Table 2:

Asymptotic behavior of the standard TAMSD-based estimator (7) (see Corollary A.1).

parameter range	rate of convergence		joint asymptotic distribution	consistency
	Lstand	Astand
0 < α < 3/2	$\sqrt{\frac{N}{\tau }}\frac{1}{{\tau }^{\alpha }}\frac{1}{\log \tau }$	$\sqrt{\frac{N}{\tau }}\frac{1}{{\tau }^{\alpha }}$	Gaussian	Yes
α = 3/2	$\sqrt{\frac{N}{\log N}}\frac{1}{{\tau }^2}\frac{1}{\log \tau }$	$\sqrt{\frac{N}{\log N}}\frac{1}{{\tau }^2}$	Gaussian	Yes
3/2 < α < 2	$\frac{N^{2-\alpha }}{{\tau }^2}\frac{1}{\log \tau }$	$\frac{N^2-\alpha }{{\tau }^2}$	2 non-Gaussian	Yes