Analysis of floating point roundoff errors in the estimation of higher-order statistics

A floating point roundoff error analysis in the estimation of higher-order statistics, moments or cumulants of real stationary processes from single data records is provided. Closed form expressions or upper bounds are derived for the mean and variance of the quantisation noise introduced in the estimation of the all-zero and all-τ (diagonal slice) moments, power, skewness and kurtosis. Numerical and simulation results show that the roundoff noise can significantly affect the moment and cumulant estimates, especially when long data records are employed for the purpose of reducing the estimation variance. The obtained results can provide guidelines in choosing a processor with the appropriate register length (in number of bits) in applications that require the calculation of higher-order statistics