Efficient reservoir management requires regular analysis of large amounts of data to provide insights for decision making in a timely fashion. Well testing provides a key source of data for production surveillance and optimization by estimating oil, water and gas rates at irregularly sampled testing times. Although a significant amount of effort is spent on ensuring the quality of these well tests, the acquired data is still likely to have large uncertainties due to the complexity of flow dynamics, and challenges in multiphase flow separation and measurement. The resulting production history measurement for a well is therefore a noisy, unevenly sampled time series with potential significant outliers. A key point of interest is to perform decline analysis, which involves monitoring production trends (the derivative of the production time series) to ensure optimal well and reservoir performance. In addition to noise, the estimation of production trends is complicated by the effect of improved/enhanced recovery mechanisms (such as water flooding, steam injection etc.), well stimulation, and communication between wells, all of which may cause the production to deviate from expected parametric decline curves. As a result of this complexity, decline analysis typically requires significant manual effort in cleaning and segmenting the data and then fitting parametric curves to the extracted segments; this is challenging to do on a regular basis for all the wells. A robust and automated method to estimate production trends will enable continuous production surveillance and optimization in fields with hundreds to thousands of wells. In this paper, we report an effective method to address this challenge using a non-parametric approach based on robust regression for joint time series modeling and derivative estimation. Some key advantages of this approach over a conventional approach are a) it does not require manual data segmentation b) it is tolerant to a high amount of noise including some bad outliers c) it does not require manual choice of parametric decline curves. We compare results with conventional approaches and demonstrate benefits on synthetic production data.