Precision livestock farming optimizes livestock production through the use of sensor information and communication technologies to support decision making, proactively and near real-time. Among available technologies to monitor foraging behavior, the acoustic method has been highly reliable and repeatable, but can be subject to further computational improvements to increase precision and specificity of recognition of foraging activities. In this study, an algorithm called Jaw Movement segment-based Foraging Activity Recognizer (JMFAR) is proposed. The method is based on the computation and analysis of temporal, statistical and spectral features of jaw movement sounds for detection of rumination and grazing bouts. They are called JM-segment features because they are extracted from a sound segment and expect to capture JM information of the whole segment rather than individual JMs. Two variants of the method are proposed and tested: (i) the temporal and statistical features only JMFAR-ns; and (ii) a feature selection process (JMFAR-sel). The JMFAR was tested on signals registered in a free grazing environment, achieving an average weighted F1-score of 93%. Then, it was compared with a state-of-the-art algorithm, showing improved performance for estimation of grazing bouts (+19%). The JMFAR-ns variant reduced the computational cost by 25.4%, but achieved a slightly lower performance than the JMFAR. The good performance and low computational cost of JMFAR-ns supports the feasibility of using this algorithm variant for real-time implementation in low-cost embedded systems. The method presented within this publication is protected by a pending patent application: AR P20220100910.