Bayesian latent autoregressive stochastic volatility: an application of naira to eleven exchangeable currencies rates

• Main Authors: R. O. Olanrewaju, J. F. Ojo, L. O. Adekola
• Format: Article
• Language: English
• Published: Ptolemy Scientific Research Press 2020-11-01
• Series: Open Journal of Mathematical Sciences
• Subjects: bayesian; gaussian; latent autoregressive; stochastic volatility (sv); markov chain monte carlo (mcmc).
• Online Access: https://pisrt.org/psr-press/journals/oms-vol-4-2020/bayesian-latent-autoregressive-stochastic-volatility-an-application-of-naira-to-eleven-exchangeable-currencies-rates/

This paper provides a procedure for estimating Stochastic Volatility (SV) in financial time series via latent autoregressive in a Bayesian setting. A Gaussian distributional combined prior and posterior of all hyper-parameters (autoregressive coefficients) were specified such that the Markov Chain Monte Carlo (MCMC) iterative procedure via the Gibbs and Metropolis-Hasting sampling method was used in estimating the resulting exponentiated forms (quadratic forms) from the posterior kernel density. A case study of Naira to eleven (11) exchangeable currencies$^,$ rates by Central Bank of Nigeria (CBN) was subjected to the estimated solutions of the autoregressive stochastic volatility. The posterior volatility estimates at \(5%\), \(50%\), and \(95%\) quantiles of \(e^{μ^2} = (0.130041, 0.1502\) and \(0.1795)\) respectively unveiled that the Naira-US Dollar exchange rates has the highest rates bartered by fluctuations.