Financial econometrics is a well established discipline providing statistical and computational tools for characterizing financial time series, but lacks algorithms and tools for big data. Deep learning, on the other hand, is a powerful tool for big data analysis but their treatment as black-boxes has hampered their use in many financial applications. This session will seat deep learning in statistical frameworks to provide model interpretability, stability and error analysis. We begin by reviewing theoretical results from approximation and statistical machine learning theory to develop intuition for neural networks from geometric and numerical analysis perspectives. Such results are appropriate for i.i.d. data only, but provide a principled approach to architecture design. In the second part of the session, we shall review concepts in autoregressive and moving average models for time series data and show how they extend to Recurrent and Convolutional Neural Networks. Relaxing the requirement of covariance stationary data, we show how dynamic exponential smoothing is used in RNNs to give state-of-the art regime switching networks such as a Long Short Term Memory (LSTM) and Gated Recurrent Unit (GRU). Finally we explain how autoencoders generalize principal component analysis (PCA) to non-linear factor analysis.