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❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

▼❡r❝❛t✐ ❊♥❡r❣❡t✐❝✐ ❡ ▼❡t♦❞✐ ◗✉❛♥t✐t❛t✐✈✐✿ ✉♥ ♣♦♥t❡ tr❛ ✉♥✐✈❡rs✐tá ❡ ❛③✐❡♥❞❡ ❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐

❆❝❝❡♥t✉r❡ ❙P❆✱ ▼✐❧❛♥ ✲ ■t❛❧②

P❛❞♦✈❛✱ ❖❝t♦❜❡r ✶✸✱ ✷✵✶✻

❈✉r✈❡

❍P❋❈ ❞❡✜♥✐t✐♦♥ ❚❤❡ ❤♦✉r❧② ♣r✐❝❡ ❢♦r✇❛r❞ ❝✉r✈❡ ✭❍P❋❈✮ q✉♦t❡❞ ✐♥ ❛ ❣✐✈❡♥ ♠❛r❦❡t ❛t ❛ ❞❛② t ✐s ❛ ♠❛t❤❡♠❛t✐❝❛❧ ❢✉♥❝t✐♦♥ ˆ ft (T, h) ❛ss♦❝✐❛t✐♥❣ t♦ ❡❛❝❤ ❞❛② T ✐♥ t❤❡ ❢✉t✉r❡ ❛ ♣r✐❝❡ ❢♦r t❤❡ ❝♦♠♠✐t♠❡♥t t♦ ❞❡❧✐✈❡r ♦♥❡ ♠❡❣❛✇❛tt✲❤♦✉r ❢♦r ❛ s♣❡❝✐✜❝ ❤♦✉r h ♦❢ t❤❛t s♣❡❝✐✜❝ ❞❛②✱ ✐✳❡✳ t❤❡ t❡r♠ str✉❝t✉r❡ ♦❢ ❡❧❡❝tr✐❝✐t② ❢♦r✇❛r❞ ♣r✐❝❡s ❛s q✉♦t❡❞ ✇✐t❤ ❤♦✉r❧② ❣r❛♥✉❧❛r✐t② ❛❝r♦ss t❤❡ ♠❛t✉r✐t② ❞✐♠❡♥s✐♦♥✳

