ABSTRACT
Time series of share returns generally display kurtosis in excess of 3 and little or no autocorrelation, even though the series of absolute or squared returns do display autocorrelation. In order to use an unconstrained optimizer such as nlm to maximize the likelihood, it is necessary to parametrize the model in terms of unconstrained parameters. The transition probabilities can be transformed via the generalized logit transform. A property of the two-state model, but not the three-state model, is that the ranges of correlations within each state are narrow and nonoverlapping. The model cross-correlations between the individual returns match the sample values very well. Stochastic volatility (SV) model–swhich, like HMMs, are special cases of state – space models –provide an alternative way of modelling time series of share returns. In the SV model without leverage, as described, there is no feedback from past returns to the (log-)volatility process.
