Traditional tests of volatility jump detection become highly biased for high frequency data. We compare the rejection rate of existing tests for jump detection based on power variation and scale variation methods with a newly adopted testing method based on principal components of functional...

Integrated covariance between pairs of realizations of a multivariate Ito process observed sparsely and irregularly with additive noise is estimated using the random lead lag estimator. The method is applied to a dataset of price processes from online auctions on ebay. This approach allows us to...