NONSYNCHRONOUS COVARIATION WITH APPLICATION TO FINANCE

Takaki HAYASHI

Keio University
Japan


ABSTRACT

We consider a generalized way to form the quadratic covariation of two semimartingales when the associated partitions over a fixed time interval are made up of nonsynchronous random time points. Its direct application is a statistical estimation problem of the covariance for high-frequency data, where time series data are assumed to be sampled from two continuous semimartingales at general stopping times in a nonsynchronous manner. A limiting distribution of the proposed variation process in such a setting is pursued at an increasing speed of sampling frequency within the fixed time domain. The result extends the existing studies on asymptotic normality of realized volatility type estimators that are based on synchronous samples.



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