# Inversion Copulas from Nonlinear State Space Models

arXiv: https://arxiv.org/abs/1606.05022 · HTML: https://mlsanity.com/paper/1606.05022/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2016.

## Built on by (most cited first, 1 of 1)

- [Large Skew-t Copula Models and Asymmetric Dependence in Intraday Equity Returns](https://mlsanity.com/paper/2308.05564/) (2023)

## Abstract (arXiv)

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.