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A PIT - Based approach to Validation of Electricity Spot Price Models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
En PIT-baserad metod för validering av elprisprismodeller (Swedish)
Abstract [en]

The modeling of electricity spot prices is still in its early stages, with various different competing models being proposed by different researchers. This makes model evaluation and comparison research an important area, for practitioners and researchers alike. However, there is a distinct lack in the literature of consensus regarding model evaluation tools to assess model validity, with different researchers using different methods of varying suitability as validation methods. In this thesis the current landscape of electricity spot price models and how they are currently evaluated is mapped out. Then, as the main contribution this research aims to make, a general and flexible framework for model validation is proposed, based on the Probability Integral Transform (PIT). The probability integral transform, which can be seen as a generalization of analyzing residuals in simple time series and regression models, transforms the realizations of a time series into independent and identically distributed U(0,1) variables using the conditional distributions of the time series. Testing model validity is with this method reduced to testing if the PIT values are independent and identically distributed U(0,1) variables. The thesis is concluded by testing spot price models of varying validity according to previous research using this framework against actual spot price data. These empirical tests suggest that PIT-based model testing does indeed point us toward the more suitable models, with especially unsuitable models being rejected by a large margin.

Abstract [sv]

Modelleringen av spotpriser på el är fortfarande i ett tidigt stadium, med många olika modeller som förespråkas av olika forskare. Detta innebär att forskning som fokuserar på modellutvärdering och jämförelse är viktig både för berörda parter i näringslivet och forskare inom detta område. Det finns dock en klar brist på konsensusmetoder att utvärdera modellers validitet, då olika forskare förespråkar olika metoder av varierande lämplighet som valideringsverktyg. I den här uppsatsen kartläggs det nuvarande landskapet av spotprismodeller och de metoder som används för att utvärdera dem. Sedan, som det huvudsakliga forskningsbidraget av detta arbete, presenteras ett generellt och flexibelt valideringsramverk som baseras på vad som kallas ”Probability Integral Transform” (PIT). PIT, vilken kan ses som en generalisering av att undersöka residualer i enkla tidsserie- och regressionsmodeller, transformerar utfallet av en tidsserie till oberoende och identiskt fördelade U(0,1) variabler med hjälp av tidsseriens betingade fördelningar. Att testa modellens validitet reduceras med denna metod till att testa om PIT – värdena är oberoende och identiskt fördelade U(0,1) variabler. Uppsatsen avslutas med tester av spotprismodeller av varierande validitet enligt litteraturen med hjälp av detta ramverk mot faktiskt spotprisdata. De empiriska testerna antyder att PIT – baserad modellvalidering faktiskt stämmer överrens med modellers validitet baserat på nuvarande konsensus, där särskilt opassande modeller förkastas med stora marginaler.

Place, publisher, year, edition, pages
2015.
Series
TRITA-MAT-E, 2015:58
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-172996OAI: oai:DiVA.org:kth-172996DiVA: diva2:855388
External cooperation
Vattenfall
Subject / course
Mathematical Statistics
Educational program
Master of Science - Industrial Engineering and Management
Supervisors
Examiners
Available from: 2015-09-21 Created: 2015-09-06 Last updated: 2015-09-21Bibliographically approved

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