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

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

136
views

0
downloads

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

Collections

Graduate School of Applied Mathematics, Project and Design

Suggestions

OpenMETU
Core

Bayesian Networks in Project Management Yet, Barbaros (John Wiley & Sons, West Sussex, UK , 2017-08-01) Bayesian networks (BNs) offer unique benefits for combining data and expert knowledge to model complex joint probability distributions. Recent advances in inference algorithms enabled efficient computation of BNs with both discrete and continuous variables that are also called hybrid BNs. Consequently, BNs have been widely used as risk assessment and decision support tools in various domains including project management. This article illustrates the use of BNs in different aspects of project m...
Bayesian Networks in Project Management Yet, Barbaros (2017-01-01) Bayesian networks (BNs) offer unique benefits for combining data and expert knowledge to model complex joint probability distributions. Recent advances in inference algorithms enabled efficient computation of BNs with both discrete and continuous variables that are also called hybrid BNs. Consequently, BNs have been widely used as risk assessment and decision support tools in various domains including project management. This article illustrates the use of BNs in different aspects of project management and ...
BAYESIAN UNIT-ROOT TESTING IN STOCHASTIC VOLATILITY MODELS WITH CORRELATED ERRORS Kalaylıoğlu Akyıldız, Zeynep Işıl; Ghosh, Sujit K. (2013-12-01) A series of returns are often modeled using stochastic volatility models. Many observed financial series exhibit unit-root non-stationary behavior in the latent AR(1) volatility process and tests for a unit-root become necessary, especially when the error process of the returns is correlated with the error terms of the AR(1) process. In this paper, we develop a class of priors that assigns positive prior probability on the non-stationary region, employ credible interval for the test, and show that Markov Ch...
Disparity disambiguation by fusion of signal- and symbolic-level information Ralli, Jarno; Diaz, Javier; Kalkan, Sinan; Krueger, Norbert; Ros, Eduardo (Springer Science and Business Media LLC, 2012-01-01) We describe a method for resolving ambiguities in low-level disparity calculations in a stereo-vision scheme by using a recurrent mechanism that we call signal-symbol loop. Due to the local nature of low-level processing it is not always possible to estimate the correct disparity values produced at this level. Symbolic abstraction of the signal produces robust, high confidence, multimodal image features which can be used to interpret the scene more accurately and therefore disambiguate low-level interpretat...
Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market Savku, E.; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2020-08-01) We apply dynamic programming principle to discuss two optimal investment problems by using zero-sum and nonzero-sum stochastic game approaches in a continuous-time Markov regime-switching environment within the frame work of behavioral finance. We represent different states of an economy and, consequently, investors' floating levels of psychological reactions by aD-state Markov chain. The first application is a zero-sum game between an investor and the market, and the second one formulates a nonzero-sum sto...

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.