In musical performances with expressive tempo modulation, the tempo variation can be modelled as a sequence of tempo arcs. Previous authors have used this idea to estimate series of piecewise arc segments from data. In this paper we describe a probabilistic model for a time-series process of this nature, and use this to perform inference of single- and multi-level arc processes from data. We describe an efficient Viterbi-like process for MAP inference of arcs. Our approach is score-agnostic, and together with efficient inference allows for online analysis of performances including improvisations, and can predict immediate future tempo trajectories.