Forecasting Issues in Energy Markets within a Reg-ARIMA Framework

Authors: Ilaria Lucrezia Amerise

Abstract:

Electricity markets throughout the world have undergone substantial changes. Accurate, reliable, clear and comprehensible modeling and forecasting of different variables (loads and prices in the first instance) have achieved increasing importance. In this paper, we describe the actual state of the art focusing on reg-SARMA methods, which have proven to be flexible enough to accommodate the electricity price/load behavior satisfactory. More specifically, we will discuss: 1) The dichotomy between point and interval forecasts; 2) The difficult choice between stochastic (e.g. climatic variation) and non-deterministic predictors (e.g. calendar variables); 3) The confrontation between modelling a single aggregate time series or creating separated and potentially different models of sub-series. The noteworthy point that we would like to make it emerge is that prices and loads require different approaches that appear irreconcilable even though must be made reconcilable for the interests and activities of energy companies.

Keywords: Forecasting problem, interval forecasts, time series, electricity prices, reg-plus-SARMA methods.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3607751

References:

[1] Amerise, I. L., Tarsitano, A.: Point and interval forecasts of electricity demand with Reg-SARMA models. Submitted (2018).
[2] Box, G. E. P. and Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco (1976).
[3] Chatfield, C. (2000). Time series forecasting. Chapman & Hall/CRC, Boca Raton.
[4] Charlton, N., 1, Singleton, C.: A refined parametric model for short term load forecasting. International Journal of Forecasting, 30 364–368 (2014).
[5] Diebold, F. X. (2007). Elements of forecasting. 4th Edition. Thomson South-Western. Available on line: http://threeplusone.com/fieldguide.
[6] Engle, R. and Mustafa, C. and Rice, J. (1992). “Modeling peak electricity demand”. Journal of Forecasting, 11, 241 – 251.
[7] Feldstein, M. S.: The error of forecast in econometric models when the forecast-period exogenous variables are stochastic. Econometrica, 39, 55–60 (1971).
[8] Findley, D. F., C. Monsell, B. C., Bell, W. R., Otto, M. C., Chen, B-C.: An iterative GLS approach to maximum likelihood estimation of regression models with ARIMA errors. Journal of Business & Economic Statistics, 16, 127–152 (1998).
[9] Gilchrist, W.: Statistical Forecasting. John Wiley & Sons, London (1976).
[10] Green, W. H.: Econometric Analysis (7th Edition): International edition. Pearson Education Limited (2012).
[11] Harvey, A. C., Phillips, G. D. A.: Maximum likelihood estimation of regression models with autoregressive-moving average disturbances. Biometrika, 66, 49–58 (1979).
[12] Koreisha, S. G., Pukkila, T.: Linear methods for estimating ARMA and regression models with serial correlation. Communications in Statistics-Simulation, 19, 71–102 (1990).
[13] Kavalieris, L., Hannan, E. J., Salau, M.: Generalized least squares estimation of ARMA models. Journal of Time Series Analysis, 24, 165–172 (2003).
[14] Poskitt, D., Salau, M.: On the relationship between generalized least squares and Gaussian estimation of vector ARMA models. Journal of Time Series Analysis, 16, 617–645 (1995).
[15] Tarsitano, A., Amerise, I. L.: Short-term load forecasting using a two-stage sarimax model. Energy, 133, 108–114 (2017).