On the Estimation of Correlation Functions of Solar Wind Turbulence Signals

Spectral and correlation analysis are essential tools to investigate the turbulent properties of the solar wind from in-situ spacecraft observations. Most of these statistical techniques are based on estimators of autocorrelation functions (ACF), power spectral densities (PSD) as well as other important statistical averages. An important assumption often made is that spacecraft signals are stationary, i.e. invariant under time shifts. However, standard analysis of these data shows that ACFs depend on the interval length, which suggests that the signal may not be truly stationary. This lack of stationarity makes it difficult to determine turbulence correlation times (or lengths) using ACF. In this work we use a recently introduced new methodology, based on conditional statistics, to estimate ACF of turbulent fluctuations that does not depend on the interval length. This technique can be used to calculate ACF in long solar wind intervals with data gaps, or containing a mixture of solar wind streams with different properties, by using conditional statistics to restrict the analysis to the regime of interest. The consistency of the conditioned ACF estimator, i.e. its convergence to the true ensemble-averaged autocorrelation, is verified in numerical simulations and used to investigate the turbulence correlation time of solar wind signals. We study the effect of interval length conditional ACF using simulation and observation data from Parker Solar Probe. The spectral properties of both methods will also be compared.