def test_smoke(data, period, use_mle, deseasonalize, use_test, diff, model):
if period is None and isinstance(data, np.ndarray):
return
res = ThetaModel(
data,
period=period,
deseasonalize=deseasonalize,
use_test=use_test,
difference=diff,
method=model,
).fit(use_mle=use_mle)
assert "b0" in str(res.summary())
res.forecast(36)
res.forecast_components(47)
assert res.model.use_test is (use_test and res.model.deseasonalize)
assert res.model.difference is diff
ax.set_title("Housing Starts")
plt.tight_layout(pad=1.0)
# We could alternatively fit the log of the data. Here it makes more
# sense to force the deseasonalizing to use the additive method, if needed.
# We also fit the model parameters using MLE. This method fits the IMA
#
# $$ X_t = X_{t-1} + \gamma\epsilon_{t-1} + \epsilon_t $$
#
# where $\hat{\alpha}$ = $\min(\hat{\gamma}+1, 0.9998)$ using
# `statsmodels.tsa.SARIMAX`. The parameters are similar although the drift
# is closer to zero.
tm = ThetaModel(np.log(housing), method="additive")
res = tm.fit(use_mle=True)
print(res.summary())
# The forecast only depends on the forecast trend component,
# $$
# \hat{b}_0
# \left[h - 1 + \frac{1}{\hat{\alpha}}
# - \frac{(1-\hat{\alpha})^T}{\hat{\alpha}} \right],
# $$
#
# the forecast from the SES (which does not change with the horizon), and
# the seasonal. These three components are available using the
# `forecast_components`. This allows forecasts to be constructed using
# multiple choices of $\theta$ using the weight expression above.
res.forecast_components(12)