Inversion Copulas from Nonlinear State Space Models

TL;DR

This paper introduces a novel method to construct copulas from nonlinear state space models, enabling flexible time series modeling with arbitrary margins and improved forecasting accuracy.

Contribution

It presents a new approach to create inversion copulas from nonlinear state space models, enhancing modeling flexibility and forecast performance.

Findings

Inversion copulas improve fit for inflation and electricity data.

Flexible margins enhance density forecast accuracy.

Models capture serial dependence effectively.

Abstract

We propose to construct copulas from the inversion of nonlinear state space models. These allow for new time series models that have the same serial dependence structure of a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas with flexible margins improve the fit and density forecasts of quarterly U.S. broad inflation and electricity inflation.