Gaussian processes with skewed Laplace spectral mixture kernels for long-term forecasting

Abstract Long-term forecasting involves predicting a horizon that is far ahead of the last observation. It problem high practical relevance, for instance companies in order to decide upon expensive long-term investments. Despite recent progress and success Gaussian processes (GPs) based on spectral mixture kernels, remains challenging these kernels because they decay exponentially at large horizons. This mainly due their use Gaussians model densities. Characteristics signal important can be unravelled by investigating distribution Fourier coefficients (the training part of) signal, which non-smooth, heavy-tailed, sparse, skewed. The heavy tail skewness characteristics such distributions domain allow capture long-range covariance time domain. Motivated observations, we propose densities using skewed Laplace (SLSM) its peaks, sparsity, non-smoothness, characteristics. By applying inverse Transform this density obtain new GP kernel forecasting. In addition, adapt lottery ticket method, originally developed prune weights neural network, GPs automatically select number components. Results extensive experiments, including multivariate series, show beneficial effect proposed SLSM extrapolation robustness choice