Power transformations of absolute returns and long memory estimation

Different power transformations of absolute returns of various financial assets have been found to display different magnitudes of sample autocorrelations, a property referred to as the Taylor effect. In this paper, we consider the long memory stochastic volatility model for the returns, under which, the asymptotic rate of decay of the autocorrelations of powers of absolute returns is governed by their long memory parameter. Although the true long memory parameter of powers of absolute returns is the same across different powers, we show that the local Whittle estimator of the long memory parameter has finite-sample bias that differs across the power transformations chosen. A Monte-Carlo experiment provides evidence in support of our theoretical finding that the reported variation of the estimates of the long memory parameter for power transformations of returns could be due to finite-sample bias of the estimator. The local Whittle estimates of powers of absolute returns for the S&P500 index and the DM/USD exchange rate are also examined.