A naive attempt using Kinetic Component Analysis

A naive implementation of trading rules on Kinetic Component Analysis. Anyone care to improve trading rules (entry/exit)?

71
Total Returns
--
Alpha
--
Beta
--
Sharpe
--
Sortino
--
Max Drawdown
--
Benchmark Returns
--
Volatility
--
 Returns 1 Month 3 Month 6 Month 12 Month
 Alpha 1 Month 3 Month 6 Month 12 Month
 Beta 1 Month 3 Month 6 Month 12 Month
 Sharpe 1 Month 3 Month 6 Month 12 Month
 Sortino 1 Month 3 Month 6 Month 12 Month
 Volatility 1 Month 3 Month 6 Month 12 Month
 Max Drawdown 1 Month 3 Month 6 Month 12 Month
from quantopian.pipeline import Pipeline
from quantopian.pipeline.data.builtin import USEquityPricing
from quantopian.algorithm import attach_pipeline, pipeline_output
from quantopian.pipeline.filters.morningstar import Q1500US
from quantopian.pipeline.classifiers.morningstar import Sector
from quantopian.pipeline.factors.morningstar import MarketCap

import cvxpy as cvx
import numpy as np
import pandas as pd
from pykalman import KalmanFilter

def fitKCA(t,z,q,fwd=0):
'''
Inputs:
t: Iterable with time indices
z: Iterable with measurements
q: Scalar that multiplies the seed states covariance
fwd: number of steps to forecast (optional, default=0) '''
#1) Set up matrices A,H and a seed for Q
h=1. / t.shape[0]
A=np.array([[1,h,.5*h**2, 1./6.*h**3],
[0,1,h,h**2],
[0,0,1,h],
[0,0,0,1]])

Q=q*np.eye(A.shape[0])
#2) Apply the filter
kf=KalmanFilter(transition_matrices=A,transition_covariance=Q)
#3) EM estimates
kf=kf.em(z)
#4) Smooth
x_mean,x_covar=kf.smooth(z)
#5) Forecast
for fwd_ in range(fwd):
x_mean_,x_covar_=kf.filter_update(filtered_state_mean=x_mean[-1],
filtered_state_covariance=x_covar[-1])
x_mean=np.append(x_mean,x_mean_.reshape(1,-1),axis=0)
x_covar_=np.expand_dims(x_covar_,axis=0)
x_covar=np.append(x_covar,x_covar_,axis=0)
#6) Std series
x_std=(x_covar[:,0,0]**.5).reshape(-1,1)
for i in range(1,x_covar.shape[1]):
x_std_=x_covar[:,i,i]**.5
x_std=np.append(x_std,x_std_.reshape(-1,1),axis=1)
return x_mean,x_std,x_covar

def initialize(context):

context.weights = None
context.leverage = 1.0
context.days = 60
context.output = None
context.sign = 0
context.cumret = 0
context.x_mean = 0
context.SPY = sid(8554)
date_rules.every_day(),
time_rules.market_open(minutes=90))

schedule_function(record_vars,
date_rules.every_day(),
time_rules.market_close(minutes=1))

hist = data.history([context.SPY], 'price', 250, '1d').resample('W').last()
dmret = np.log1p(hist.pct_change().dropna().values[:, 0])
dcumret = np.cumsum(dmret, axis=0)
t = np.asarray(range(0, dcumret.shape[0]))
d_mean, d_std, d_cov = fitKCA(t, dcumret, 0.01, 0)

hist = data.history([context.SPY], 'price', 120, '1d').dropna(axis=1)
mmret = np.log1p(hist.pct_change().dropna().values[:, 0])
mcumret = np.cumsum(mmret, axis=0)
context.x_mean = mcumret[-1]
t = np.asarray(range(0, mmret.shape[0]))
m_mean, m_std, m_cov = fitKCA(t, mcumret, 0.01, 0)

hist = data.history([context.SPY], 'price', 60, '1d')
smret = np.log1p(hist.pct_change().dropna().values[:, 0])
scumret = np.cumsum(smret, axis=0)
t = np.asarray(range(0, scumret.shape[0]))
s_mean, s_std, s_cov = fitKCA(t, scumret, 0.01, 0)

shortvel = s_mean[-1, 1]
midvel = m_mean[-1, 1]
longvel = d_mean[-1, 1]
shortacc = s_mean[-1, 2]
midacc = m_mean[-1, 2]
longacc = d_mean[-1, 2]
context.x_mean = m_mean[-1, 0]
sign = 0
std = pd.rolling_std(scumret, window=15)[15:]

if shortvel > 0 and shortacc > 0 and midvel > 0 and longvel > 0 and midacc > 0 and longacc > 0 and context.x_mean > 0:
sign = np.median(std) / std[-1]
elif shortvel < -0 and shortacc < 0 and midvel < 0 and longvel < 0 and midacc < 0 and longacc < 0 and context.x_mean < 0:
sign = -np.median(std) / std[-1]
elif shortvel > 0 and shortacc > 0 and context.SPY in context.portfolio.positions and context.portfolio.positions[context.SPY].amount > 0:
return
elif shortvel < 0 and shortacc < 0 and context.SPY in context.portfolio.positions and context.portfolio.positions[context.SPY].amount < 0:
return

sign = min(2.0, abs(sign)) * np.sign(sign)
context.sign = sign

for i, sid in enumerate(hist.columns):
order_target_percent(sid, sign)

def record_vars(context, data):
record(p=context.cumret, kalman=context.x_mean, sign=context.sign)

There was a runtime error.
6 responses

Hi Pravin -

What is Kinetic Component Analysis? And why might it work?

