What question did this study set out to answer?

This research aims to estimate non-fundamental ARMA models with innovations exhibiting unknown heteroskedasticity.

May 30, 2026Open Access

Time domain estimation of non-fundamental ARMA models in the presence of heteroskedasticity of unknown form

Key Points

This research aims to estimate non-fundamental ARMA models with innovations exhibiting unknown heteroskedasticity.
Proposes a minimum distance objective function based on predictability of innovations.
Estimates models using a GMM estimator on inflation data from 29 OECD countries.
Avoids explicit parametrization of the volatility process and maximum likelihood procedures.
Finds widespread evidence for non-fundamentalness across the estimated ARMA models.
Demonstrates that the proposed GMM estimator is consistent and asymptotically normal.

Abstract

This paper considers time domain estimation of possibly non-fundamental (that is, non-causal and/or non-invertible) non-Gaussian linear ARMA models with martingale difference innovations that may display conditional heteroskedasticity of unknown form. Instead of explicitly parametrizing the underlying volatility process (the higher order dependence) and employing maximum likelihood procedures, we propose a time domain minimum distance objective function based on innovations predictability using second and third powers of past innovations. Using the proposed efficient GMM estimator, which is consistent and asymptotically normal, we estimate possibly non-fundamental ARMA models to inflation data from 29 OECD countries and find widespread evidence on non-fundamentalness.

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Cite This Study

Lobato et al. (Wed,) studied this question.

synapsesocial.com/papers/6a1a7ecb0307b78509431546 https://doi.org/https://doi.org/10.1016/j.jeconom.2026.106265

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