939046228727629
outcome: 0
1.0459010317044735
0.3797781937354797
outcome: 1
1.4767852905041183
2.6925532642785357
outcome: 1
1.268974436015745
3.9912707097803017
outcome: 0
1.449360690223031
1.9167093840717446
outcome: 0
1.457395769673124
2.755539980609435
outcome: 0
1.1844691398659355
5.247796159923566
outcome: 1
1.1311366732941155
4.403402001078635
outcome: 1
1.0967394212497457
4.246703526787578
outcome: 0
1.1865491518662368
1.3627353450173827
outcome: 1
0.8790190771179229
4.661125765140837
outcome: 1
1.083783634712261
7.717478421668398
outcome: 1
1.0384099412204035
7.452443677674064
outcome: 0
1.246289483584276
3.880375062244843
outcome: 1
0.9118464038774756
5.5708955338746575
outcome: 0
0.988253380275436
6.939346241004681
outcome: 1
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3.1421430772557595
outcome: 0
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2.9523935230392633
outcome: 0
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1.6493922797742269
outcome: 1
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6.21108046897864
outcome: 0
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outcome: 1
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3.653876693318198
outcome: 0
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2.3837858544694983
outcome: 0
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3.116178568186786
outcome: 0
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0.08690612701610154
outcome: 0
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0.9195202515333296
outcome: 0
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4.1301753568958475
outcome: 0
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1.2727462103170448
outcome: 1
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1.0041101301435924
outcome: 1
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3.9418819886325305
outcome: 1
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outcome: 1
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outcome: 0
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outcome: 1
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outcome: 1
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outcome: 0
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outcome: 1
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array([[  37, 1243],
       [  11,  819]])

from sklearn.metrics import accuracy_score
score = accuracy_score(actual, [1 if p > 0 else 0 for p in predicted])
print('Accuracy:', round(score * 100,2), '%')

Accuracy: 40.57 %

import seaborn as sns
cm = confusion_matrix(actual, [1 if p > 0 else 0 for p in predicted])
fig, ax = plt.subplots(figsize=(5, 5))
sns.heatmap(cm, annot=True, ax = ax, fmt='g')

ax.set_title('Confusion Matrix') 
ax.set_xlabel('Predicted')
ax.set_ylabel('Actual')

ax.xaxis.set_ticklabels(['up day','down day'])
ax.yaxis.set_ticklabels(['up day','down day'])
ax.set_yticklabels(ax.get_yticklabels(), rotation = 0, fontsize = 8)
ax.set_xticklabels(ax.get_xticklabels(), rotation = 90, fontsize = 8)  
plt.show()