Anomaly detection and forecasting are two fundamental problems in time series analysis. Although these problems have been investigated in the literature previously, the assumptions therein are too restrictive for autonomous analysis. Common examples of limiting assumptions include perfect knowledge about the time series seasonality and/or presence of anomaly free time windows. Current practice is to manually input this knowledge into anomaly detection and forecasting systems which negate any possibility of autonomous analysis. This paper relaxes these assumptions by jointly estimating the latent components (viz.~seasonality, level changes, and spikes) in the observed time series without assuming the availability of anomaly-free time windows. The novel and flexible two stage approach proposed herein is based on (a) sparse modeling of the different latent components of the time series and (b) ARMA modeling for fitting the error. The approach leads to a solution for anomaly detection with control over type-I errors. Further, by design, the method is robust against anomalies in the observation window when it is used to solve the forecasting problem by extrapolation. Experiments are conducted with both synthetic and real datasets to demonstrate the efficacy of the proposed method. We compare our approach to various popular baselines. The presented approach outperforms baseline algorithms for anomaly detection in all our experiments and performs favorably for the forecasting task.