Exact Likelihood for Inverse Gamma Stochastic Volatility Models

Roberto Leon-Gonzalez and Blessings Majon
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Blessings Majon: National Graduate Institute for Policy Studies, Tokyo, Japan

No 24-03, GRIPS Discussion Papers from National Graduate Institute for Policy Studies

Abstract: We obtain a novel analytic expression of the likelihood for a stationary inverse gamma Stochastic Volatility (SV) model. This allows us to obtain the Maximum Likelihood Estimator for this non linear non Gaussian state space model. Further, we obtain both the filtering and smoothing distributions for the inverse volatilities as mixtures of gammas and therefore we can provide the smoothed estimates of the volatility. We show that by integrating out the volatilities the model that we obtain has the resemblance of a GARCH in the sense that the formulas are similar, which simplifies computations significantly. The model allows for fat tails in the observed data. We provide empirical applications using exchange rates data for 7 currencies and quarterly inflation data for four countries. We find that the empirical fit of our proposed model is overall better than alternative models for 4 countries currency data and for 2 countries inflation data.

Keywords: Hypergeometric Function; Particle Filter; Parallel Computing; Euler Acceleration. (search for similar items in EconPapers)
Pages: 56 pages
Date: 2024-04
New Economics Papers: this item is included in nep-rmg
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https://grips.repo.nii.ac.jp/record/2000096/files/DP24-3.pdf (application/pdf)

Related works:
Working Paper: Exact Likelihood for Inverse Gamma Stochastic Volatility Models (2023)
Working Paper: Exact Likelihood for Inverse Gamma Stochastic Volatility Models (2023)
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