Bayesian Unit Root Test İn Stochastic Volatility Models With Correlated Errors And Autoregressive Model Of Order P

Date

2010-04-01

Author

Kalaylıoğlu Akyıldız, Zeynep Işıl

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The purpose of this project is to develop a Bayesian Markov Chain Monte Carlo (MCMC) based unit-root testing procedure to test for nonstationarity in the extended Stochastic Volatility (eSV) Model which we describe below. A basic SV (bSV) model specifies that i) conditional mean equation is modeled as a nonlinear stochastic function of unobserved volatilities, ii) the logarithm of the unobserved volatility follows a log-normal autoregressive model of order 1, iii) the innovations in the volatility model and the innovations in the conditional mean equation are independent. The bSV model has been used for many financial series such as stock indices and exchange rates. In the presence of nonstationary volatility, the past shocks on the current volatility remain persistent and this creates an uncertain business environment. Frequentist and Bayesian unit root tests have been developed to test for nonstationarity of volatility in bSV models (see 2.a). However it has been observed that bSV is too restrictive for many financial series. We extend the model (eSV) to allow i) higher order log-normal autoregressive model for conditional volatility, ii) leverage effect which means nonzero correlation between the innovations in the volatility model and innovations in the conditional mean equation. This project will develop a Bayesian MCMC unit root testing methodology in regard to testing nonstationarity of volatilities in eSV. Also we will design a Monte Carlo sampling experiment to evaluate the performances of unit root tests with bSV and eSV in the presence of model misspecifications. This project will extend the Bayesian MCMC unit root testing procedure (2008) to the eSV model that allows correlated errors and a general autoregressive model for log volatility. Already high dimension of the parameter space in bSV will be higher with the join of the parameter representing the leverage effect and the parameters of the higher order autoregressive model for volatilities in eSV. The project will develop an MCMC algorithm to overcome the above mentioned curse of dimensionality in estimating the model parameters. The project will uncover how sensitive the Bayesian approach for unit root testing in this model to the prior belief about the covariance matrix of the mean and volatility innovations and amount of test's robustness to misspecified autoregressive models. It will also assess the performance of the test by estimating the likelihood of false negatives and false positives by designing an extensive Monte Carlo experiment.

URI

https://hdl.handle.net/11511/61656

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Graduate School of Applied Mathematics, Project and Design

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Citation Formats

Z. I. Kalaylıoğlu Akyıldız, “Bayesian Unit Root Test İn Stochastic Volatility Models With Correlated Errors And Autoregressive Model Of Order P,” 2010. Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/61656.