Bayesian State-Space Models
A Bayesian state-space model treats the state-space model parameters Θ as random variables, rather than fixed but unknown quantities, with joint prior distribution Π(Θ). This treatment leads to a more flexible model and intuitive inferences. Bayesian models also support linear and nonlinear state and observation equations, and enable you to specify specific non-Gaussian state disturbances, observation innovations, or custom observation distributions.
To start a Bayesian state-space model analysis, choose the right object for your model:
For a Bayesian view of the standard state-space model, optionally with linear non-Gaussian state disturbances or observation innovations, use
For a Bayesian model with nonlinear state transitions or measurement sensitivity function with linear errors, or for a model with a custom observation probability density, use
Filter State Particles
- What Are State-Space Models?
Learn state-space model definitions and how to create a state-space model object.
- What Is the Kalman Filter?
Learn about the Kalman filter, and associated definitions and notations.
- Analyze Linearized DSGE Models
Analyze a dynamic stochastic general equilibrium (DSGE) model using Bayesian state-space model tools.
- Perform Outlier Detection Using Bayesian Non-Gaussian State-Space Models
Detect outliers in a time series using non-Gaussian error distributions in a Bayesian state-space model.
- Fit Bayesian Stochastic Volatility Model to S&P 500 Volatility
Fit a Bayesian stochastic volatility model to daily S&P 500 closing returns, and then forecast the volatility into a two-week horizon.