A mathematical approach to detect the Taylor property in TARCH processes

We analyze the presence of the Taylor property in a well-known class of models for financial time series, the threshold ARCH (TARCH) model. This property is the theoretical counterpart of the stylized fact known as Taylor effect, detected in several empirical studies which have shown that the autocorrelations of the absolute returns are larger than those of the squared returns. We establish that the Taylor property is present for some parameterizations of the first order TARCH model. As this fact is strongly dependent on the distribution of the generating white noise, we analyze and compare, for several distributions of that process, the sets of parameterizations of the model presenting the Taylor property. Finally, a simulation study strongly suggests that TARCH models are considerably more likely to capture the Taylor effect than ARCH ones.