Learning Bayesian Statistics

#124 State Space Models & Structural Time Series, with Jesse Grabowski

Jan 22, 2025

Jesse Grabowski, PhD candidate at Paris 1 Pantheon-Sorbonne and principal data scientist at PyMC Labs, dives into the intricate world of state space models in time series analysis. He discusses the powerful adaptability of Bayesian methods in econometrics, emphasizing how they enhance forecasting accuracy. Grabowski highlights the balance between model complexity and simplicity, the significance of understanding trends, and the practical applications of innovations and latent states. Plus, he unwraps the role of the Kalman filter in managing dynamic data.

01:35:43

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Episode guests

Jesse Grabowski

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Quick takeaways

State space models enhance the analysis of time series data by effectively capturing complex dynamics through trends, seasonality, and autoregressive components.

The Kahneman filter utilizes Bayesian inference to manage uncertainty in dynamic systems, refining predictions by continuously updating beliefs based on incoming data.

Composability in state-space models allows for tailored approaches that integrate various components, resulting in more robust forecasts adapted to data-specific characteristics.

Deep dives

Introduction to State-Space Models

State-space models serve as a powerful tool in the analysis of time series data, allowing for flexibility in modeling both observed and hidden states. These models decompose time series into various components including trends, seasonality, and autoregressive elements, making them capable of capturing complex dynamics. By employing a recursive form, state-space models enable one to update estimates over time as new data becomes available, which is essential for forecasting. This method contrasts with simpler models by incorporating the notion of recursion where future states depend on past states, thereby reflecting more realistic scenarios in data analysis.

Intro

3min

Embracing Bayesian Methods in Econometrics

15min

Understanding State Space Models in Time Series Analysis

16min

Understanding State Space Models

19min

Mastering Seasonality in Time Series Analysis

5min

Exploring State Space Models in Time Series Analysis

17min

State Space Models and the Kalman Filter

13min

Navigating Challenges and Connections

3min

The Power of Critical Thinking

3min

10.

Integrating New Features and Community Engagement in Bayesian Statistics

2min

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Takeaways:

Bayesian statistics offers a robust framework for econometric modeling.
State space models provide a comprehensive way to understand time series data.
Gaussian random walks serve as a foundational model in time series analysis.
Innovations represent external shocks that can significantly impact forecasts.
Understanding the assumptions behind models is key to effective forecasting.
Complex models are not always better; simplicity can be powerful.
Forecasting requires careful consideration of potential disruptions. Understanding observed and hidden states is crucial in modeling.
Latent abilities can be modeled as Gaussian random walks.
State space models can be highly flexible and diverse.
Composability allows for the integration of different model components.
Trends in time series should reflect real-world dynamics.
Seasonality can be captured through Fourier bases.
AR components help model residuals in time series data.
Exogenous regression components can enhance state space models.
Causal analysis in time series often involves interventions and counterfactuals.
Time-varying regression allows for dynamic relationships between variables.
Kalman filters were originally developed for tracking rockets in space.
The Kalman filter iteratively updates beliefs based on new data.
Missing data can be treated as hidden states in the Kalman filter framework.
The Kalman filter is a practical application of Bayes' theorem in a sequential context.
Understanding the dynamics of systems is crucial for effective modeling.
The state space module in PyMC simplifies complex time series modeling tasks.

Chapters:

00:00 Introduction to Jesse Krabowski and Time Series Analysis

04:33 Jesse's Journey into Bayesian Statistics

10:51 Exploring State Space Models

18:28 Understanding State Space Models and Their Components

40:39 Composability of State Space Models

48:36 Understanding Trends and Derivatives

52:35 The Importance of Seasonality in Time Series

56:41 Components of Time Series Analysis

01:00:46 Exogenous Regression in State Space Models

01:06:41 Impulse Response Functions and Causality

01:11:30 Why Kalman Filter Is So Powerful

01:24:28 Future Directions and Applications

Thank you to my Patrons for making this episode possible!

