This paper explores the fit of a stochastic volatility model, in which the Box-Cox transformation of the squared volatility follows an autoregressive Gaussian distribution, to the continuously compounded daily returns of the Australian stock index. Estimation was difficult, and over-fitting likely, because more variables are present than data. We developed a revised model that held a couple of these variables fixed and then, further, a model which reduced the number of variables significantly by grouping trading days. A Metropolis-Hastings algorithm was used to simulate the joint density and derive estimated volatilities. Though autocorrelations were higher with a smaller Box-Cox transformation parameter, the fit of the distribution was much better.
Worcester Polytechnic Institute
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Volfson, Alexander, "Exploring the optimal Transformation for Volatility" (2010). Masters Theses (All Theses, All Years). 472.
Metropolis-Hastings algorithm, Bayes, Empirical Bayes, stochastic volatility, Box-Cox transformation