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Title: Semi-continuous time series for sparse data with volatility clustering Authors:  Sarka Hudecova - Charles University (Czech Republic)
Michal Pesta - Charles University (Czech Republic) [presenting]
Abstract: Time series containing a non-negligible portion of possibly dependent zeros, whereas the remaining observations are positive, are considered. They are regarded as GARCH processes consisting of non-negative values. The aim lies in the estimation of the omnibus model parameters taking into account the semi-continuous distribution. The hurdle distribution, together with dependent zeros, causes the classical GARCH estimation techniques to fail. Two different likelihood-based approaches are derived, namely the maximum likelihood estimator and a new quasi-likelihood estimator. Both estimators are proved to be strongly consistent and asymptotically normal. Predictions with bootstrap add-ons are proposed. The empirical properties are illustrated in a simulation study, which demonstrates the computational efficiency of the methods employed. The developed techniques are presented through an actuarial problem concerning sparse insurance claims.