Semiparametric and parametric distributional forecasting of univariate time series using non‐Gaussian ARMA models based on D‐vines

Abstract A methodology for modelling and forecasting univariate time series using non‐Gaussian ARMA and seasonal ARIMA models based on D‐vine copulas is proposed. By combining a parametric D‐vine process to describe serial dependence with a nonparametric or parametric model of the marginal distribution, the method offers improved modelling and distributional forecasting for time series that have a non‐Gaussian distribution and a nonlinear dependence on past values. While D‐vine copula‐based models of univariate time series are known to generalize the classical Gaussian autoregressive (AR) model, an innovative method of parametrization based on the Kendall partial autocorrelation function is shown to permit models that generalize any ARMA model. Simulations and examples of real data show the forecasting advantages of using non‐Gaussian and nonlinear serial dependence structures, as well as the advantages of improved marginal modelling that are offered by a copula approach.