GSoC 2016 #5

Dynamic Factor Model

There is one more item in my proposal, which I haven't yet mention in my reports, although I've been working on it before refactoring phase and TVP model implementation. This is a Markov switching dynamic factor model, we will use its following specification:

y, as usual, is an observation process, and (1) is an observation equation. f is a factor, changing according to (2) - factor transition equation, which is a VAR model with Markov switching intercept. Observation error is a VAR model, too, as (3) states.

Statsmodels already has a non-switching DFM realization in statespace.dynamic_factor.py file, which has almost the same specification, but without Markov switching intercept term in factor transition equation, so the first challenge was to extend DynamicFactor class and add analogous, but non-switching intercept. This parameter is required, because it is used for switching intercept initialization in Maximum Likelihood Estimation. regime_switching/switching_dynamic_factor.py and regime_switching/tests/test_switching_dynamic_factor.py files contain my experiments with MS-DFM, which were unsuccessful due to reasons, discussed in the next section.

Irresistible obstacles

Non-switching DynamicFactor class is a big piece of code itself, and since a lot of its functionality is shared with switching model, the only right solution is to extend it by SwitchingDynamicFactor class. The problem is that this class wasn't supposed to be extended, so it was quite tricky until I realised that it's a bad idea. For example, I have to substitute DynamicFactor's KalmanSmoother instance by an ugly descendant of KimSmoother with some interface changes to achieve compatibility with non-switching model. After a series of similar sophisticated manipulations I came up with a thought that it's impossible to construct a SwitchingDynamicFactor class without changes in the parent class. However, in my experience there are not so many changes needed.

Another problem is about testing data. I use this Gauss code sample from Kim and Nelson book. This is the only code I know to test MS-DFM against. But the disappointment is that this testing model is incompatible with presented formerly - observation equation contains lagged factor terms, while ours uses only the current factor. I also tried to use some tricks, the main was to group lagged factors into one vector factor. After several errors and considerations, I figured out that this is a bad idea, because a transition noise covariance matrix becomes singular. The only solution I see now is to extend DFM and MS-DFM model, so that they could handle lagged factors in observation equation, but this is a time-consuming challenge.

What's next?

The thing I'm working on right now is constructing a generic forecasting to Kim filter, which is the last important feature to be added. I spent a couple of days just thinking how to implement this, but now I'm finally writing the code. Forecasting should be a very visual thing, so I would add it to the existing notebooks, which is also a kind of testing.

Literature

[1] - "State-space Models With Regime Switching" by Chang-Jin Kim and Charles R. Nelson.