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, which requires one’s model be linear and shocks eps_t to be Gaussian, the tempered particle filter does not impose such restrictions.

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
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Reca Sarfati
Senior Research Analyst

I am a 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.