We study the multifractal effects of linear and non-linear transformations for monofractal time series and apply these findings to measure the 'true' unbiased multifractality for volatility series calculated in various ways for different world stock markets. A difference is stressed between the 'naive' multifractal effects calculated directly within MF-DFA as the spread of generalized Hurst exponents Δh=h(q→-∞)-h(q→∞) and the unbiased multifractal effect received after subtraction of multifractal residual noise generated as the result of nonlinear transformation of monofractal signal. This way the unbiased multifractal effect of volatility series, caused only by multifractality of price time series, is separated for real financial stocks. Finally, we compare and discuss obtained results from different world stocks.

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