Forecasting Load Using Continuous-time Fractionally Auto-Regressive Integrated Moving-Average Models with Discrete Data

Abstract

In a deregulated economy, it is important to forecast load on daily. It has many applications including energy purchasing and generation, load switching, contract evaluation, and infrastructure development. A large variety of mathematical methods have been developed for load forecasting. In this paper, we used a continuous-time autoregressive fractionally integrated moving average (CRAFIMA) model, which is defined as the stationary solution of a stochastic differential equation driven by a standard fractional Brownian motion. Like the discrete-time ARFIMA model, the CRAFIMA model is useful for studying time series with short memory, long memory and anti-persistence. Optimization issues including hyper-parameter selection and feature selection are also discussed. The study found that all three coefficients of the Hurst parameters are positive which is an advantage of using CRAFIMA algorithm. Based on this observations we conclude that self-similarity of the deseasonalized load Y(t) plays an important role in load prediction problems. The study also shows that the higher the Hurst exponent H , the bigger the range of short-term forecasting time horizons where the CRAFIMA model yields more accurate results than fitted ARIMA and f ARIMA models.