Empirical characteristic process
= Empirical characteristic process
{title2=$\mathcal C_n(u)$}
The centered process $\mathcal C_n(u)=\sqrt n(\varphi_n(u)-\varphi(u))$ describes fluctuations of the <empirical characteristic function>. At a fixed frequency, its real and imaginary parts satisfy a <multivariate central limit theorem>. A process-level limit requires further control over the frequency index.