Convergence of the Guesstimation Algorithm

Abstract

Economists attempting to build econometric or forecasting models are frequently restricted due to data scarcity in terms of short time series of data, and also of parameter non constancy and under-specification. In this case, a realistic alternative is often to guess rather than to estimate parameters of such models. An algorithm of repetitive guessing (drawing) parameters from iteratively changing distributions, with the objective of minimizing the squares of ex-post prediction errors, weighted by penalty weights and subject to a learning process, has been recently introduced. Despite obvious advantages, especially when applied for undersized empirical models with a large number of parameters, applications of Repetitive Stochastic Guesstimation have been, so far, limited. This has presumably been caused by the lack of rigorous proof of its convergence. Such proof for a class of linear models, both identifiable (in the economic sense) and not, is provided in this article.

Keywords:

• General linear model
• Martingale
• Prior beliefs
• Probabilistic algorithms

Mathematics Subject Classification:

• Primary 62P20
• Secondary 82B31

Acknowledgments

For the final phase of this work the author acknowledges Grant 1202/2007 of the National University Research Council, Romania (CNCSIS). A special debt is owed to Prof. W.W. Charemza, Leicester University for years of guidance and a constant stream of support. I am also grateful to an anonymous reviewer for helpful comments on an earlier draft of the article. I am solely responsible for any remaining deficiencies.