Yusuke Saito, Avi Bryant, Ero Carrera, Giuliano Cruz, Tim Gasser, James Wade, Tradd Salvo, William Benton, James Ahloy, Robin Taylor,, Chad Scherrer, Zwelithini Tunyiswa, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Ian Moran, Paul Oreto, Colin Caprani, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Hugo Botha, Vinh Nguyen, Marcin Elantkowski, Adam C. Smith, Will Kurt, Andrew Moskowitz, Hector Munoz, Marco Gorelli, Simon Kessell, Bradley Rode, Patrick Kelley, Rick Anderson, Casper de Bruin, Philippe Labonde, Michael Hankin, Cameron Smith, Tomáš Frýda, Ryan Wesslen, Andreas Netti, Riley King, Yoshiyuki Hamajima, Sven De Maeyer, Michael DeCrescenzo, Fergal M, Mason Yahr, Naoya Kanai, Steven Rowland, Aubrey Clayton, Jeannine Sue, Omri Har Shemesh, Scott Anthony Robson, Robert Yolken, Or Duek, Pavel Dusek, Paul Cox, Andreas Kröpelin, Raphaël R, Nicolas Rode, Gabriel Stechschulte, Arkady, Kurt TeKolste, Gergely Juhasz, Marcus Nölke, Maggi Mackintosh, Grant Pezzolesi, Avram Aelony, Joshua Meehl, Javier Sabio, Kristian Higgins, Alex Jones, Gregorio Aguilar, Matt Rosinski, Bart Trudeau, Luis Fonseca, Dante Gates, Matt Niccolls, Maksim Kuznecov, Michael Thomas, Luke Gorrie, Cory Kiser, Julio, Edvin Saveljev, Frederick Ayala, Jeffrey Powell, Gal Kampel, Adan Romero, Will Geary, Blake Walters, Jonathan Morgan, Francesco Madrisotti, Ivy Huang, Gary Clarke, Robert Flannery, Rasmus Hindström, Stefan, Corey Abshire and Mike Loncaric.

Links from the show:

Jesse on GitHub: https://github.com/jessegrabowski
Jesse on LinkedIn: www.linkedin.com/in/jessegrabowski
Jesse on Google Scholar: https://scholar.google.com/citations?user=vOCjGPwAAAAJ&hl=en
State space presentation repo: https://github.com/jessegrabowski/statespace-presentation/tree/main
Try the statespace module on pymc-experimental: https://github.com/pymc-devs/pymc-experimental
Durbin, James, and Siem Jan Koopman. Time series analysis by state space methods, Oxford, 2012: https://academic.oup.com/book/16563?login=false
Hyndman, Rob and George Athanasopoulos, Forecasting: Principals and Practice, 3rd Edition. Otexts, 2018: https://otexts.com/fpp3/
Roger Labbe, Kalman and Bayesian Filters in Python: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
Quantecon.org: https://quantecon.org/
Lecture on Kalman Filtering: https://python.quantecon.org/kalman.html
Mamba – Linear-Time Sequence Modeling with State Spaces (state spaces in machine learning): https://arxiv.org/abs/2312.00752
Paper explanation: https://www.youtube.com/watch?v=9dSkvxS2EB0
Good lecture on the statistics of the Kalman filter: https://www.youtube.com/watch?v=8lPBkkbtNW8
And on structural state space models: https://www.youtube.com/watch?v=2vf-d_fRCXs

Transcript

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Learning Bayesian Statistics

#124 State Space Models & Structural Time Series, with Jesse Grabowski

Episode guests

Podcast summary created with Snipd AI

Quick takeaways

Deep dives

Introduction to State-Space Models

The Role of the Kahneman Filter

Applications Across Disciplines

Composability of State-Space Models

The Future and Challenges of Bayesian Methods

Remember Everything You Learn from Podcasts