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Point forecasting of univariate time series is a challenging problem withextensive work having been conducted. However, nonparametric probabilisticforecasting of time series, such as in the form of quantiles or predictionintervals is an even more challenging problem. In an effort to expand thepossible forecasting paradigms we devise and explore an extrapolation-basedapproach that has not been applied before for probabilistic forecasting. Wepresent a novel quantile Fourier neural network is for nonparametricprobabilistic forecasting of univariate time series. Multi-step predictions areprovided in the form of composite quantiles using time as the only input to themodel. This effectively is a form of extrapolation based nonlinear quantileregression applied for forecasting. Experiments are conducted on eight realworld datasets that demonstrate a variety of periodic and aperiodic patterns.Nine naive and advanced methods are used as benchmarks including quantileregression neural network, support vector quantile regression, SARIMA, andexponential smoothing. The obtained empirical results validate theeffectiveness of the proposed method in providing high quality and accurateprobabilistic predictions.

A Composite Quantile Fourier Neural Network for Multi-Step Probabilistic Forecasting of Nonstationary Univariate Time Series