Nonlinear Forecast Error Variance Decompositions with Hermite Polynomials [Submitted]
Draft Available Here: https://arxiv.org/abs/2503.11416
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 effects of shocks. Simulation results from standard nonlinear models are provided as illustrations and an application to a TVAR of fiscal policy shocks is examined.
Presentations: Canadian Economics Association (UQAM, Scheduled), The 2025 RCEA International Conference in Economics, Econometrics, and Finance (New Jersey City University, Scheduled)
Forecast Relative Error Decompositions, with Christian GOURIEROUX [Submitted]
Draft Available Here: https://arxiv.org/abs/2406.17708
Abstract: 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.
Presentations: University of Toronto, NBER-NSF Time Series Conference 2024 (UPenn, Poster), Conference on Real-Time Data Analysis, Methods and Applications in Macroeconomics and Finance (Bank of Canada, Poster), Canadian Econometrics Study Group (YorkU, Poster), CFE-CM Statistics Conference (King's College London)
Nonlinear Impulse Response Functions and Local Projections, with Christian GOURIEROUX
Draft Available Here: https://arxiv.org/abs/2305.18145
Abstract: The goal of this paper is to extend the nonparametric estimation of Impulse Response Functions (IRFs) by means of Local Projection (LP) in a nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for a Markov process, and explain how their Impulse Response Functions are directly linked to the Nonlinear Local Projection (NLP), as in the case for the linear setting. We then present a NLP estimator, and compare its asymptotic properties to that of IRFs obtained through direct estimation. We also explore issues of identification for the nonlinear IRF in the multivariate framework, which remarkably differs in comparison to the Gaussian linear case. In particular, we show that identification is conditional on the uniqueness of dynamic deconvolution and provide sufficient conditions for this uniqueness. Then, we consider IRF and LP in augmented Markov models.
Presentations: NBER-NSF Time Series Conference 2023 (UQAM, Poster), Canadian Econometrics Study Group* (McMaster, Poster)
*Awarded the Best Student Poster Award at the 38th Annual Canadian Econometrics Study Group Meeting