Evaluations of likelihood based surveillance of volatility
Abstract: The volatility of asset returns are important in finance.
Different likelihood based methods of statistical surveillance for
detecting a change in the variance are evaluated. The differences are how
the partial likelihood ratios are weighted. The full likelihood ratio,
Shiryaev-Roberts, Shewhart and the CUSUM methods are derived in case of an
independent and identically distributed Gaussian process. The behavior of
the methods is studied both when there is no change and when the change
occurs at different time points. The false alarms are controlled by the
median run length. Differences and limiting equalities of the methods are
shown. The performances when the process parameters for which the methods
are optimized for differ from the true values of the parameters are
evaluated. The methods are illustrated on a period of Standard and Poor’s
500 stock market index.
Keywords: surveillance; statistical process control; monitoring; likelihood ratio; Shewhart; CUSUM; (follow links to similar papers)
JEL-Codes: C10; (follow links to similar papers)
20 pages, January 1, 2007
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