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Anomaly detection in time series data is a critical task in various domains, including finance, healthcare, cybersecurity and industry. Traditional methods, such as time series decomposition, clustering, and density estimation, have provided robust solutions for identifying anomalies that exhibit distinct patterns or significant deviations from normal data distributions. Recent advancements in machine learning and deep learning have further enhanced these capabilities. This paper introduces a novel method for anomaly detection that combines the strengths of autoencoders and recurrent neural networks (RNNs) with an reconstruction error feedback mechanism based on Mean Squared Error. We compare our method against classical techniques and recent approaches like OmniAnomaly, which leverages stochastic recurrent neural networks, and the Anomaly Transformer, which introduces association discrepancy to capture long-range dependencies and DCDetector using contrastive representation learning with multi-scale dual attention. Experimental results demonstrate that our method achieves superior overall performance in terms of precision, recall, and F1 score. The source code is available at http://github.com/mribrahim/AE-FAR