Robust Estimation of Nonstationary, Fractionally Integrated, Autoregressive, Stochastic Volatility

Download or read book Robust Estimation of Nonstationary, Fractionally Integrated, Autoregressive, Stochastic Volatility written by Mark J. Jensen and published by . This book was released on 2017 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical volatility studies have discovered nonstationary, long-memory dynamics in the volatility of the stock market and foreign exchange rates. This highly persistent, infinite variance--but still mean reverting--behavior is commonly found with nonparametric estimates of the fractional differencing parameter d, for financial volatility. In this paper, a fully parametric Bayesian estimator, robust to nonstationarity, is designed for the fractionally integrated, autoregressive, stochastic volatility (SV-FIAR) model. Joint estimates of the autoregressive and fractional differencing parameters of volatility are found via a Bayesian, Markov chain Monte Carlo (MCMC) sampler. Like Jensen (2004), this MCMC algorithm relies on the wavelet representation of the log-squared return series. Unlike the Fourier transform, where a time series must be a stationary process to have a spectral density function, wavelets can represent both stationary and nonstationary processes. As long as the wavelet has a sufficient number of vanishing moments, this paper's MCMC sampler will be robust to nonstationary volatility and capable of generating the posterior distribution of the autoregressive and long-memory parameters of the SV-FIAR model regardless of the value of d. Using simulated and empirical stock market return data, we find our Bayesian estimator producing reliable point estimates of the autoregressive and fractional differencing parameters with reasonable Bayesian confidence intervals for either stationary or nonstationary SV-FIAR models.