APPLICATION OF THE COMPLEX AUTOREGRESSIVE MODEL TO SOLAR RADIATION FORECAST OVER NIGERIA.

Abstract

A comparative predictive ability of the complex autoregressive (CAR) model and the conventional autoregressive (AR) model has been studied using the monthly mean daily global solar radiation data for a period of 13 years (1977-1989) obtained from 14 meteorological stations in Nigeria. Employing harmonic analysis, strong annual and semi-annual cycles were detected and removed to achieve weak stationarity of the monthly mean daily global solar radiation series. A preliminary analysis of the modified series showed significant autocorrelations at Sokoto, Nguru, Kano, Maiduguri, Bauchi, Yola, Minna, Ibadan and Benin and insignificant autocorrelations at Jos, Bida, Ikeja, Enugu and Port Harcourt. Further analysis of the series from stations with significant autocorrelations showed that a non-seasonal autoregressive model of order 1 (i.e. AR(1)) was identified as adequate. The modified series for all the study stations were then transformed into Fourier series such that each station is fitted with a wave number corresponding to the spatial scale. The resulting Fourier coefficients were used to construct the CAR model for each station. The CAR model was employed alongside the traditional AR model to conduct monthly independent forecast experiments for 29 months. An assessment of the performance of the two models for each month forecast showed that the CAR model gave higher coefficient of determination at 10 stations namely; Bauchi (35.25%), Jos (40.29%), Minna (57.92%), Yola (87.00%), Bida (38.85%), Ibadan (44.17%), Ikeja (17.43%), Enugu (39.82%), Benin (26.64%), and Port Harcourt (17.90%) compared to the traditional AR model with higher values at 4 stations namely; Sokoto (47.15%), Nguru (68.47%), Kano (56.36%), and Maiduguri (79.68%). It was noted that the CAR model proved superior to the conventional AR model only at those stations whose underlying generating process is weakly or non-autoregressive. Consequently the CAR model was suggested for prediction of monthly mean of daily global solar radiation at the stations within the coastal region where the underlying process was found to be weakly autoregressive. The traditional AR iii model on the other hand was found to be more effective in the sub-sahelian region. Within the midland and Guinea savannah regions, the most effective model for prediction of monthly mean daily global solar radiation tended to be strongly dependent on the specific station.