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Anomaly detection on time series data is increasingly common across various industrial domains that monitor metrics in order to prevent potential accidents and economic losses. However, a scarcity of labeled data and ambiguous definitions of anomalies can complicate these efforts. Recent unsupervised machine learning methods have made remarkable progress in tackling this problem using either single-timestamp predictions or time series reconstructions. While traditionally considered separately, these methods are not mutually exclusive and can offer complementary perspectives on anomaly detection. This paper first highlights the successes and limitations of prediction-based and reconstruction-based methods with visualized time series signals and anomaly scores. We then propose AER (Auto-encoder with Regression), a joint model that combines a vanilla auto-encoder and an LSTM regressor to incorporate the successes and address the limitations of each method. Our model can produce bi-directional predictions while simultaneously reconstructing the original time series by optimizing a joint objective function. Furthermore, we propose several ways of combining the prediction and reconstruction errors through a series of ablation studies. Finally, we compare the performance of the AER architecture against two prediction-based methods and three reconstruction-based methods on 12 well-known univariate time series datasets from NASA, Yahoo, Numenta, and UCR. The results show that AER has the highest averaged F1 score across all datasets (a 23.5% improvement compared to ARIMA) while retaining a runtime similar to its vanilla auto-encoder and regressor components. Our model is available in Orion, an open-source benchmarking tool for time series anomaly detection.