❆❝❛❞❡♠✐❝ ❛♥❞ ✐♥❞✉str✐❛❧ r❡❧❡✈❛♥❝❡✿

✶

▼❛r❦✐♥❣ ❡♥❡r❣② ♣♦rt❢♦❧✐♦s t♦ ♠❛r❦❡t q✉♦t❡s ✭❚❡✐①❡✐r❛ ▲♦♣❡s ✭✷✵✵✼✮✮✱

✷

❈❛❧✐❜r❛t✐♥❣ ❛r❜✐tr❛❣❡ ♠♦❞❡❧s ✭■s❧②❛❡✈✲❉❛t❡ ✭✷✵✶✺✮✮✱

✸

❆♥❛❧②③✐♥❣ r✐s❦ ♣r❡♠✐❛ ✭❋r❡st❛❞✲❇❡♥t❤✲❑♦❡❦❡❜❛❦❦❡r ✭✷✵✶✵✮✮✱

✹

❈♦♥❝❡✐✈✐♥❣ ❛♥❞ t❡st✐♥❣ ♣r♦♣ tr❛❞✐♥❣ r✉❧❡s ✭❋✉r✐♦✲▲✉❝✐❛ ✭✷✵✵✾✮✮✱

✺

❈♦♥s✉♠♣t✐♦♥ ♦♣t✐♠✐③❛t✐♦♥ ✐♥ ❡♥❡r❣②✲✐♥t❡♥s✐✈❡ ♣r♦❝❡ss❡s ✭▲✐♠❛ ✭✷✵✶✺✮✮✱

✻

❘❡❛❧ ♦♣t✐♦♥ ❜❛s❡❞ ♣❤②s✐❝❛❧ ❛ss❡t ✈❛❧✉❛t✐♦♥ ✭◆❛s❛❦❦❛❧❛❛✲❋❧❡t❡♥ ✭✷✵✵✺✮✮✳

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

▲✐t❡r❛t✉r❡

❋❧❡t❡♥✲▲❡♠♠✐♥❣ ✭✷✵✵✸✮ ❜❡♥❝❤♠❛r❦ ♣❛r❛♠❡tr✐❝ ❝✉r✈❡ ✜tt✐♥❣ t♦ ❛ ♣r♦♣r✐❡t❛r② ❡q✉✐❧✐❜r✐✉♠ ♠♦❞❡❧✳ ❑♦❡❦❦❡❜❛❦❦❡r✲❖s❆❞❧❛♥❞ ✭✷✵✵✹✮ ❛♥❞ ❇❡♥t❤✲❑♦❡❦❡❜❛❦❦❡r✲❖❧❧♠❛r ✭✷✵✵✼✮ ❝♦♠❜✐♥❡ s❡❛s♦♥❛❧✐t✐❡s ✇✐t❤ s♣❧✐♥❡s ❛♥❞ ♠✐♥✐♠✐③❡ ❝✉r✈❡ ❝♦♥✈❡①✐t②✳ ❇♦r❛❦ ❛♥❞ ❲❡r♦♥ ✭✷✵✵✽✮ ♣r♦♣♦s❡ ❛ ♣❛rs✐♠♦♥✐♦✉s✱ s♠♦♦t❤✱ ❛♥❞ s❡❛s♦♥❛❧ ❢♦r✇❛r❞ ❝✉r✈❡✳ ❍✐❧❞♠❛♥♥✲❑❛✛❡✲❆♥❞❡rs♦♥ ✭✷✵✶✷✮ ♠♦❞❡❧ ❤♦✉r❧② ♣r✐❝❡s✳ P❛r❛s❝❤✐✈✲❋❧❡t❡♥✲❙❝❤✉r❧❡ ✭✷✵✶✺✮ ❡①t❡♥❞ ❇❡♥t❤ ❡t ❛❧✳ ✭✷✵✵✼✮ ♠❡t❤♦❞ t♦ ❛❝❝♦✉♥t ❢♦r ❤♦✉r❧② ❣r❛♥✉❧❛r✐t② ❛♥❞ ✇❡❛t❤❡r✲❧✐♥❦❡❞ ❢❛❝t♦rs✳

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

■ss✉❡

❲❡ ♣✉t ❢♦r✇❛r❞ ❛ ❘❛t✐♦♥❛❧ ❈♦♥str✉❝t✐✈❡ ❉❡✜♥✐t✐♦♥ ♦❢ ❡❧❡❝tr✐❝✐t② ❢♦r✇❛r❞ ❝✉r✈❡ ✇✐t❤ t❤✐♥ ❣r❛♥✉❧❛r✐t②✳ ❈♦♥str✉❝t✐✈❡ ❂ ❆❧❣♦r✐t❤♠✐❝✳ ❘❛t✐♦♥❛❧ ❂ ❈♦♠♣❧②✐♥❣ ✇✐t❤ ✺ ❞❡s✐r❛❜❧❡ ♣r♦♣❡rt✐❡s✿

✶

❘❛✇ ♣r✐❝❡ s❡r✐❡s ✉♥❞❡r❣♦ ❛ ✜❧t❡r✐♥❣ ♣r♦❝❡❞✉r❡ t♦ ✜♥❡❧② ❞❡t❡❝t ❛♥❞ s✐♥❣❧❡ ♦✉t ❞❛t❛ ♦✉t❧✐❡rs❀

