Fitting a SSM with additional exogenous variables.

[Imon Palit]

Hi there,

Relative newbie to the world of SSM and have recently found this amazing package!

I need to fit the following model

 

where the innovations u_{i,t} and v_{i,t) are uncorrelated and HFT^S and nHFT^S are exogenous variables ( HFT^S_tilda and HFT^S_ntilda are residuals of these variables from an AR model).

Can the sm.tsa.DynamicFactor or sm.tsa.UnobservedComponents functions be used to fit such a model off the shelf or do I need to create my own set-up/class inputting the matrices etc?

Model comes from:

Jonathan Brogaard, Terrence Hendershott, Ryan Riordan, High-Frequency Trading and Price Discovery, The Review of Financial Studies, Volume 27, Issue 8, August 2014, Pages 2267–2306,

Thanks in advance!

 

[Chad Fulton]

Hello,

There's nothing off-the-shelf in Statsmodels that fits this setup, but you can create a custom state space model that will work with that model. Some examples of this are available at:

- A very simple example of this is: https://www.statsmodels.org/stable/statespace.html#custom-state-space-models

- A more detailed notebook that goes through setting up a custom state space model is: https://www.statsmodels.org/stable/examples/notebooks/generated/statespace_custom_models.html

Hope that helps,

Chad

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[Imon Palit]

The pointers on how to create custom set-ups look great.

Thanks for the tip!

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