оценочная функция; оценщик
- To overcome this problem, Parkinson (1980) devised an estimator of the variance of price changes (X) that uses the high and low prices during the time period from t -1 to t .
- With minimal loss of efficiency, the Garman and Klass estimator can be approximated by which is the weighted average of the Parkinson estimator and the "classical" estimator.
- The relationship between these two estimators was found to be unstable across shares and over time, suggesting that the fixed weighting scheme used in the Garman and Klass estimator may not be optimal in reality.
- When the number of transactions per period is 500 their estimator understates the true variance by about 11%.
- Parkinson suggested that, since the natural logarithm of prices is normally distributed, his formula applies to ln F t rather than to F t , and his variance estimator for the logarithms of futures price changes (log returns) in .
- Given that the only available pieces of information are the high, low and closing prices, they derived the minimum variance unbiased estimator of Var (ln F t ), which is more efficient than the Parkinson estimator.
- Beckers (1983) used daily data on 208 US shares for 7.25 years (1973-;80) to test the performance of the Parkinson and classical estimators and, since it is the weighted sum of these two estimators, the Garman and Klass estimator.
- Garman and Klass defined the classical estimator of as , which is equivalent to applying the formula where , (the mean of ), and n = 1.
- Garman and Klass provided a table of factors to adjust upwards the values of their estimator which requires knowing the number of transactions per time period.
- The equation for this new estimator is .