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
posterior distribution.
Functions
Topics
- 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.