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Excerpt from Estimating the Covariance Matrix From Unsynchronized High Frequency Financial Data
The estimation of the covariance matrix of financial prices is necessary in port folio optimization and risk management. Besides sample covariance, many other estimators have been proposed (stein 1975, Dey and Srinivasan However, estimating the covariance matrix from daily data can have serious problems. Jobson and Korkie (1980) indicated that, in some cases, it is better to use the identical matrix instead of the sample covariance matrix in the port folio selection. The problem is that the number of observations is not enough to estimate all entries of a big covariance matrix. To get around the problem, one may want to collect more data over longer time interval. However, the changing condition of markets may prevent us to do so. Another approach is to impose constrains on the covariance matrix to reduce the number of free parameters (frost and Savaino, The constrain may be subjective and not re¿ect the reality of the market. This paper explores another possibility of using high frequency data. Because of fast-growing computer power, data is now available in ultra - high frequency, such as tick-by - tick. Exchange rates, for example, can easily have over one million observations in one year.
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