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Pair trading using KF #1

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116 changes: 105 additions & 11 deletions kalman_filter.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3,11 +3,13 @@
import matplotlib.pyplot as plt
import numpy as np
#from pykalman import KalmanFilter
from statsmodels.tsa.stattools import adfuller
from filterpy.kalman import KalmanFilter

STOCKS = ['BAJFINANCE', 'KOTAKBANK', 'MINDTREE', 'NIFTY_50', 'NIFTY_BANK', 'RELIANCE', 'ULTRACEMCO']
RELATIVE_PATH = "/Users/rushil.goradia/Documents/brokerage_docs/kf/samplestockindextimeseries/"
NUM_STATES = 3
STOCKS = ['BAJFINANCE', 'RBLBANK']
#STOCKS = ['ONGC', 'MGL']
RELATIVE_PATH = "/Users/rushil.goradia/Documents/brokerage_docs/kf/pair_trading/"
NUM_STATES = 1

def plot_closing_price(stock_name, stock_data):
plt.figure()
Expand All @@ -34,11 +36,38 @@ def plot_closing_price(stock_name, stock_data):
plt.xlabel("Days")
#print(stock_data['residual'])

def plot_pair_trade(all_stocks_data):
plt.figure()
ax1 = plt.subplot(4,1,1)
#print(all_stocks_data[STOCKS[1]]['log_close'][NUM_STATES:])
plt.plot(all_stocks_data[STOCKS[1]]['log_close'][NUM_STATES:])
plt.plot(all_stocks_data[STOCKS[0]]['log_close'][NUM_STATES:])
predicted_y = all_stocks_data['residual'] + all_stocks_data[STOCKS[0]]['log_close'][NUM_STATES:]
plt.plot(predicted_y)
plt.legend(["actual_x","actual_y", "prediction_y"])
plt.title("Pair trading")

ax1 = plt.subplot(4,1,2, sharex=ax1)
plt.plot(all_stocks_data['residual'])
print(adfuller(all_stocks_data['residual'][20:]))
plt.title("Error in kf prediction")
plt.xlabel("Days")
plt.ylabel("Log Price error (Rs)")
#plt.ylim([-500,500])

plt.subplot(4,1,3, sharex=ax1)
plt.plot(all_stocks_data['predict'][:,0])
plt.ylabel("Slope (beta)")

plt.subplot(4,1,4, sharex=ax1)
plt.plot(all_stocks_data['predict'][:,1])
plt.ylabel("intercept (alpha)")



def get_stock_data(stock_name):
stock_data = {}
stock_data['log_close'] = []
full_path = RELATIVE_PATH + stock_name + ".csv"
with open(full_path) as csvfile:
csv_rows = csv.DictReader(csvfile)
Expand All @@ -54,6 +83,7 @@ def get_stock_data(stock_name):
value = row[key]
if key == 'Close':
value = float(value)
stock_data['log_close'] += [np.log(value)]
stock_data[key] += [value]
# if ind == 0:
# print(stock_data)
Expand All @@ -70,9 +100,9 @@ def kf_update(X, P, Y, H, R):
IS = R + np.dot(H, np.dot(P, H.T))
K = np.dot(P, np.dot(H.T, np.linalg.inv(IS)))
X = X + np.dot(K, (Y - IM))
P = P - np.dot(K, np.dot(IS, K.T))
LH = gauss_pdf(Y, IM, IS)
return (X, P, K, IM, IS, LH)
P = P - np.dot(K, np.dot(H, P))
#LH = gauss_pdf(Y, IM, IS)
return (X, P, K, IM, IS)

def gauss_pdf(X, M, S):
if np.shape(M)[1] == 1:
Expand All @@ -93,6 +123,69 @@ def gauss_pdf(X, M, S):
P = exp(-E)
return (P[0],E[0])

def run_kalman_filter_pair(stock1, stock2):
print(len(stock1['log_close']))
print(len(stock2['log_close']))
assert len(stock1['log_close']) == len(stock2['log_close'])
# x = [beta; alpha], slope and intercept
A = np.array([[1.0, 0.0],
[0.0, 1.0]], dtype=float)
# measurement update matrix
# y[k]: Actual closing price at time k from data
# y[k] = H*X[k]
H = np.array([[1.0, 1.0]], dtype=float)
# Covariance of measurement noise (actual stock price)
R = 0.1
# Initial state (first 3 days price)
X = np.array([stock1['log_close'][0]/stock2['log_close'][0], 0.0], dtype=float).T
# Constantly updated covariance of state
P = np.array([[0.1, 0.],
[0., 0.01]], dtype=float)
# Process noise covariance (how much do you trust the model)
Q = np.zeros((2,2), dtype=float)
Q[0,0] = 0.1
Q[1,1] = 0.1
B = np.zeros((2, 1))
U = 0

num_measurements = len(stock1['log_close'][NUM_STATES:])
prediction_result = np.zeros((num_measurements,2))
correction_result = np.zeros((num_measurements,2))
kalman_gain = np.zeros((num_measurements,))
residual = np.zeros((num_measurements,))
# prediction_cov = np.zeros((num_measurements,2))
measurements = np.array(stock1['log_close'][NUM_STATES:])
H_term = np.array(stock2['log_close'][NUM_STATES:])
for ind, (meas, h) in enumerate(zip(measurements,H_term)):
#predict, gives us X[k|k-1]
(X, P) = kf_predict(X, P, A, Q, B, U)
#print(X[0])

prediction_result[ind,0] = X[0][0]
prediction_result[ind,1] = X[0][1]
#print(kf.K)
#print(prediction_result[ind])

#correct
Y = np.array([[meas]])
H[0,0] = h
(X, P, K, IM, IS) = kf_update(X, P, Y, H, R)
# X[k|k]
correction_result[ind,0] = X[0][0]
correction_result[ind,1] = X[0][1]

#debug
kalman_gain[ind] = np.linalg.norm(K)
#print(IM[0][0])
residual[ind] = IM[0][0] - meas
#print(prediction_result)

return {
'predict':prediction_result,
'correct': correction_result,
'kalman_gain':kalman_gain,
'residual': residual,
}


def run_kalman_filter(stock_name, stock_data):
Expand Down Expand Up @@ -142,7 +235,7 @@ def run_kalman_filter(stock_name, stock_data):

#correct
Y = np.array([[meas]])
(X, P, K, IM, IS, LH) = kf_update(X, P, Y, H, R)
(X, P, K, IM, IS) = kf_update(X, P, Y, H, R)
# X[k|k]
correction_result[ind] = X[0][0]

Expand Down Expand Up @@ -172,14 +265,15 @@ def run_kalman_filter(stock_name, stock_data):

if args.run_filter:
for stock_name in STOCKS:
kf_results = run_kalman_filter(stock_name, all_stocks_data[stock_name])
kf_results = run_kalman_filter_pair(all_stocks_data[STOCKS[0]],all_stocks_data[STOCKS[1]])

all_stocks_data[stock_name].update(kf_results)
all_stocks_data.update(kf_results)


if args.plot_all_stocks:
for stock_name in STOCKS:
plot_closing_price(stock_name, all_stocks_data[stock_name])
#for stock_name in STOCKS:
#plot_closing_price(stock_name, all_stocks_data[stock_name])
plot_pair_trade(all_stocks_data)
plt.show()
#print(all_stocks_data[stock_name]['Close'])

Expand Down
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