✷

❈✉r✈❡ s❤❛♣❡ ❡♠❜❡❞s ❛ ❝♦♠♣r❡❤❡♥s✐✈❡ ❜✉♥❞❧❡ ♦❢ ♣❡r✐♦❞✐❝❛❧ ♣❛tt❡r♥s ✉♥✈❡✐❧❡❞ ❜② ♣❛st q✉♦t❡s❀

✸

❈✉r✈❡ ❧❡✈❡❧ ✐s ❥♦✐♥t❧② ❝♦♥s✐st❡♥t t♦ st❛♥❞✐♥❣ ❜❛s❡❧♦❛❞ ❛♥❞ ♣❡❛❦❧♦❛❞ ❢✉t✉r❡s q✉♦t❛t✐♦♥s❀

✹

❈✉r✈❡ ♣❛t❤ s❛t✐s✜❡s r❡❣✉❧❛r✐t② ♣r♦♣❡rt✐❡s✿ s♠♦♦t❤♥❡ss✱ ♠♦♥♦t♦♥✐❝✐t② ♣r❡s❡r✈❛t✐♦♥✱ ❝r♦ss✲s❡❝t✐♦♥❛❧ st❛❜✐❧✐t②✱ t✐♠❡ ❧♦❝❛❧♥❡ss ✭❍❛❣❛♥✲❲❡st ✭✷✵✵✻✮✮❀

✺

❋♦r✇❛r❞ ❡st✐♠❛t❡ q✉❛❧✐t② ✐s ❛ss❡ss❡❞ t❤r♦✉❣❤ ❞❡❞✐❝❛t❡❞ ❡♠♣✐r✐❝❛❧ t❡sts✳

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❊①❛♠♣❧❡ ♦❢ ❢✉t✉r❡s ♠❛r❦❡t ❞❛t❛

❋✐❣✉r❡✿ ❋✉t✉r❡s ♠❛r❦❡t ❞❛t❛ ❢r♦♠ ❊❊❳✱ ◆♦✈❡♠❜❡r ✼✱ ✷✵✶✸✳ ❙❡tt❧❡♠❡♥t ♣r✐❝❡s ❛r❡ ❣✐✈❡♥ ✐♥ ❊✉r✴▼❲❤✳

Jan14 Apr14 Jul14 Oct14 Feb15 May15 Aug15 Dec15 25 30 35 40 45 50 55 60 Baseload Peakload

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

■❞❡❛

✶

❘❡❞✉❝t✐♦♥ t♦ ❢♦r✇❛r❞ ❦❡r♥❡❧✿ ♦❜s F = ✶ τ e − τ b τe

τb ft(u)du

→ ft(·) → ❛❧❧ ♣r✐❝❡s✳

✷

❈♦♥str✉❝t✐♦♥ ♦❢ ❢♦r✇❛r❞ ❦❡r♥❡❧✿ ❆P❚✿ ❆r❜✐tr❛❣❡✲❢r❡❡ s♣♦t ♠♦❞❡❧ dS (t) → ft(u) := E∗

t [S(u)]❀

❖✉r ♠❡t❤♦❞ ✐s ❞②♥❛♠✐❝ ♠♦❞❡❧ ✐♥❞❡♣❡♥❞❡♥t✿ ft(u) := Λt(u) + εt(u) + ϕt (u) ,

Λ → P❡r✐♦❞✐❝❛❧ ♣❛tt❡r♥s ✭❍✐st♦r✐❝❛❧ ✐♥❢♦r♠❛t✐♦♥✮✱ εt → ❈❛❧✐❜r❛t✐♦♥ t♦ ❜❛s❡❧♦❛❞ ❢♦r✇❛r❞s ✭❘✐s❦✲♥❡✉tr❛❧ ✐♥❢♦r♠❛t✐♦♥✮✱ ϕt → ❈❛❧✐❜r❛t✐♦♥ ♦❢ ♣❡❛❦❧♦❛❞ ❢♦r✇❛r❞s ✭❘✐s❦✲♥❡✉tr❛❧ ✐♥❢♦r♠❛t✐♦♥✮✳

