1 AR IMA GARCH. Electr ic ity pr ice foreca sting m ethods com b in ing AR IM A and GARCH w ith conf idence in terva ls

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1 Vol. 36 No. 12 Dec ARIM A GARCH,, (, ) :,,A IC,,AR IMA GARCH,,,, PJM, :; ; A IC; AR IMA; GARCH; : ( ) : (19572),,,, : TM 29; F : A: (2008) Electr ic ity pr ice foreca sting m ethods com b in ing AR IM A and GARCH w ith conf idence in terva ls ZENG M ing, ZHAO Yong2liang, ZHANG J ing ( School of Business Adm inistration, North China Electric Power Univ., Beijing , China) Abstract:Base on research on existing methods for electricity price forecasting, a new combined method with confidence intervals is proposed. The run test was used to judge the price series stationarity and the A IC criterion method was app lied to determ ine the order, so the subjectivity can be avoided and the forecasting accuracy can be improved. Moreover, the AR IMA and GARCH were effectively combined though heteroscedasticity determ ination for electricity price error series. Al2 so, the price forecasting method with confidence intervals is p roposed, which overcomes the shortcom ings of single2point forecasting and increases the algorithm flexibility to enable the participators to choose the price fluctuation range according to their expectations on price forecasting accuracy. The model is p roved effective by data on PJM market. Key words: electricity p rice; run test; A IC criterion; AR IMA algorithm, GARCH algorithm; confidence interval,, [ 124 ],, [ 527 ],,,,,,, AR IMA GARCH,,,, 1AR IMA GARCH 1. 1 (1)

2 2 ( 1491) 2008, 36 (12) P t P, P -,+, (2) N, N = N 1 + N 2, N 1 N 2 + -, r, N 1, N 2 15, Z = r - E ( r) D ( r) N (0, 1), E ( r) = 2N 1N 2 N D ( r) = 2N 1N 2 (2N 1 N 2 - N ) N 2 (N - 1) (1) + 1 (2) (3),Z,, Z < 1. 96,,, 1. 2 (1) { P t }, g P t = P t+1 - P t, t = 1, 2, (4) { g P t },{ g P t },,, (2) { P t },24 h,, g P t = P t+24 - P t, t = 1, 2, (5),, 1. 3 A IC ARMA ( p^, q) { P t }, 2 a ( p, q),a IC : A IC ( p, q) ^ = ln 2 a ( p, q) + 2 ( p + q) /N (6) p, q, { P t },(6) A IC, ( 6), 1. 4,AR IMA, P t, { E t } E t = P t - P t (7),,, ( Spearman) [ 8 ] { E t }, : (1) {E t }OLSe t ; (2) e t E t, n r s = 1-6 ( e t - E t ) 2 (3) t t = r s n r 2 s n ( n 2-1) (8) n - 2 t (9) 1 -, t > t /2 ( n - 2), ;, { E t },AR IMA ;,GARCH 1. 5,,

3 , AR IMA GARCH 3 ( 1492),,,,: (1) AR IMA P t; (2) :,, P t ; (3) :( 3), P t, P t,, M ( P ( t) ) - t = t ( n - 1) (10) S / n M ( P t ) ; S ; n ; 1), 1 -, t /2 ( n - M ( P ( t) ) - P{ t /2 ( n - 1) } S / n,: P ( t) = P ( t) - S = 1 - (11) n t /2 ( n - 1) (12),[ P ( t), P ( t) ] 1. 6 AR IMA GARCH ( 1): (1) ; (2), ;,(3) ; (3) A IC AR IMA; (4) ; (5) ; ; (10) ; (6),( 7 ) ; (7) AR IMA; (8) ; (9),,(13) ;,(7) ; (10) ARCH; (11) ARCH, ; (12) 7; 7, ARCH ;, GARCH (1, 1); (13) 1AR IMA GARCH 2AR IMA GARCH PJM AR IMA GARCH 1,24,, 15: 00 18: ,,,,, ,, 1, 24 h;,,,arma, A IC, ARMA ( p, q)p = 15, q = 14, A IC, A IC = , ARMA ( p, q) :

4 4 ( 1493) 2008, 36 (12) 1 PJM : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : < (B ) P t = (B ) e t B n P t = P t+n - P t B n e t = e t+n - e t < (B ) = B B B B B B B B B B B B B B B 15 (B ) = B B B B B B B B B B B B B B 14 e t, 2. 2, ARMA (15, 14)6 12 h ARMA 3,ARMA (15, 14)

5 , AR IMA GARCH 5 ( 1494),,,,, 2. 3 : 95% (1 - = 1-5% ), r s = ,t = ,t = < t /2 ( n - 2) = ,AR IMA,, ARMA A IC, ARMA ( p, q)p = 4, q = 2, A IC, A IC = , ARMA (4, 2) : : A (B ) e t = C (B ) t A (B ) = B B B B 4 C (B ) = B B 2, 4,, % : : : : : : : : : : : : : : : : : : : : : : : : ,2 2. 4, ARMA ( 15, 14 ) ARMA (4, 2),, ,, : [ 1 ] Contrersa J, Espinola R, Nogales F J, et al. AR IMA Model to Predict N ext2day Electricity Prices[ J ]. IEEE Trans on

6 Vol. 36 No. 12 Dec , 1, 2 (1., ; 2., ) :,,,,,,, : ; ; ; : ( ) ; (06JG102) :(19642),,,, : TM73 : A: (2008) O ptim iza tion design of genera tion capac ity adequacy ba sed on in tegra ted resource plann ing TAN Zhong2fu 1, L IU L i2ping 1, L IU X ue2song 2 ( Institute of Electricity Econom ics, North China Electric Power Univ., Beijing , China; 2. Shenyang Power Supp ly Company, Shenyang , China) Abstract: The factors influencing the generation capacity adequacy ( GCA) in the electricity market are analyzed, and the regional outsourcing and demand2side response were used as the reserve capacity resource to coordinate the availa2 ble generation capacity. Based on that, the GCA is defined and a GCA evaluation method which can quantitatively e2 valuate the system s adequacy is p roposed. Consequently, the goal that the GCA can be monitored and ensured is a2 chieved. The effectiveness of the method is verified through an examp le. Key words: electricity market; generation capacity; reserve capacity; adequacy evaluation 1 ( Generation Capacity Ade2 quacy, GCA),,,,,, [ 2 ] Power System s, 2003, 18 (3) : [ 2 ],,,. AR IMA [ J ]., 2004, 24 ( 12) : [ 3 ] Contrersa J, PlazsaM A, Esp inola R, et al. Day2ahead Elec2 tricity Price Forecasting U sing the W avelet Transform and AR IMA Model[ J ]. IEEE Trans on Power System s, 2005, 20 (2) : [ 4 ] Garcia R C, Contreras J, M van Akkeren, et al. A GARCH Forecasting Model to Predict Day2Ahead Electricity Prices [ J ]. IEEE Trans on Power System s, 2005, 20 ( 2 ) : [ 5 ],,. [ J ]., 2000, 24 (22) : [ 6 ] Szkuta B R, Sanabria L A, D illon T S. Electricity Price Short2term Forecasting U sing A rtificial Neural Networks[ J ]. IEEE Trans on Power Systems, 1999, 14 (3) : [ 7 ],,,. [ J ]., 2005, 31 ( 4) : 32233, 55. [ 8 ],. [M ]. :, : :

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