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Model description
Stochastic volatility models are used in mathematical finance to describe the evolution of asset returns,
which typically exhibit changing variances over time. As an illustration we use a dataset
previously analyzed by Harvey et al. (1994), and later by several other authors.
The data consist of a time series of daily pound/dollar exchange rates {z_{t}} from the period 01/10/81 to 28/6/85.
The series of interest are the daily meancorrected returns {y_{t}}, given by the transformation
y_{t} = log(z_{t})log(z_{t1})
 average[logz_{i}logz_{i1}].
The stochastic volatility model allows the variance of y_{t} to vary smoothly with time.
This is achieved by assuming that y_{t} ~ N(0,s_{t}),
where s_{t} = exp{0.5(m_{x}+x_{t})}.
Here, the smoothly varying component {x_{t}} is assumed to follow an autoregression
x_{t} = bx_{t1} + e_{t},
where e_{t} ~ N(0,s^{2}).
Further details about the model can be found here: sdv.pdf.