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❈♦♥str✉❝t✐♦♥

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❉❛t❛

▼❛r❦❡t✿ ❊P❊❳ ❙♣♦t ❙❊ ❛♥❞ ❊❊❳ P♦✇❡r ❉❡r✐✈❛t✐✈❡s❀ ❉❛t❛✿

• ❙♣♦t

→ ✷✹×✷✱✺✷✺ ♦❜s✳ ❬❏❛♥✳ ✶✱ ✷✵✵✾ ✲ ◆♦✈✳ ✷✼✱ ✷✵✶✺❪❀ ❋♦r✇❛r❞ → ❜❛s❡❧♦❛❞ ❛♥❞ ♣❡❛❦❧♦❛❞✱ ♦♥ ◆♦✈✳ ✷✼✱ ✷✵✶✺✳

❋✐❧t❡r✐♥❣✿

Aug09 Dec10 May12 Sep13 Feb15

• 60
• 40
• 20

20 40 60 80 100 Filtered prices Filter for preprocessing Identified Outliers Aug09 Dec10 May12 Sep13 Feb15 10 20 30 40 50 60 70 80 90 Daily price Filtered daily trend

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❆♥❛❧②s✐s ♦❢ ♣r❡❞✐❝t❛❜❧❡ ❝♦♠♣♦♥❡♥ts

❆ s❡❛s♦♥❛❧✐t② ❢✉♥❝t✐♦♥ ❢♦r t❤❡ ●❡r♠❛♥ ♠❛r❦❡t

Λ(u) = a ❝♦s ✷π ✸✻✺ u + b

• ▲♦♥❣ t❡r♠ ✭▲❚✮

+

✼

• j=✶

cj✶(u ∈ dayj)

• ❲❡❡❦❧② ✭❲✮

+

✷✹

• h=✶

✹

• l=✶

dh,l✶(u ∈ hourh ∩ u ∈ Cl)

• ❉❛✐❧② ✭❉✮

, ✇❤❡r❡✿ u ∈ R✱ ❛♥❞ a, cj, dh,l ∈ R ∀h, j, k, l ❛♥❞ b ∈ [✵, ✷π]✳ dayj ❢♦r j = ✶, . . . , ✼ ✿❂ t❤❡ s❡t ♦❢ ♣♦✐♥ts ✐♥ t❤❡ jt❤ ❞❛② ♦❢ t❤❡ ✇❡❡❦ ✭✐✳❡✳ j = ✶ r❡❢❡r t♦ ❙✉♥❞❛② . . . ✱ j = ✼ r❡❢❡r t♦ ❙❛t✉r❞❛②✮✳ hourh✱ h = ✶, . . . , ✷✹✱ ✿❂ t❤❡ s❡t ♦❢ ♣♦✐♥ts ✐♥ t❤❡ ht❤ ❤♦✉r ♦❢ ❛ ❞❛②✳ C✶ := ✇♦r❦✐♥❣ ❞❛②s ✐♥ t❤❡ ❝♦❧❞ s❡❛s♦♥ ✭❢r♦♠ ❖❝t♦❜❡r t♦ ▼❛r❝❤✮✳ C✷ := ♥♦♥✲✇♦r❦✐♥❣ ❞❛②s ✐♥ t❤❡ ❝♦❧❞ s❡❛s♦♥ ✭❢r♦♠ ❖❝t♦❜❡r t♦ ▼❛r❝❤✮✳ C✸ := ✇♦r❦✐♥❣ ❞❛②s ✐♥ t❤❡ ✇❛r♠ s❡❛s♦♥ ✭❢r♦♠ ❆♣r✐❧ t♦ ❙❡♣t❡♠❜❡r✮✳ C✹ := ♥♦♥✲✇♦r❦✐♥❣ ❞❛②s ✐♥ t❤❡ ✇❛r♠ s❡❛s♦♥ ✭❢r♦♠ ❆♣r✐❧ t♦ ❙❡♣t❡♠❜❡r✮✳ ✷✹

