ABSTRACT We derive a general and robust estimator of a large class of parametric specifications of time‐varying unconditional volatility of financial returns, both univariate and multivariate, and establish the Consistency and Asymptotic Normality (CAN) of the estimator. A number of well‐known and widely used parametric specifications, for many of which asymptotic results have not been specifically established, are contained in the class. The estimator is robust in the sense that the exact specification of the conditional volatility dynamics need not be known or estimated, and in the sense that the stochastic component need not be strictly stationary. The latter is especially important in light of recent findings, which document that financial returns are frequently characterised by a non‐stationary zero‐process. Our estimator is also robust to the well‐known “curse of dimensionality” in multivariate models due to its equation‐by‐equation nature. While our estimator does not require the exact specification of the conditional volatility dynamics to be known or estimated, our results imply that the scaled GARCH(1,1) specification is well‐defined under both correct and incorrect specifications. So we provide methods for its estimation in a second step. Also, due to the assumptions we rely upon, our results extend directly to the Multiplicative Error Model (MEM) interpretation of volatility models. This means our results can also be applied to other non‐negative processes like volume, duration, realised volatility, dividends, unemployment, and so on. Three numerical applications illustrate the versatility of our results.
Lee, Adam & Mesters, Geert (2024)
Locally robust inference for non-Gaussian linear simultaneous equations models
All parameters in linear simultaneous equations models can be identified (up to permutation and sign) if the underlying structural shocks are independent and at most one of them is Gaussian. Unfortunately, existing inference methods that exploit such identifying assumptions suffer from size distortions when the true distributions of the shocks are close to Gaussian. To address this weak non-Gaussian problem we develop a locally robust semi-parametric inference method which is simple to implement, improves coverage and retains good power properties. The finite sample properties of the methodology are illustrated in a large simulation study and an empirical study for the returns to schooling.
Hoesch, Lukas; Lee, Adam & Mesters, Geert (2024)
Locally Robust Inference for Non-Gaussian SVAR models
All parameters in structural vector autoregressive (SVAR) models are locally identified when the structural shocks are independent and follow non‐Gaussian distributions. Unfortunately, standard inference methods that exploit such features of the data for identification fail to yield correct coverage for structural functions of the model parameters when deviations from Gaussianity are small. To this extent, we propose a locally robust semiparametric approach to conduct hypothesis tests and construct confidence sets for structural functions in SVAR models. The methodology fully exploits non‐Gaussianity when it is present, but yields correct size/coverage for local‐to‐Gaussian densities. Empirically, we revisit two macroeconomic SVAR studies where we document mixed results. For the oil price model of Kilian and Murphy (2012), we find that non‐Gaussianity can robustly identify reasonable confidence sets, whereas for the labor supply–demand model of Baumeister and Hamilton (2015) this is not the case. Moreover, these exercises highlight the importance of using weak identification robust methods to assess estimation uncertainty when using non‐Gaussianity for identification.
