Abstract
In this paper, the gamma test is used to determine the order of lag-k tail dependence existing in financial time series. Using standardized return series, statistical evidences based on the test results show that jumps in returns are not transient. New time series models which combine a specific class of max-stable processes, Markov processes, and GARCH processes are proposed and used to model tail dependencies within asset returns. Estimators for parameters in the models are developed and proved to be consistent and asymptotically joint normal. These new models are tested on simulation examples and some real data, the S&P 500.
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