Title: When Complexity Is Good: Do We Need Recurrent Deep Learning For Time Series Outlier Detection?. Abstract: Outlier detection is a critical part of understanding a dataset and extracting results. Outlier detection is used in different domains for various reasons; including detecting stolen credit cards, spikes of energy usage, web attacks, or in-home activity monitoring. Within this paper, we look at when it is appropriate to apply recurrent deep learning methods for time series outlier detection versus non-recurrent methods. Recurrent deep learning methods have a larger capacity for learning complex representations in time series data. We apply these methods to various synthetic and real-world datasets, including a dataset containing information about the in-home movement of people living with dementia in a clinical study cross-referenced with their recorded unplanned hospital admissions and infection episodes. We also introduce two new outlier detection methods, that can be useful in detecting contextual outliers in time series data where complex temporal relationships and local variations in the time series are important.