Discussion Papers 601 - Statistics Norway, December 2009

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Arvid Raknerud and Øivind Skare

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

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.

Keywords: stochastic volatility, financial econometrics, Ornstein-Uhlenbeck processes, indirect inference, state space models, exchange rates

JEL classification: C13, C22, C51,G10

Acknowledgement: We appreciate useful comments from Terje Skjerpen, Anders Rygh Swensen and participants at the 3rd International Conference on Computational and Financial Econometrics (CFE) held on 29-31 October 2009, in Limassol, Cyprus. Accompanying software written in C++ code (with R-interface) can be downloaded from http://folk.uio.no/skare/SV/. Financial support from the Norwegian Research Council ("Finansmarkedsfondet") is gratefully acknowledged.

Address:
Arvid Raknerud, Statistics Norway, Research Department. E-mail: rak@ssb.no Øivind Skare, Norwegian Institute of Public Health and University of Bergen, Department of Public Health and Primary Health Care. E-mail: oivind.skare@medisin.uio.no

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