arXiv subjects

Quinlan Lee

Publications and source records attributed to Quinlan Lee.

4 recordsLinked to original sources

arXiv2025

Identification of Impulse Response Functions for Nonlinear Dynamic Models

We explore the issues of identification for nonlinear Impulse Response Functions in nonlinear dynamic models and discuss the settings in which the problem can be mitigated. In particular, we introduce the nonlinear autoregressive representation with Gaussian innovations and characterize the identified set. This set arises from the multiplicity of nonlinear innovations and transformations which leave invariant the standard normal density. We then discuss possible identifying restrictions, such as non-Gaussianity of independent sources, or identifiable parameters by means of learning algorithms, and the possibility of identification in nonlinear dynamic factor models when the underlying latent factors have different dynamics. We also explain how these identification results depend ultimately on the set of series under consideration.

econ.EM↗

arXiv2025

Nonlinear Forecast Error Variance Decompositions with Hermite Polynomials

A novel approach to Forecast Error Variance Decompositions (FEVD) in nonlinear Structural Vector Autoregressive models with Gaussian innovations is proposed, called the Hermite FEVD (HFEVD). This method employs a Hermite polynomial expansion to approximate the future trajectory of a nonlinear process. The orthogonality of Hermite polynomials under the Gaussian density facilitates the construction of the decomposition, providing a separation of shock effects by time horizon, by components of the structural innovation and by degree of nonlinearity. A link between the HFEVD and nonlinear Impulse Response Functions is established and distinguishes between marginal and interaction contributions of shocks. Simulation results from standard nonlinear models are provided as illustrations and an application to fiscal policy shocks is examined.

econ.EM↗

arXiv2024

Forecast Relative Error Decomposition

We introduce a class of relative error decomposition measures that are well-suited for the analysis of shocks in nonlinear dynamic models. They include the Forecast Relative Error Decomposition (FRED), Forecast Error Kullback Decomposition (FEKD) and Forecast Error Laplace Decomposition (FELD). These measures are favourable over the traditional Forecast Error Variance Decomposition (FEVD) because they account for nonlinear dependence in both a serial and cross-sectional sense. This is illustrated by applications to dynamic models for qualitative data, count data, stochastic volatility and cyberrisk.

econ.EM↗

arXiv2023

Nonlinear Impulse Response Functions and Local Projections

The goal of this paper is to extend the nonparametric estimation of Impulse Response Functions (IRF) by means of local projections in the nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for Markov processes and explain how their IRFs are directly linked to the Nonlinear Local Projection (NLP), as in the case for the linear setting. We present a fully nonparametric LP estimator in the one dimensional nonlinear framework, compare its asymptotic properties to that of IRFs implied by the nonlinear autoregressive model and show that the two approaches are asymptotically equivalent. This extends the well-known result in the linear autoregressive model by Plagborg-Moller and Wolf (2017). We also consider extensions to the multivariate framework through the lens of semiparametric models, and demonstrate that the indirect approach by the NLP is less accurate than the direct estimation approach of the IRF.

econ.EM↗