Bayesian State-Space Model
A Bayesian state-space model treats the linear 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 allow you to specify non-Gaussian state disturbances and observation innovations.
Bayesian state-space model analyses involve drawing samples from the joint posterior distribution Π(θ|Dt), which is composed of the joint prior and data likelihood computed by the standard Kalman filter, where Dt is the response and predictor data set. Econometrics Toolbox™ uses a Markov chain Monte Carlo algorithm, such as the Metropolis-Hastings sampler, to sample from the posterior.
To start a Bayesian state-space model analysis, create a model object
that best describes the structure of the state-space (from which the
likelihood is inferred) and your prior assumptions on the joint
distribution of the parameters by using
bssm. Then, using the model and data, you can estimate
characteristics of the posterior distributions or draw samples from the
- 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.