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 nonlinear 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 seven 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 four countries currency data and for two countries inflation data.

Roberto Leon‐Gonzalez

Blessings Majoni

Journal of Time Series Analysis

在过去的 30 年中，时间序列分析已成为数理统计中最重要和最广泛使用的分支之一。其应用领域从神经生理学到天体物理学，涵盖经济预测、生物数据研究、控制系统、信号处理与通信和振动工程等知名领域。《时间序列分析杂志》创刊于 1980 年，现已成为该领域的领先期刊，发表关于基础理论和应用的论文，以及涉及该主题主要领域最新进展的评论论文和关于理论发展的简短交流。编委由许多世界领先的时间序列分析专家组成。

Over the past 30 years, time series analysis has become one of the most important and widely used branches of mathematical statistics. Its applications span various fields, from neurophysiology to astrophysics, including economic forecasting, biological data research, control systems, signal processing and communication, and vibration engineering. The Journal of Time Series Analysis was established in 1980 and has since become a leading journal in this field, publishing research papers on fundamental theories and applications, as well as review articles on the latest developments in major areas related to the topic and brief communications on theoretical advancements. The editorial board consists of many of the world's leading experts in time series analysis.

在过去的30年中，时间序列分析已成为数理统计中最重要和最广泛使用的分支之一。它的应用领域涵盖了从神经生理学到天体物理学的多个领域，包括经济预测、生物数据研究、控制系统、信号处理与通信以及振动工程等。《Journal of Time Series Analysis》创刊于1980年，现已成为该领域的领先期刊，发表关于基础理论和应用的研究论文，以及涉及该主题主要领域最新进展的评论论文和关于理论发展的简短交流。期刊的编委会由许多世界领先的时间序列分析专家组成。

Category	Quartile
数学	4
数学, 数学跨学科应用	4
数学, 统计学与概率论	4

Exact likelihood for inverse gamma stochastic volatility models

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	2