Outliers and structural breaks in time series using state space models and indicator saturation approach

With the rapid growth of available data, many companies are struggling to identify valuable trends and important changes in the data structure. Unexpected changes in unobserved components of time series, such as shocks or trend changes, can significantly impact the choice of the best fitting model, diagnostic tests, and forecast creation. To create valuable insights, the automatic detection of outliers and structural changes is more often necessary than merely desired. Kalman filteringand smoothing techniques have proved to be both precise and flexible in extracting unobserved components in time series. With incorporation of the indicator saturation approach and step-wise variable selection, we develop a technique to effectively identify outliers and changes in structural time series, including detection of the particular type of outlier or change. Considering the basic structural model, we focus on the detection of four types: additive outliers, level shifts, trendchanges, and seasonal additive outliers. We use Monte Carlo simulations to investigate the performance of the algorithms under different variances, outlier magnitudes, and locations. Next, wecompare the simulation results with the performance on a real data set with eight time series of hierarchical structure, in comparison to alternative outlier detection techniques. We found that thedeveloped method is able to capture the time series structure without over-fitting; therefore, the detection procedure is more precise. On the other hand, in comparison to the alternative techniques,our approach is computationally more expensive. Thus it should be used carefully with respect to specific use cases.