A new Quadratic ARCH model for the conditional variance of a time series is introduced. This model can be interpreted as a second-order Taylor approximation to the unknown conditional variance function, or as the quadratic projection of the squared series on the information set. This model is also the most general quadratic version possible within the class of ARCH models, and emcompases the Augmented ARCH model, the linear standard deviation model in Robinson (1991) and the Asymmetric ARCH model in Engle (1990).
It turns out that although its time series properties are very similar to those GARCH models, it avoids some of their criticisms. In an application to a century of daily US stock returns, QARCH models are also easy to incorporate in multivariate models so as to capture dynamic asymmetric effects that GARCH rules out. These effects seem to be present in an empirical application of a latent factor model with QARCH effects for stock returns on 26 UK sectors.
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