Also, since you are using daily data, could your code be written as a pipeline custom factor (so that it could be combined with other factors, in a single algo)?

Thanks,

Grant

Hi Grant,

Here is the paper. It could be written as a pipeline factor but first I want to get it working with a single asset. Mostly predicting futures.

Best regards,
Pravin

In the source code, he initialises the state transition matrix A to be equal to

A=np.array([[1,h,.5*h**2, 1./6.*h**3],
[0,1,h,h**2],
[0,0,1,h],
[0,0,0,1]])

Can someone give an explanation as to how is this derived?

In the paper, A is taken to be

A = np.array([[1,h,h**2],
[0,1,h],
[0,0,1]])

Thanks!

Oh dear, I misread 0.5 to be 5. This is straightforward.

I tried to put this in pipeline. pipeline loads for a long time and then errors out on schedule function with
TimeoutException: Too much time spent in handle_data and/or scheduled functions. 50 second limit exceeded.

23
Total Returns
--
Alpha
--
Beta
--
Sharpe
--
Sortino
--
Max Drawdown
--
Benchmark Returns
--
Volatility
--
 Returns 1 Month 3 Month 6 Month 12 Month
 Alpha 1 Month 3 Month 6 Month 12 Month
 Beta 1 Month 3 Month 6 Month 12 Month
 Sharpe 1 Month 3 Month 6 Month 12 Month
 Sortino 1 Month 3 Month 6 Month 12 Month
 Volatility 1 Month 3 Month 6 Month 12 Month
 Max Drawdown 1 Month 3 Month 6 Month 12 Month
from quantopian.pipeline import Pipeline
from quantopian.pipeline.data.builtin import USEquityPricing
from quantopian.algorithm import attach_pipeline, pipeline_output
from quantopian.pipeline.filters.morningstar import Q1500US, Q500US
from quantopian.pipeline.classifiers.morningstar import Sector
from quantopian.pipeline.factors.morningstar import MarketCap
from quantopian.pipeline.factors import CustomFactor, AverageDollarVolume

import numpy as np
import pandas as pd
from pykalman import KalmanFilter

class KCA(CustomFactor):
inputs = [USEquityPricing.close]
window_length = 100
outputs = ['velocity', 'acceleration']

def compute(self, today, assets, out, close):

def fitKCA(t, z, q, fwd=0):

h = 1. / t.shape[0]
A = np.array([[1, h, .5 * h ** 2, 1. / 6. * h ** 3],
[0, 1, h, h ** 2],
[0, 0, 1, h],
[0, 0, 0, 1]])

Q = q * np.eye(A.shape[0])

kf = KalmanFilter(transition_matrices=A, transition_covariance=Q)

kf = kf.em(z)

x_mean, x_covar = kf.smooth(z)

for fwd_ in range(fwd):
x_mean_, x_covar_ = kf.filter_update(filtered_state_mean=x_mean[-1],
filtered_state_covariance=x_covar[-1])
x_mean = np.append(x_mean, x_mean_.reshape(1, -1), axis=0)
x_covar_ = np.expand_dims(x_covar_, axis=0)
x_covar = np.append(x_covar, x_covar_, axis=0)

x_std = (x_covar[:, 0, 0] ** .5).reshape(-1, 1)
for i in range(1, x_covar.shape[1]):
x_std_ = x_covar[:, i, i] ** .5
x_std = np.append(x_std, x_std_.reshape(-1, 1), axis=1)
return x_mean, x_std, x_covar

close[np.isnan(close)] = 0
close = pd.DataFrame(close)
sret = np.log1p(np.array(close.pct_change().loc[1:, :].values))
cumret = np.cumsum(sret, axis=0)
cumret[np.isnan(cumret)] = 0
cols = cumret.shape[0]
t = np.asarray(range(0, cumret.shape[0]))
velocity = np.zeros(np.shape(t)[0])
acceleration = np.zeros(np.shape(t)[0])

for column_index in range(0, cols):

z = np.array(cumret[:, column_index])
avg, _, _ = fitKCA(t, z, 0.1, fwd=0)

velocity[column_index] = avg[-1, 1]
acceleration[column_index] = avg[-1, 2]

out.velocity[:] = velocity
out.accleration[:] = acceleration

def initialize(context):

context.weights = None
context.output = None
context.sign = 0
context.cumret = 0

attach_pipeline(make_pipeline(context), 'kinetic')

date_rules.every_day(),
time_rules.market_open(minutes=90))

schedule_function(record_vars,
date_rules.every_day(),
time_rules.market_close(minutes=1))

def make_pipeline(context):

pipe = Pipeline()
acc, vel = KCA()

pipe = Pipeline(
columns={
'acceleration': acc,
'velocity': vel,
},
screen = Q500US()
)
return pipe

context.output = pipeline_output('kinetic')
context.security_list = context.output.index

print context.output

def record_vars(context, data):
record(leverage=context.account.leverage)
There was a runtime error.

In general, you should call pipeline_output in before_trading_start, as opposed to a scheduled function or handle_data. The before_trading_start function has a 5 minute limit as opposed to scheduled functions and handle_data which have a 50 second limit. There has been some discussion on another thread about ways that might change at some point in the future, but for now the best solution is to call pipeline_output in before_trading_start, save the result in a context variable, and then reference the context variable in other parts of the algorithm.

Let me know if this helps.

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