Neural Decomposition of Time-Series Data for Effective Generalization

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 data set of unemployment rates as reported by the U.S. Department of Labor Statistics, a time-series of monthly international airline passengers, the monthly ozone concentration in downtown Los Angeles, 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 long short-term memory network, echo-state networks, autoregressive integrated moving average (ARIMA), seasonal ARIMA, support vector regression with a radial basis function, and Gashler and Ashmore's model.