Neural decomposition of time-series data

We present a neural network technique for the analysis and extrapolation of time-series data called Neural Decomposition (ND). Units with a sinusoidal activation function are used to perform a Fourier-like decomposition of training samples into a sum of sinusoids, augmented by units with nonperiodic activation functions to capture linear trends and other nonperiodic components. We show how careful weight initialization can be combined with regularization to form a simple model that generalizes well. Our method generalizes effectively on the Mackey-Glass series, a dataset of unemployment rates as reported by the U.S. Department of Labor Statistics, a time-series of monthly international airline passengers, and an unevenly sampled time-series of oxygen isotope measurements from a cave in north India. We find that ND outperforms popular time-series forecasting techniques including LSTM, echo state networks, (S)ARIMA, and SVR with a radial basis function.