Pushing the frontiers of time-series information processing in ever-growing edge devices with stringent resources has been impeded by the system's ability to process information and learn locally on the device. Local processing and learning typically demand intensive computations and massive storage as the process involves retrieving information and tuning hundreds of parameters back in time. In this work, we developed a memristor-based echo state network accelerator that features efficient temporal data processing and in-situ online learning. The proposed design is benchmarked using various datasets involving real-world tasks, such as forecasting the load energy consumption and weather conditions. The experimental results illustrate that the hardware model experiences a marginal degradation (~4.8%) in performance as compared to the software model. This is mainly attributed to the limited precision and dynamic range of network parameters when emulated using memristor devices. The proposed system is evaluated for lifespan, robustness, and energy-delay product. It is observed that the system demonstrates a reasonable robustness for device failure below 10%, which may occur due to stuck-at faults. Furthermore, 246X reduction in energy consumption is achieved when compared to a custom CMOS digital design implemented at the same technology node.