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Indirect inference methods for stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck processes

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Abstract

This paper aims to develop new methods for statistical inference in a class of stochastic volatility models for financial data based on non-Gaussian Ornstein-Uhlenbeck (OU) processes. Our approach uses indirect inference methods: First, a quasi-likelihood for the actual data is estimated. This quasi-likelihood is based on an approximative Gaussian state space representation of the OU-based model. Next, simulations are made from the data generating OU-model for given parameter values. The indirect inference estimator is the parameter value in the OU-model which gives the best "match" between the quasi-likelihood estimator for the actual data and the quasi-likelihood estimator for the simulated data. Our method is applied to Euro/NOK and US Dollar/NOK daily exchange rates for the period 1.7.1989 until 15.12.2008. Accompanying R-package, that interfaces C++ code is documented and can be downloaded.

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  • Arvid Raknerud & Øivind Skare, 2009. "Indirect inference methods for stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck processes," Discussion Papers 601, Statistics Norway, Research Department.
    • Handle: RePEc:ssb:dispap:601
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    File URL: https://www.ssb.no/a/publikasjoner/pdf/DP/dp601.pdf
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    Keywords

    stochastic volatility; financial econometrics; Ornstein-Uhlenbeck processes; indirect inference; state space models; exchange rates;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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