h=✶ dh,l = ✵,

l = ✶, . . . , ✹✳

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

▲♦♥❣ t❡r♠ ❛♥❞ ✇❡❡❦❧② ♣r❡❞✐❝t❛❜❧❡ ❝♦♠♣♦♥❡♥ts

❋✐❣✉r❡✿ ❊st✐♠❛t❡❞ ❞❛✐❧② s❡❛s♦♥❛❧✐t② ❢✉♥❝t✐♦♥ ✭❧♦♥❣ t❡r♠ ❛♥❞ ✇❡❡❦❧②✮ ❢r♦♠ ❏❛♥✉❛r② ✶✱ ✷✵✶✹ t♦ ❉❡❝❡♠❜❡r ✸✶✱ ✷✵✶✹✳

Jan Feb Apr May Jul Sep Oct Dec −15 −10 −5 5 Seasonality estimated over the first year

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❉❛✐❧② s❤❛♣❡

❋✐❣✉r❡✿ ❍♦✉r❧② s❡❛s♦♥❛❧✐t② ♣r♦✜❧❡✿ ✈❛r✐❛❜❧❡s dh,l ❛r❡ ♣❧♦tt❡❞ ❢♦r h = ✶, . . . , ✷✹✳ ❲♦r❦✐♥❣ ❞❛②s ✲ ❝♦❧❞ s❡❛s♦♥ ◆♦♥✲✇♦r❦✐♥❣ ❞❛②s ✲ ❝♦❧❞ s❡❛s♦♥

2 4 6 8 10 12 14 16 18 20 22 24 −20 −15 −10 −5 5 10 15 20 Hourly profile cluster C1 2 4 6 8 10 12 14 16 18 20 22 24 −20 −15 −10 −5 5 10 15 20 Hourly profile cluster C2

❲♦r❦✐♥❣ ❞❛②s ✲ ✇❛r♠ s❡❛s♦♥ ◆♦♥✲✇♦r❦✐♥❣ ❞❛②s ✲ ✇❛r♠ s❡❛s♦♥

2 4 6 8 10 12 14 16 18 20 22 24 −20 −15 −10 −5 5 10 15 20 Hourly profile cluster C3 2 4 6 8 10 12 14 16 18 20 22 24 −20 −15 −10 −5 5 10 15 20 Hourly profile cluster C4

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

▼❛r❦❡t ❝♦♥s✐st❡♥❝② ❛❞❥✉s♠❡♥t

❇❛s❡❧♦❛❞ ❝♦♥s✐st❡♥❝② ❛❞❥✉s♠❡♥t ❲❡ ❞❡✜♥❡ ε t❤r♦✉❣❤ t❤❡ ♠♦♥♦t♦♥❡ ❝♦♥✈❡① s♣❧✐♥❡ ♣✉t ❢♦r✇❛r❞ ✐♥ ✭❍❛❣❛♥ ❲❡st✱ ✷✵✵✻✮ t❤❛t ❣✉❛r❛♥t❡❡s

✶ ❈♦♥s✐st❡♥❝② t♦ ❜❛s❡❧♦❛❞ ❢✉t✉r❡s✳ ✷ P♦s✐t✐✈✐t② ♦❢ ε✳ ✸ ❈♦♥t✐♥✉✐t② ♦❢ ε✳ ✹ ▼♦♥♦t♦♥✐❝✐t② ♦❢ ε✳

