GAUSS™ Programs for the Estimation of State-Space Models with ARCH Errors: A User's Guide

State-space models have long been popular in explaining the evolution of various economic variables. This is mainly because they generally have more economic content than do others in their class of parsimonious models (for example, VARs). Yet, in spite of their advantages, use of these models until recently was limited by the assumption that all the innovations therein had to be conditionally normally distributed. Consequently, one could not model conditionally heteroskedastic series within that framework. The study by Harvey, Ruiz, and Sentana (1992) changed that. These authors showed how ARCH effects could be handled in a state-space framework, whether such innovations were in the measurement equations or in the transition ones. For these purposes, the authors modified the usual Kalman filter and developed an approximate (or quasi-optimal) filter to estimate these models. An application of the above framework was made recently by Kichian (1999) to estimate Canadian potential output. Because no code was publicly available at that time to perform this task, GAUSS programs were developed at the Bank of Canada. In fact, the code allows for the estimation of a wide variety of state-space models with or without ARCH errors. This paper explains how to use this Bank code. We show, step-by-step, how to use the programs and give several examples. Also included is additional code for calculating out-of-sample forecast errors on the observable variables in order to assess the goodness of fit of the estimated models.