advanced-algorithmic-trading

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6.3.2 Model Specification in PyMC3
Now that the returns have been calculated attention will turn towards specifying the Bayesian
model via the priors described above. As in previous chapters the model is instantiated via the
pm.Model() syntax in a with context. Each prior is then defined as above:
def configure_sample_stoch_vol_model(log_returns, samples):
"""
Configure the stochastic volatility model using PyMC3
in a ’with’ context. Then sample from the model using
the No-U-Turn-Sampler (NUTS).
Plot the logarithmic volatility process and then the
absolute returns overlaid with the estimated vol.
"""
print("Configuring stochastic volatility with PyMC3...")
model = pm.Model()
with model:
sigma = pm.Exponential(’sigma’, 50.0, testval=0.1)
nu = pm.Exponential(’nu’, 0.1)
s = GaussianRandomWalk(’s’, sigma**-2, shape=len(log_returns))
logrets = pm.StudentT(
’logrets’, nu,
lam=pm.math.exp(-2.0*s),
observed=log_returns
)
..
..
It remains to sample the model with the No-U-Turn Sampler MCMC procedure.
6.3.3 Fitting the Model with NUTS
Now that the model has been specified it is possible to run the NUTS MCMC sampler and
generate a traceplot in a similar manner to that carried out in the previous chapter on Bayesian
Linear Regression. Thankfully PyMC3 abstracts much of the implementation details of NUTS
away from us, allowing us to concentrate on the important procedure of model specification.
For this example 2000 samples are used in the NUTS sampler. Note that this will take some
time to calculate. It took 15-20 minutes on my desktop PC to produce the plots below. The
API for sampling is very straightforward. Under a with context the model simply utilises the
pm.sample method to produce a trace object that can later be used for visualisation of marginal
parameter distributions and the sample trace itself:
..
..
print("Fitting the stochastic volatility model...")
with model:
trace = pm.sample(samples)