Strongly Consistent Estimation of the Extended $\ell_1$-Sum of $ϕ$-Mixing Coefficients from a Single Trajectory

Khaleghi and Lugosi asked whether the sum of the $ϕ$-mixing (uniform-mixing) coefficients of a real-valued discrete-time stationary ergodic process can be consistently estimated from a single sample path. We construct a deterministic sequence of Borel statistics that, for every such process, converg