This is essentially a Python port of MARSS, though it isn't aiming for exact feature/interface parity. There is a fair amount of model validation code in MARSS that is not yet present in this library, so you need to be a lot more careful about model specification if you're going to use this. This library will let you do a lot of things that aren't valid, and mostly that will result in your fit diverging pretty obviously, but not necessarily always. I hope to add better validation over time.
You can find some detail about which models are and are not admissible here.
This is a simple ARMA(1, 1) model, represented in the Hamilton form
y = arma_generate_sample(ar=[1, -0.4], ma=[1, 0.2], nsample=1000, scale=1)
kf = KalmanFilter(
y,
B = np.array([
['phi', 0],
[1.0, 0]
]),
Q = np.array([
[1.0, 0],
[0, 0]
]),
Z = np.array([[1.0, 'theta']]),
R = np.array([['measurement_noise']])
)
kf.fit()This should output something like:
Starting EM on: B, Z, R
[0] ll: -1867.349491
[10] ll: -1462.598377
[20] ll: -1438.460797
[30] ll: -1428.766103
[40] ll: -1423.972850
[50] ll: -1421.256981
[60] ll: -1419.564740
[70] ll: -1418.434631
[80] ll: -1417.639221
[90] ll: -1417.055898
[100] ll: -1416.613761
[110] ll: -1416.269444
[120] ll: -1415.995182
[130] ll: -1415.772502
[140] ll: -1415.588714
[150] ll: -1415.434856
[160] ll: -1415.304445
[170] ll: -1415.192692
[180] ll: -1415.095996
Fitted:
phi: 0.4616
theta: 0.2144
measurement_noise: 0.0427
Minimizing: B, Z, R
Starting likelihood: -1415.10 (-1415.10)
Minimized: -1413.78
Fitted:
phi: 0.4822
theta: 0.1567
measurement_noise: 0.0000
.fit() uses a combination of the EM algorithm and BFGS to automatically fit your model. It is just a convenience wraper for:
kf.em(tol=0.1)
kf.minimize()