# Tempered Particle Filter

Herbst, Edward and Schorfheide, Frank, ‘‘Tempered Particle Filtering.’’ Journal of Econometrics, vol. 210, no. 1, 2019, pp. 26-44., doi:10.1016/j.jeconom.2018.11.003.

The tempered particle filter is a particle filtering method which can approximate the log-likelihood value implied by a general (potentially non-linear) state space system (with potentially non-Gaussian innovations) of the following representation:

### General State Space System

s_{t+1} = Phi(s_t, eps_t)  (transition equation)
y_t     = Psi(s_t) + u_t   (measurement equation)

eps_t ~ F_{eps}( . ; 0)
u_t   ~ N(0, E)
Cov(eps_t, u_t) = 0


Notice above that unlike the Kalman filter, the tempered particle filter does not impose that one’s model is linear and shocks eps_t are Gaussian.

Documentation and code are located in src/filters/tempered_particle_filter. An example script is located in docs/examples/tempered_particle_filter.

### Installation and Versioning

StateSpaceRoutines.jl is a registered Julia package in the general registry, currently compatible with Julia v1.0 and v1.1. To install, open your Julia REPL, type ] (enter Julia’s package manager), and run

pkg> add StateSpaceRoutines

###### Ph.D. Student in Economics

I am an Economics Ph.D. candidate at MIT, and former Senior Research Analyst on the dynamic stochastic general equilibrium (DSGE) team in the Macroeconomic and Monetary Studies function at the NY Fed. Views expressed are my own.