When the log-price process incorporates a jump component, realised variance will no longer estimate the integrated variance since its probability limit will be determined by the continuous and jump components. Instead realised bipower variation, tripower variation and quadpower variation are consistent estimators of integrated variance even in the presence of jumps. In this paper we derive the limit distributions of realised tripower and quadpower variation, allowing us to compare these three estimators of integrated variance. Using the limit theories for the differences of the errors, tests for jumps are proposed for each estimator. Using simulated data, the performance of each of these tests is compared. The tests are also applied to empirical data but results need to be taken carefully as market microstructure effects may contaminate real data.
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Paper provided by Banco de México in its series Working Papers with number
2006-10.
Find related papers by JEL classification: C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation G19 - Financial Economics - - General Financial Markets - - - Other
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