The main objective of this study is to propose a computational pipeline for the recognition of normal and abnormal activities based on smartphone accelerometer data. Methods and techniques that have been previously evaluated are further evolved and applied for the recognition of a large set of separate activities as well as a sequence of activities simulating a common scenario of daily living as a more realistic approach. For these purposes, the MobiAct dataset which encompass a set of normal activities of daily living (ADLs) and abnormal activities (falls) was used. The results show a classification accuracy of 99% for the recognition of separate ADLs, while a reduction of 5% is observed for the recognition of the scenarios.