Falls are among the leading causes of injuries or death for the elderly, and the prevalence is especially high for patients suffering from neurological diseases like Parkinson's disease (PD). Today, inertial measurement units (IMUs) can be integrated unobtrusively into patients' everyday lives to monitor various mobility and gait parameters, which are related to common risk factors like reduced balance or reduced lower-limb muscle strength. Although stair ambulation is a fundamental part of everyday life and is known for its unique challenges for the gait and balance system, long-term gait analysis studies have not investigated real-world stair ambulation parameters yet. Therefore, we applied a recently published gait analysis pipeline on foot-worn IMU data of 40 PD patients over a recording period of two weeks to extract objective gait parameters from level walking but also from stair ascending and descending. In combination with prospective fall records, we investigated group differences in gait parameters of future fallers compared to non-fallers for each individual gait activity. We found significant differences in stair ascending and descending parameters. Stance time was increased by up to 20 % and gait speed reduced by up to 16 % for fallers compared to non-fallers during stair walking. These differences were not present in level walking parameters. This suggests that real-world stair ambulation provides sensitive parameters for mobility and fall risk due to the challenges stairs add to the balance and control system. Our work complements existing gait analysis studies by adding new insights into mobility and gait performance during real-world gait.