  We consider an autocorrelation function of a quantum mechanical system
through the lens of the so-called recursive method, by iteratively evaluating
Lanczos coefficients, or solving a system of coupled differential equations in
the Mori formalism. We first show that both methods are mathematically
equivalent, each offering certain practical advantages. We then propose an
approximation scheme to evaluate the autocorrelation function, and use it to
estimate the equilibration time $\tau$ for the observable in question. With
only a handful of Lanczos coefficients as the input, this scheme yields an
accurate order of magnitude estimate of $\tau$, matching state-of-the-art
numerical approaches. We develop a simple numerical scheme to estimate the
precision of our method. We test our approach using several numerical examples
exhibiting different relaxation dynamics. Our findings provide a new practical
way to quantify the equilibration time of isolated quantum systems, a question
which is both crucial and notoriously difficult.
