advanced-algorithmic-trading

195
Utilise the Kalman Filter from the PyKalman package
to calculate the slope and intercept of the regressed
ETF prices.
"""
delta = 1e-5
trans_cov = delta / (1 - delta) * np.eye(2)
obs_mat = np.vstack(
[prices[etfs[0]], np.ones(prices[etfs[0]].shape)]
).T[:, np.newaxis]
kf = KalmanFilter(
n_dim_obs=1,
n_dim_state=2,
initial_state_mean=np.zeros(2),
initial_state_covariance=np.ones((2, 2)),
transition_matrices=np.eye(2),
observation_matrices=obs_mat,
observation_covariance=1.0,
transition_covariance=trans_cov
)
state_means, state_covs = kf.filter(prices[etfs[1]].values)
return state_means, state_covs
Finally we plot these values as returned from the previous function. To achieve this we simply
create a Pandas DataFrame of the slopes and intercepts at time values t using the index from
the prices DataFrame and plot each column as a subplot:
def draw_slope_intercept_changes(prices, state_means):
"""
Plot the slope and intercept changes from the
Kalman Filter calculated values.
"""
pd.DataFrame(
dict(
slope=state_means[:, 0],
intercept=state_means[:, 1]
), index=prices.index
).plot(subplots=True)
plt.show()
The output is given in Figure 13.2.
Clearly the time-varying slope changes dramatically over the 2011 to 2016 period, dropping
from around 1.38 in 2011 to around 0.9 in 2016. It is not difficult to see that utilising a fixed
hedge ratio in a pairs trading strategy would be far too rigid.
In addition the estimate of the slope is relatively noisy. This can be controlled by the delta
variable given in the code above but has the effect of also reducing the responsiveness of the filter