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

Learning Bayesian Statistics

Proudly sponsored by PyMC Labs, the Bayesian Consultancy. Book a call, or get in touch!

• My Intuitive Bayes Online Courses
• 1:1 Mentorship with me

Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work!

Visit our Patreon page to unlock exclusive Bayesian swag ;)

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