Time series anomaly detection receives increasing research interest given the growing number of data-rich application domains. Recent additions to anomaly detection methods in research literature include deep learning algorithms. The nature and performance of these algorithms in sequence analysis enable them to learn hierarchical discriminating features and time-series temporal nature. However, their performance is affected by the speed at which the time series arrives, the use of a fixed threshold, and the assumption of Gaussian distribution on the prediction error to identify anomalous values. An exact parametric distribution is often not directly relevant in many applications and it’s often difficult to select an appropriate threshold that will differentiate anomalies with noise. Thus, implementations need the Prediction Interval (PI) that quantifies the level of uncertainty associated with the Deep Neural Network (DNN) point forecasts, which helps in making a better-informed decision and mitigates against false anomaly alerts. To achieve this, a new anomaly detection method is proposed that computes the uncertainty in estimates using quantile regression and used the quantile interval to identify anomalies. Similarly, to handle the speed at which the data arrives, an online anomaly detection method is proposed where a model is trained incrementally to adapt to the concept drift that improves prediction. This is implemented using a window-based strategy, in which a time series is broken into sliding windows of sub-sequences as input to the model. To adapt to concept drift, the model is updated when changes occur in the new arrival instances. This is achieved by using anomaly likelihood which is computed using the Q-function to define the abnormal degree of the current data point based on the previous data points. Specifically, when concept drift occurs, the proposed method will mark the current data point as anomalous. However, when the abnormal behavior continues for a longer period of time, the abnormal degree of the current data point will be low compared to the previous data points using the likelihood. As such, the current data point is added to the previous data to retrain the model which will allow the model to learn the new characteristics of the data and hence adapt to the concept changes thereby redefining the abnormal behavior. The proposed method also incorporates feature extraction to capture structural patterns in the time series. This is especially significant for multivariate time-series data, for which there is a need to capture the complex temporal dependencies that may exist between the variables. In summary, this thesis contributes to the theory, design, and development of algorithms and models for the detection of anomalies in both static and evolving time series data. Several experiments were conducted, and the results obtained indicate the significance of this research on offline and online anomaly detection in both static and evolving time-series data. In chapter 3, the newly proposed method (Deep Quantile Regression Anomaly Detection Method) is evaluated and compared with six other prediction-based anomaly detection methods that assume a normal distribution of prediction or reconstruction error for the identification of anomalies. Results in the first part of the experiment indicate that DQR-AD obtained relatively better precision than all other methods which demonstrates the capability of the method in detecting a higher number of anomalous points with low false positive rates. Also, the results show that DQR-AD is approximately 2 – 3 times better than the DeepAnT which performs better than all the remaining methods on all domains in the NAB dataset. In the second part of the experiment, sMAP dataset is used with 4-dimensional features to demonstrate the method on multivariate time-series data. Experimental result shows DQR-AD have 10% better performance than AE on three datasets (SMAP1, SMAP3, and SMAP5) and equal performance on the remaining two datasets. In chapter 5, two levels of experiments were conducted basis of false-positive rate and concept drift adaptation. In the first level of the experiment, the result shows that online DQR-AD is 18% better than both DQR-AD and VAE-LSTM on five NAB datasets. Similarly, results in the second level of the experiment show that the online DQR-AD method has better performance than five counterpart methods with a relatively 10% margin on six out of the seven NAB datasets. This result demonstrates how concept drift adaptation strategies adopted in the proposed online DQR-AD improve the performance of anomaly detection in time series. / Petroleum Technology Development Fund (PTDF)