Dynamical Factor Models (DFM) Implementation (GSOC 2025)

[andreacate]

Dynamical Factor Models (DFM) Implementation

This PR provides a first draft implementation of Dynamical Factor Models as part of my application proposal for the PyMC GSoC 2025 project. A draft of my application report can be found at this link.

Overview

• Added DFM.py with initial functionality

Current Status

This implementation is a work in progress and I welcome any feedback

Next Steps

• Vectorize the construction of the transition and selection matrices (possibly by reordering state variables).
• Add support for measurement error.

[zaxtax]

Looks interesting! Just say when you think it's ready for review

[fonnesbeck]

cc @jessegrabowski

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See visual diffs & provide feedback on Jupyter Notebooks.

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[andreacate]

Thanks for the feedback!

I'm still exploring the best approach for implementing Dynamic Factor Models.
I've added a simple custom DFM model in a Jupyter notebook, which I plan to use as a prototype and testing tool while developing the main BayesianDynamicFactor class.

[jessegrabowski]

Some tests are failing due to missing constants. You might have lost some changes in the reset/rebasing process

[jessegrabowski]

Left some comments. I didn't look over the tests because they still seem like WIP, but seem to be on the right track!

[jessegrabowski]

I did a deeper pass on everything except the build_symbolic_graph method. I need to spend more time on that because it's gotten quite complex.

I'll finish ASAP.

[jessegrabowski]

final tiny comments. This looks great!

[jessegrabowski]

Can you make a little ascii diagram of how A B C fit together, or just write T = BlockDiag(A, B, C) before you introduce the names block A block B. Reading it I felt like "hey wait did I miss something"

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jessegrabowski commented on 2025-08-30T09:48:40Z
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Ipman was also a pretty good movie, but the sequels sucked.

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jessegrabowski commented on 2025-08-30T09:48:41Z
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Is this why you choose factor_order = 2 later? It would be nice to make a more obvious bridge between this section and the final statistical model. You don't actually model the data that this analysis is based on (you do the log differences ultimately), so it's a bit of a loose connection.

andreacate commented on 2025-08-30T09:55:06Z
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Yes sure, you are right. No I have not made decision about parameters, since I wanted just to replicate what was done in Stats. Cointegration was not present in Stats, I was just curious at the beginning. I can just delete the cells about cointegration

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jessegrabowski commented on 2025-08-30T09:48:42Z
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You can consider cutting this section IMO, and just say "Looking at the graphs, these time series are obviously non-stationary"

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jessegrabowski commented on 2025-08-30T09:48:42Z
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Here's a fancier ADF test function that I use if you want. It matches the output of STATA, and gives all 3 variants of the ADF test:

`py

def ADF_test_summary(df, maxlag=None, autolag='BIC', missing='error'):
    if missing == 'error':
        if df.isna().any().any():
            raise ValueError("df has missing data; handle it or pass missing='drop' to automatically drop it.")
            
    if isinstance(df, pd.Series):
        df = df.to_frame()
        
    for series in df.columns:
        data = df[series].copy()
        if missing == 'drop':
            data.dropna(inplace=True)
            
        print(series.center(110))
        print(('=' * 110))
        line = 'Specification' + ' ' * 15 + 'Coeff' + ' ' * 10 + 'Statistic' + ' ' * 5 + 'P-value' + ' ' * 6 + 'Lags' + ' ' * 6 + '1%'
        line += ' ' * 10 + '5%' + ' ' * 8 + '10%'
        print(line)
        print(('-' * 110))
        spec_fixed = False
        for i, (name, reg) in enumerate(zip(['Constant and Trend', 'Constant Only', 'No Constant'], ['ct', 'c', 'n'])):
            stat, p, crit, regresult = sm.tsa.adfuller(data, regression=reg, regresults=True, maxlag=maxlag,
                                                       autolag=autolag)
            n_lag = regresult.usedlag
            gamma = regresult.resols.params[0]
            names = make_var_names(series, n_lag, reg)
            reg_coefs = pd.Series(regresult.resols.params, index=names)
            reg_tstat = pd.Series(regresult.resols.tvalues, index=names)
            reg_pvals = pd.Series(regresult.resols.pvalues, index=names)

            line = f'{name:<21}{gamma:13.3f}{stat:15.3f}{p:13.3f}{n_lag:11}{crit["1%"]:10.3f}{crit["5%"]:12.3f}{crit["10%"]:11.3f}'
            print(line)

            for coef in reg_coefs.index:
                if coef in name:
                    line = f"\t{coef:<13}{reg_coefs[coef]:13.3f}{reg_tstat[coef]:15.3f}{reg_pvals[coef]:13.3f}"
                    print(line)
`

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jessegrabowski commented on 2025-08-30T09:48:43Z
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Plot the transformed data and comment before you run the stationarity test

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jessegrabowski commented on 2025-08-30T09:48:43Z
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They're not that simple, because you constrained the sign. You should comment on the prior choices here, in addition to in the comments.

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jessegrabowski commented on 2025-08-30T09:48:45Z
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Add some commentary on what is being shown here

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jessegrabowski commented on 2025-08-30T09:48:45Z
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Show this before sampling

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jessegrabowski commented on 2025-08-30T09:48:46Z
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Use constrained_layout so the labels and titles aren't crushed together. Also consider sharex='col' ? Currently it looks like all the estimates are the same.

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jessegrabowski commented on 2025-08-30T09:48:46Z
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The legend is wrong -- the gray are recessions, not HDI. Is the HDI plotted here, but it's just really tight? If so, comment on this.

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jessegrabowski commented on 2025-08-30T09:48:47Z
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Commentary? What is state 0 (consider renaming the title to be clear, like Estimated Latent Factor 1)? Add recessions?

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jessegrabowski commented on 2025-08-30T09:48:48Z
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typo: Statsmodels

[jessegrabowski]

The notebook also looks great!

Could you add some more headings, and motivate all the analysis that you're doing with some commentary? Make sure the piece connect together clearly. I'd move the Bayesian latent factor graph above the Coincident index.

I would also suggest you comment on the fact that the optimizer doesn't converge in the statsmodels model. It ends up being "close enough", but make some hay out of the fact that MCMC doesn't "converge", it explores all equiprobable solutions, which in this case is important because the model is only weakly identified.

[andreacate]

Yes sure, you are right. No I have not made decision about parameters, since I wanted just to replicate what was done in Stats. Cointegration was not present in Stats, I was just curious at the beginning. I can just delete the cells about cointegration

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jessegrabowski commented on 2025-09-05T15:49:38Z
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Line #4.    print("\nDesign matrix (Z):")

Put all of these prints inside a with np.printoptions(linewidth=1000, precision=3, suppress=True): block (you can tinker with those settings but it will make this cell prettier)

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jessegrabowski commented on 2025-09-05T15:49:39Z
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With the usual energy plot, we assess the behavior of the sampling procedure by examining the overlap between energy levels. Sampling is successful when the two distributions overlap.

[jessegrabowski]

This was amazing work, congratulations on a very successful GSoC @andreacate 🥳 🎉