P❡❛❦❧♦❛❞ ❝♦♥s✐st❡♥❝② ❛❞❥✉st♠❡♥t P❡❛❦❧♦❛❞ ❝♦♥s✐st❡♥❝② ❛❞❥✉st♠❡♥t ϕ ✐s ♦❜t❛✐♥❡❞ t❤r♦✉❣❤ ❛ ❝♦♥st❛♥t ♣❛t❤✇✐s❡ s❤✐❢t ♦♥ ♣❡❛❦ ❛♥❞ ♦✛✲♣❡❛❦ ❤♦✉rs ❢♦r ✇♦r❦❞❛②s ♦♥❧②✳ ❚❤❡ ❛❞❥✉st♠❡♥t ✐s ❝♦♥str❛✐♥❡❞ t♦ ♥♦t ❛✛❡❝t ❜❛s❡❧♦❛❞ ❝♦♥s✐st❡♥❝②✳

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❈✉r✈❡

Dec15 Jan16 Mar16 Apr16 Jun16 Aug16 Sep16 Nov16 10 20 30 40 50 60 Hourly Price Baseload Peakload Dec15 Jan16 5 10 15 20 25 30 35 40 45 50 55 Hourly Price Baseload Peakload

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

✽✳ ❈✉r✈❡ ❉❡❝♦♠♣♦s✐t✐♦♥

Dec15 Jan16 Mar16 Apr16 Jun16 Aug16 Sep16 Nov16

• 20
• 10

10 20 30 40 Lambda Epsilon Phi Dec15 Jan16

• 15
• 10
• 5

5 10 15 20 25 30 35 Lambda Epsilon Phi

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

▲♦❝❛❧♥❡ss

❈r♦ss✲s❡❝t✐♦♥❛❧ ❧♦❝❛❧♥❡ss ❂ ❆♥② ❝❤❛♥❣❡ ♦❝❝✉rr✐♥❣ ♦♥ ✇❤❛t❡✈❡r s❡❣♠❡♥t❡❞ ❜❛s❡❧♦❛❞ q✉♦t❡ ✭❡✳❣✳✱ s♣♦t ♣r✐❝❡ ❞♦✇♥ ❜② ✷✵ ❊❯❘✴▼❲❤ ❢r♦♠ ❋❡❜✳ ✷✽✱ ✷✵✶✸ q✉♦t❡ ♦❢ ✺✸✳✾✻✮ ❡①❝❧✉s✐✈❡❧② ❛✛❡❝ts ❝✉r✈❡ ❡st✐♠❛t❡ ♦♥ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣ ❞❡❧✐✈❡r② ✐♥t❡r✈❛❧ ❛s ✇❡❧❧ ❛s ♦♥ t❤❡ t✇♦ ❛❞❥❛❝❡♥t ♦♥❡s✳

▼❛①✐♠✉♠ s♠♦♦t❤♥❡ss ✭❇❡♥t ❡t ❛❧✳ ✭✷✵✵✼✮✮ ❖✉r ♠♦❞❡❧

Mar13 Jun13 Sep13 Jan14 Apr14 Jul14 Oct14 10 15 20 25 30 35 40 45 50 55 60 28 February 2013 28 February 2013 Stressed Mar13 Jun13 Sep13 Jan14 Apr14 Jul14 Oct14 15 20 25 30 35 40 45 50 55 28 February 2013 28 February 2013 Stressed

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❙t❛❜✐❧✐t②

❚✐♠❡ st❛❜✐❧✐t② ❂ ❙♠❛❧❧ ♣❡rt✉r❜❛t✐♦♥s ✐♥ ✐♥♣✉t ❞❛t❛ ✭❡✳❣✳✱ ✷✻✲✷✼✲✷✽✴✷✴✷✵✶✸✮ ❡♥t❛✐❧ ❛ s❧✐❣❤t ❝✉r✈❡ ✈❛r✐❛t✐♦♥✳

▼❛①✐♠✉♠ s♠♦♦t❤♥❡ss ■♥t❡r♣♦❧❛t✐♦♥ ❖✉r ♠♦❞❡❧

Mar13 Jun13 Sep13 Jan14 Apr14 Jul14 Oct14 10 20 30 40 50 60 70 26 February 2013 27 February 2013 28 February 2013 Mar13 Jun13 Sep13 Jan14 Apr14 Jul14 Oct14 25 30 35 40 45 50 55 60 65 26 February 2013 27 February 2013 28 February 2013

