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The research reported in this article focuses on a comparison of two different approaches to setting error bounds, or prediction intervals, on short-term forecasting of solar irradiation as well as solar and wind farm output. Short term in this instance relates to the time scales applicable in the Australian National Electricity Market (NEM), which operates on a five-minute basis throughout the year. The Australian Energy Market Operator (AEMO) has decided in recent years that, as well as point forecasts of energy, it is advantageous for planning purposes to have error bounds on those forecasts. We use quantile regression as one of the techniques to construct the bounds. This procedure is compared to a method of forecasting the conditional variance by use of either ARCH/GARCH or exponential smoothing, whichever is more appropriate for the specific application. The noise terms for these techniques must undergo a normalising transformation before their application. It seems that, for certain applications, quantile regression performs better, and the other technique for some other applications. [ABSTRACT FROM AUTHOR]

We prove an extended Granger–Johansen representation theorem (GJRT) for finite‐ or infinite‐order integrated autoregressive time series on Banach space. We assume only that the resolvent of the autoregressive polynomial for the series is analytic on and inside the unit circle except for an isolated singularity at unity. If the singularity is a pole of finite order the time series is integrated of the same order. If the singularity is an essential singularity the time series is integrated of order infinity. When there is no deterministic forcing the value of the series at each time is the sum of an almost surely convergent stochastic trend, a deterministic term depending on the initial conditions and a finite sum of embedded white noise terms in the prior observations. This is the extended GJRT. In each case the original series is the sum of two separate autoregressive time series on complementary subspaces – a singular component which is integrated of the same order as the original series and a regular component which is not integrated. The extended GJRT applies to all integrated autoregressive processes irrespective of the spatial dimension, the number of stochastic trends and cointegrating relations in the system and the order of integration. [ABSTRACT FROM AUTHOR]