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ARMA representation of integrated and realized variances

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Abstract

This paper derives the ARMA representation of integrated and realized variances when the spot variance depends linearly on two autoregressive factors, i.e. SR-SARV(2) models. This class of processes includes affine, GARCH diffusion, and CEV models, as well as the eigenfunction stochastic volatility and the positive Ornstein–Uhlenbeck models. We also study the leverage effect case, and the relationship between the weak GARCH representation of returns and the ARMA representation of realized variances. Finally, various empirical implications of these ARMA representations are considered. We find that it is possible that some parameters of the ARMA representation are negative. Hence, the positiveness of the expected values of integrated or realized variances is not guaranteed. We also find that for some frequencies of observations, the continuous time model parameters may be weakly or not identified through the ARMA representation of realized variances.

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