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Semiparametric Bayesian inference of long-memory stochastic volatility models. (English) Zbl 1062.62232
The author considers a long-memory stochastic volatility model defined as \[ y_{t}=\sigma\exp\{h_{t}\}\xi_{t},\quad (1-L)^{d}h_{t}=\sigma_{\eta}\eta_{t},\quad t=1,\dots,T, \] where at time \(t\) the mean corrected return from holding a financial instrument is \(y_{t}\), and \(h_{t}\) is the unobservable log volatility that behaves as a fractionally integrated process. It is assumed that \(| d |<1/2\) and that the innovations \(\xi_{t}\) and \(\eta_{t}\) are uncorrelated standard normal white noise processes. The fractional differencing operator is \((1-L)^{d}\), where \(L\) is the lag operator, and \(x_{t-s}=L^{s}x_{t}\) is defined by its binomial expansion.
It is described how to quickly and efficiently sample from the posterior distribution of long-memory stochastic volatility model parameters with Markov chain Monte Carlo simulators. The author proposes a Markov chain Monte Carlo simulator in the wavelet domain that converges quickly to the target density and produces a mix of draws from the desired posterior distribution. The proposed algorithm augments the latent volatility wavelet coefficients with the long-memory stochastic volatility parameters. Using simulated and empirical stock return data the author finds that the proposed algorithm produces uncorrelated draws of the posterior distribution and point estimates that rival existing long-memory stochastic volatility estimators.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
65C40 Numerical analysis or methods applied to Markov chains
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F15 Bayesian inference
91B28 Finance etc. (MSC2000)
Software:
Ox; longmemo; sapa
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