Single-molecule manipulation studies can provide quantitative information about the physical properties of complex biological molecules without ensemble artifacts obscuring the measurements. We demonstrate computational techniques which aim at more fully utilizing the wealth of information contained in noisy experimental time series. The "noise" comes from multiple sources, e.g. inherent thermal motion, instrument measurement error, etc. The primary focus of this article is a methodology for using time domain based methods for extracting the effective molecular friction from single-molecule pulling data. We studied molecules composed of 8 tandem repeat titin I27 domains, but the modeling approaches have applicability to other single-molecule mechanical studies. The merits and challenges associated with applying such a computational approach to existing single-molecule manipulation data are also discussed.