Research Article

Time-Series Regression Model for Prediction of Mean Daily Global Solar Radiation in Al-Ain, UAE

Table 4

ARIMA model parameters.

ARMA ( 𝑝 , π‘ž )AR coefficients ( 𝑑 value)MA coefficients ( 𝑑 value)Model remarkNormalized BIC (SPSS)AIC, SBC, SE, SSE

(4, 3) πœ™ 1 = 0 . 5 4 9 4 ( 2 7 . 2 3 2 ) πœƒ 1 = 0 . 0 7 2 1 ( 5 . 7 4 8 ) A I C = 2 4 0 8 . 1 0 3 7
πœ™ 2 = βˆ’ 0 . 1 1 9 3 ( βˆ’ 9 . 1 7 6 ) πœƒ 2 = βˆ’ 0 . 1 1 0 9 ( βˆ’ 9 . 1 1 4 ) βˆ’2.159 S B C = 2 4 5 1 . 5 2 1 1
πœ™ 3 = 1 . 0 0 6 4 ( 7 8 . 0 4 8 ) πœƒ 3 = 0 . 9 5 7 2 ( 7 8 . 8 1 0 ) S S E = 4 1 1 . 7 0 7 0
πœ™ 4 = βˆ’ 0 . 4 5 3 4 ( βˆ’ 2 5 . 8 9 1 ) S E = 0 . 3 3 6 2

(4, 4) πœ™ 1 = 0 . 5 2 7 2 ( 1 3 . 0 9 4 ) πœƒ 1 = 0 . 0 4 8 3 ( 1 . 1 1 6 ) Over-fitting A I C = 2 4 1 0 . 0 4 5 3
πœ™ 2 = βˆ’ 0 . 0 9 5 4 ( βˆ’ 4 . 6 0 5 ) πœƒ 2 = βˆ’ 0 . 0 9 4 2 ( βˆ’ 5 . 3 8 5 ) βˆ’2.150 S B C = 2 4 5 9 . 6 6 5 2
πœ™ 3 = 0 . 9 8 6 6 ( 4 7 . 7 1 8 ) πœƒ 3 = 0 . 9 4 2 0 ( 4 9 . 8 9 1 ) S S E = 4 1 1 . 7 0 1 0
πœ™ 4 = βˆ’ 0 . 4 3 6 9 ( βˆ’ 1 1 . 7 3 7 ) πœƒ 4 = 0 . 0 1 6 6 ( 0 . 4 5 2 ) S E = 0 . 3 3 6 2

(2, 1) πœ™ 1 = 1 . 4 5 0 4 ( 7 6 . 7 8 9 ) πœƒ 1 = 0 . 9 6 9 9 ( 9 7 . 0 8 7 ) A I C = 2 4 1 6 . 2 3 8 5
πœ™ 2 = βˆ’ 0 . 4 5 6 8 ( βˆ’ 2 6 . 5 6 1 ) βˆ’2.168 𝐒 𝐁 𝐂 = 𝟐 πŸ’ πŸ‘ πŸ’ . πŸ– πŸ’ πŸ“ πŸ—
S S E = 4 1 3 . 5 6 3 6
S E = 0 . 3 3 6 7

(3, 1) πœ™ 1 = 1 . 4 5 0 4 ( 7 5 . 1 8 3 ) πœƒ 1 = 0 . 9 7 1 9 ( 9 8 . 7 8 0 ) Over-fitting A I C = 2 4 1 7 . 9 7 8 3
πœ™ 2 = βˆ’ 0 . 4 4 6 1 ( βˆ’ 1 5 . 7 3 2 ) βˆ’2.165 S B C = 2 4 4 2 . 7 8 8 2
πœ™ 3 = βˆ’ 0 . 0 0 8 7 ( βˆ’ 0 . 5 0 7 ) S S E = 4 1 3 . 5 3 3 6
S E = 0 . 3 3 6 8

(2, 2) πœ™ 1 = 1 . 4 6 9 2 ( 4 0 . 1 5 4 ) πœƒ 1 = 0 . 9 9 2 0 ( 2 4 . 5 7 5 ) Over-fitting  A I C = 2 4 1 7 . 9 8 6 2
πœ™ 2 = βˆ’ 0 . 4 7 4 6 ( βˆ’ 1 3 . 4 4 1 ) πœƒ 2 = βˆ’ 0 . 0 1 8 5 ( βˆ’ 0 . 5 1 0 ) βˆ’2.165  S B C = 2 4 4 2 . 7 9 6 2
S S E = 4 1 3 . 5 3 4 5
S E = 0 . 3 3 6 8