State Space Models

• Defined in terms of a pair of equations
  • Observation equation: $y_t = Z_t^T \alpha_t + \varepsilon_t$
    • It links the observed data $y_t$ to a latent d-dimensional state vector $\alpha_t$
  • State equation: $\alpha_{t+1} = T_t \alpha_t + R_t \eta_t$
    • It governs the evolution of the state vector $\alpha_t$ through time

Bayesian Structural Time Series

It is a state space model with a specific structure that allows for easy interpretation and forecasting. It is also a flexible framework for modeling time series data with multiple sources of information. paper pymc notebook pymc discussion

Note that there is another stream of Bayesian structural time series models that seems not using the state space model framework. Forecasting with Structural AR Timeseries