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❋✐t ◗✉❛❧✐t② ■

❋✉t✉r❡s ♣r✐❝❡s r✐s❦ ♣r❡♠✐❛ ❋✉t✉r❡s ♣r✐❝❡s ✐♥❝♦r♣♦r❛t❡ r✐s❦ ♣r❡♠✐❛ ❛♥❞ t❤✉s t❤❡ r❡❛❧✐③❡❞ s♣♦t ♣r✐❝❡ ❝❛♥♥♦t ❜❡ ✉s❡❞ ❛s ❜❡♥❝❤♠❛r❦ t♦ ❛ss❡ss t❤❡ ❍P❋❈ ✜t q✉❛❧✐t②✳ ❲❡ ♥❡❡❞ t♦ ❜✉✐❧❞ ✜❝t✐t✐♦✉s ❢✉t✉r❡s q✉♦t❡s t❤❛t ❝❛♥ ❜❡ ❝♦♠♣❛r❡❞ t♦ r❡❛❧✐③❡❞ ❞❛②✲❛❤❡❛❞ ♣r✐❝❡✳

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❋✐t ◗✉❛❧✐t② ■■

❋✐❣✉r❡✿ ❇❛❝❦t❡st✐♥❣ t❤❡ ✜t q✉❛❧✐t② ❢♦r t✵ = ❙❡♣t❡♠❜❡r ✶✱ ✷✵✶✷✳ ❋✐rst✱ ✇❡ ❝❛❧✐❜r❛t❡ t❤❡ s❡❛s♦♥❛❧✐t② ❢✉♥❝t✐♦♥ ♦♥ r❡❛❧✐③❡❞ ♣r✐❝❡s ♣r❡❝❡❞✐♥❣ t✵✱ ❛♥❞ ✇❡ ✉s❡ ♣r✐❝❡s ❢♦❧❧♦✇✐♥❣ t✵ t♦ ❝♦♠♣✉t❡ ✜❝t✐t✐♦✉s ❢✉t✉r❡s q✉♦t❛t✐♦♥s✳

10/24/11 02/01/12 05/11/12 08/19/12 11/27/12 03/07/13 06/15/13 −200 −150 −100 −50 50 100 150 200 Realized hourly price Seasonality estimation before t0 Fictitious futures construction after t0 t0 = 1−Sep−2012

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❋✐t ◗✉❛❧✐t② ■■■

❚❡st✐♥❣ t❤❡ q✉❛❧✐t② ♦❢ ❢♦r✇❛r❞ ❡st✐♠❛t❡s ✇✳r✳t✳ ❇❡♥t❤ ❡t ❛❧✳ ✭✷✵✵✼✮✬s ▼❙■✳ ❉❛t❛✿ ✶✻ ❡✈❛❧✉❛t✐♦♥ ❞❛t❡s ❂ ✜rst ❞❛② ✐♥ ❏❛♥✳✱ ❆♣r✳✱ ❏✉❧✳ ✷✵✶✵ → ✷✵✶✸✳ Pr✐❝❡s ♣r❡❝❡❞✐♥❣ ❛♥ ❡✈❛❧✉❛t✐♦♥ → ♣❡r✐♦❞✐❝❛❧ ♣❛tt❡r♥s ❡st✐♠❛t❡✳ Pr✐❝❡s ❢♦❧❧♦✇✐♥❣ ❡❛❝❤ ❡✈❛❧✉❛t✐♦♥

avg

→ ✜❝t✐t✐♦✉s ❜❛s❡❧♦❛❞s✴♣❡❛❦❧♦❛❞s✳ P❡r❢♦r♠❛♥❝❡ ✐♥❞❡①✿ ▼❆❉ =

✶ ✷✹♯S

• T∈S
• h=✶,...,✷✹
• ˆ

f (T, h) − ˆ S(T, h)

