Forecasting Issues in Energy Markets within a Reg-ARIMA Framework

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.




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).