Probabilistic Forecasting of Wind Power Ramps Using Autoregressive Logit Models

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Gordon Kristopher Sparks
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1 obablsc Forecasng of Wnd Poer Ramps Usng Auoregressve Log Models James W. Taylor Saїd Busness School, Unversy of Oford 8 May 5 Brunel Unversy

2 Conens Wnd poer and ramps Condonal AR log (CARL) Condonal AR mulnomal log (CARML) Emprcal evaluaon

3 Wnd Poer Daa Cree Plaska Aeolos Rokas Ieco Aeolos /6/ 9/6/ 7/7/ 4/8/ /9/ Frequency

4 obablsc Wnd Poer Forecasng 4

5 obablsc Wnd Poer Forecasng Wnd Poer Wnd Speed 5

6 Wnd Poer Ramps Sudden Large Changes =-. ( ) -.8 /6/ 9/6/ 7/7/ 4/8/ /9/ 6

7 .8.4 CARL-Indcaor Model (for <). -.4 = /6/ 9/6/ 7/7/ 4/8/ /9/ h L f oherse h I I h 7

8 CARL-GARCH h L f oherse h h For =-.: -.35 ** -.38 * -. *..7 *.88 ** 8

9 =-. ( ) 3% % % CARL-GARCH-Bernoull CARL-Indcaor-Bernoull % // 8// 5// // 9// 9

10 Mamsng a Bernoull Lkelhood As n logsc regresson, esmae CARL usng: ma T I I

11 uanle Regresson (Reve) mn β y p I y Food Ependure p Income Equvalen o mamsng lkelhood based on asymmerc Laplace (AL) densy: f AL y p p y p I y

12 Mamsng AL Lkelhood f AL y p p y p I y To esmae for a gven p, mamse AL lkelhood. Esmaor sasfes: T T I ( y ˆ ) p p To esmae p for a gven, mamse AL lkelhood (Taylor and Yu 5). Impose consran: T T Iy ˆ p p

13 =-. ( ) 3% % % CARL-GARCH-Bernoull CARL-GARCH-AL % // 8// 5// // 9// 3

14 Conens Wnd poer and ramps Condonal AR log (CARL) Condonal AR mulnomal log (CARML) Emprcal evaluaon 4

15 5 Mul-hreshold CARL K hresholds <; =-.. ML esmaon based on caegorcal dsrbuon. K j j oherse L f h h h K j j K

16 Mul-locaon CARL Bvarae Bernoull for ML esmaon. 3, 3, 3 3, 3, oherse L I and I f h j j j j j j ) ( 3) (,,,,, j j j j j j h h Aeolos Plaska

17 7 Mul-sep-ahead CARL Bvarae Bernoull for esmaon. 3, 3, 3 3, 3, oherse L I f h )) ( ( h h

18 Emprcal Evaluaon Thresholds: -.3, -., -.,.,.,.3 year of hourly observaons a 4 Cree nd farms: Esmae usng 4 monhs. Evaluae usng monh. Sep forard monh, and repea. Evaluae hour-ahead predcon: Brer N T Iy pˆ T N Brer skll score Brer BrerNave 8

19 Brer Skll Score Benchmark Threshold Mean GARCH for varance CARL for a sngle hreshold usng Bernoull CARL-Indcaor CARL-GARCH CARL for a sngle hreshold usng AL CARL-Indcaor CARL-GARCH Mul-hreshold CARL 6 hresholds hresholds Mul-sep-ahead CARL CARL-GARCH

20 Summary Adaped CARL models for nd poer ramp forecasng. Consdered mamsng AL lkelhood, as alernave o Bernoull. Ne mulnomal models: mul-hreshold mul-locaon mul-sep-ahead

21 CARL Models for Fnancal Rsk Managemen (h Kemng Yu) Esmae ereme quanle usng less ereme quanle of ereme value (EV) dsrbuon fed o eceedances. % 5% % % -% Reurns are heeroscedasc, so e allo eceedance probably and EV dsrbuon scale o be me-varyng.

22 8% 4% Eceedances Tme-varyng scale % % Eceedance obably % % % % 5% % -5% VaR(99%) Epeced shorfall (99%) %

23 Condonal Coverage for uanle Forecass Eceedances should occur randomly h probably p, so Engle and Manganell (4) es f H I( y ˆ ) p has zero uncondonal and condonal ecaon y y ˆ 3

24 Condonal Coverage for obably Forecass Eceedances should occur randomly h probably pˆ, so es f H I y pˆ has zero uncondonal and condonal ecaon. y y ppˆ 4

25 Condonal Coverage Tes Rejecons a 5% Level Benchmarks Naïve 4 4 Threshold Toal GARCH for varance CARL for a sngle hreshold usng Bernoull CARL-Indcaor CARL-GARCH CARL for a sngle hreshold usng AL CARL-Indcaor CARL-GARCH Mul-hreshold CARL 6 hresholds hresholds 6 Mul-sep-ahead CARL CARL-GARCH

January Examinations 2012

January Examinations 2012 Page of 5 EC79 January Examnaons No. of Pages: 5 No. of Quesons: 8 Subjec ECONOMICS (POSTGRADUATE) Tle of Paper EC79 QUANTITATIVE METHODS FOR BUSINESS AND FINANCE Tme Allowed Two Hours ( hours) Insrucons