• ❖✉t♣✉t✿ ✷ ♠♦❞❡❧s×✶✻ ❞❛t❡s×✸ ♣❛tt❡r♥s ❂ ✾✻ ▼❆❉ ✜❣✉r❡s✳

▼❛✐♥ r❡s✉❧t✿ ♦✉r ♠♦❞❡❧ ♦✉t♣❡r❢♦r♠s ❜❡♥❝❤♠❛r❦ ▼❙■ ♦♥ ✸✹ ♦✉t ♦❢ ✹✽ s❝❡♥❛r✐♦s✱ ✇❤✐❝❤ ❝♦rr❡s♣♦♥❞ t♦ ✼✵✳✽✸✪ ♦❢ t❤❡ s❛♠♣❧❡✳

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❈♦♥❝❧✉s✐♦♥

❈♦♥str✉❝t✐✈❡ ❞❡✜♥✐t✐♦♥ ♦❢ ❢♦r✇❛r❞ ❝✉r✈❡ ✇✐t❤ ❤♦✉r❧② ❣r❛♥✉❧❛r✐t② ✉♣✳ ❈✉r✈❡ ✐s ❥♦✐♥t❧② ❝♦♥s✐st❡♥t t♦ r✐s❦✲♥❡✉tr❛❧ ✫ ❤✐st♦r✐❝❛❧ ♠❛r❦❡t ✐♥❢♦r♠❛t✐♦♥✳ ❈✉r✈❡ ♣❛t❤s ❛r❡ s♠♦♦t❤✱ ♠♦♥♦t♦♥✐❝✱ ❝r♦ss✲s❡❝t✐♦♥❛❧❧② st❛❜❧❡✱ t✐♠❡ ❧♦❝❛❧✳ ❇❛❝❦t❡st✐♥❣ ❛♥❛❧②s✐s ✇✳r✳t✳ ❜❡♥❝❤♠❛r❦ ♠♦❞❡❧ ♦❢ ❇❡♥t❤ ❡t ❛❧✳ ✭✷✵✵✼✮✳ ❲❤❛t✬s ♥❡①t❄

❆♥❛❧②③✐♥❣ t❤❡ ✐♥t❡r♣❧❛② ❜❡t✇❡❡♥ ❍P❋❈ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❣r❛♥✉❧❛r✐t② ❛♥❞ t❤❡ ✉♥❞❡r❧②✐♥❣ ♠❛r❦❡t ♣r✐❝❡ ♦❢ r✐s❦✳ ❆❞❥✉st♠❡♥ts t♦ ❝♦♣❡ ✇✐t❤ t❤❡ ❣r❡❛t ✈❛r✐❡t② ♦❢ ❝♦♠♠♦❞✐t② ♣r✐❝❡ ❞②♥❛♠✐❝s ❢❡❛t✉r✐♥❣ ♣❡r✐♦❞✐❝❛❧ ♣❛tt❡r♥s ✭❡✳❣✳✱ ♥❛t✉r❛❧ ❣❛s✱ ❛❣r✐❝✉❧t✉r❛❧s✮

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②

❚❤❛♥❦s ❢♦r ②♦✉r ❛tt❡♥t✐♦♥✦

❘✉❣❣❡r♦ ❈❛❧❞❛♥❛ ✭♣r❡s❡♥t❡r✮✱ ●✐❛♥❧✉❝❛ ❋✉s❛✐✱ ❆♥❞r❡❛ ❘♦♥❝♦r♦♥✐ ❊❧❡❝tr✐❝✐t② ❋♦r✇❛r❞ ❈✉r✈❡s ✇✐t❤ ❚❤✐♥ ●r❛♥✉❧❛r✐t②