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Normal mixture of inverse Gaussian known as Normal-inverse Gaussian distribution is well-known in the context of modeling the stochastic volatility. In the present work, an autoregressive model for generating the sequence of volatilities is suggested so that the return series will have a stationary normal-inverse Gaussian distribution. The Laplace Transform of the innovation distribution does not have a closed form for its inversion. So the distributional properties are studied in terms of the Levy measure. The model parameters are estimated by the method of moments and a simulation is carried out to check their performance.

Autoregressive inverse Gaussian process and the stochastic volatility modeling