A new filtering inference procedure for a GED state-space volatility model

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A vast amount of methods have been developed to make inferences for volatility data, taking into account the stylized facts of rate/return data. However, the common problem is that the latent parameters of many volatility models are high-dimensional and analytically intractable. Therefore, their inference procedure requires numerical approximations using intensive computational techniques, as the Markov chain Monte Carlo, Laplace, and particle filter methods. A common strategy to overcome this problem is model linearization. This approach consists of writing the stochastic volatility model as a linear Gaussian state-space model, leading to an approximated marginal likelihood using the Kalman filter, reducing the problem’s dimensionality. This paper proposes a new filtering inference procedure with an integrated likelihood for a Generalized Error Distribution (GED) state-space volatility model without model linearization. Also, we evaluate the quality of our method approximation and introduce an approximated smoothing procedure. We use the Bayesian methods for making the inference of static parameters and perform a simulation exercise to study the estimators’ properties. Our results show that the proposed model can be reasonably estimated, and the approximation of our method is reasonable. Furthermore, we provide a case study of the pound/dollar and real/dollar exchange rate to illustrate our approach’s performance. For the real/dollar time series, the model captures a high volatility pattern due to the COVID-19 pandemic.