On Parameter Estimation in Unobserved Components Models subject to Linear Inequality Constraints

TL;DR

This paper introduces a quadratic programming-based approach for approximating nonstandard densities in unobserved components models with inequality constraints, improving sample efficiency while maintaining estimation accuracy.

Contribution

It presents a novel quadratic programming method for density approximation in constrained models, enhancing computational efficiency over existing methods.

Findings

The new method performs comparably to existing approximations in trend estimation.

It achieves better sample efficiency in posterior sampling.

The approach is applicable to models with linear inequality constraints.

Abstract

We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved components models involving inequality constraints on the parameters. For instance, Chan et al. (2016) provided a new model of trend inflation with linear inequality constraints on the stochastic trend. We implemented the proposed quadratic programming-based method for this model and compared it to the existing approximation. We observed that the proposed method works as well as the existing approximation in terms of the final trend estimates while achieving gains in terms of sample efficiency.