Paper #1182

Title:

A low dimensional Kalman filter for systems with lagged observables

Author:

Kristoffer Nimark

Date:

November 2009

Abstract:

This note describes how the Kalman filter can be modified to allow for the vector of observables to be a function of lagged variables without increasing the dimension of the state vector in the filter. This is useful in applications where it is desirable to keep the dimension of the state vector low. The modified filter and accompanying code (which nests the standard filter) can be used to compute (i) the steady state Kalman filter (ii) the log likelihood of a parameterized state space model conditional on a history of observables (iii) a smoothed estimate of latent state variables and (iv) a draw from the distribution of latent states conditional on a history of observables.

Keywords:

Kalman filter, lagged observables, Kalman smoother, simulation smoother

Area of Research:

Macroeconomics and International Economics

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