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Tidsseriemodellering av fyra oreglerade älvars vattenföring - En explorativ studie med GARCH- och Tröskelteknik

Pedersen, Dennis LU and Bengtsson, Henrik LU (2016) STAH11 20152
Department of Statistics
Abstract
This paper studies the possibility to model the water flows of four Swedish unregulated rivers between 1980-2015 with ARMA, GARCH and SETAR models. By examining the amount of water that flows through the river and what the dependence in the process looks like in general, a further understanding for effects on for example wildlife and climate changes can be developed. The process of the time series is treated as an additive process, where components of dependence can be eliminated one by one until only white noise remains. The initial distribution of the observations is fairly symmetrical after a logarithmic transformation, although it is not normally distributed, but rather multimodal. The rivers are situated in the northern parts of... (More)
This paper studies the possibility to model the water flows of four Swedish unregulated rivers between 1980-2015 with ARMA, GARCH and SETAR models. By examining the amount of water that flows through the river and what the dependence in the process looks like in general, a further understanding for effects on for example wildlife and climate changes can be developed. The process of the time series is treated as an additive process, where components of dependence can be eliminated one by one until only white noise remains. The initial distribution of the observations is fairly symmetrical after a logarithmic transformation, although it is not normally distributed, but rather multimodal. The rivers are situated in the northern parts of Sweden, which induces heavy seasonal patterns when the water freezes as well as the ice and snow melts. These seasonal patterns make it problematic to apply the ARMA+GARCH on daily observations, and it is only when monthly observations are used that the seasonality can be eliminated with S-ARIMA. After that, the observed volatility clustering in the variance can be modeled using traditional GARCH. Daily observations can be modeled using SETAR and GARCH since the threshold technique captures the majority of the seasonal patterns.
The conclusive results are that it is possible to eliminate the structural dependence and achieve approximate white noise in the process with the selected models. Though it is difficult to distinguish any difference in the parameter choosing between the four rivers despite large differences in water volume and geographical location. Modeling with monthly observations does not seem to reflect the structure of the water flows in a highly detailed resolution, but rather, it tends to indicate a smoothening effect that generates simple models with white noise. Modeling with daily observations gives a more complex structure, where SETAR in some cases is incapable of reacting to the quick changes in the process. This leaves a desire for a better integrated model to efficiently separate the complex dependence structure in the river water flows. (Less)
Abstract (Swedish)
Denna uppsats undersöker möjligheten att modellera fyra svenska oreglerade älvars vattenföring mellan 1980-2015 med hjälp av ARMA-, GARCH- och SETAR-modeller. Genom att studera den mängd vatten som transporteras i vattendrag och hur dess beroendestruktur ser ut i allmänhet kan förståelse om bland annat djurliv och klimateffekter fördjupas. Tidsseriens process behandlas som ett additivt system där komponenter kan elimineras succesivt så att endast vitt brus kvarstår. Grundfördelningen är efter logtransformation relativt symmetrisk. Dock är den inte normalfördelad, utan snarare multimodal. Älvarna är belägna i norra Sverige, vilket medför kraftigt säsongsberoende när vattnet fryser respektive isen smälter. Detta säsongsberoende gör det... (More)
Denna uppsats undersöker möjligheten att modellera fyra svenska oreglerade älvars vattenföring mellan 1980-2015 med hjälp av ARMA-, GARCH- och SETAR-modeller. Genom att studera den mängd vatten som transporteras i vattendrag och hur dess beroendestruktur ser ut i allmänhet kan förståelse om bland annat djurliv och klimateffekter fördjupas. Tidsseriens process behandlas som ett additivt system där komponenter kan elimineras succesivt så att endast vitt brus kvarstår. Grundfördelningen är efter logtransformation relativt symmetrisk. Dock är den inte normalfördelad, utan snarare multimodal. Älvarna är belägna i norra Sverige, vilket medför kraftigt säsongsberoende när vattnet fryser respektive isen smälter. Detta säsongsberoende gör det problematiskt att applicera ARMA+GARCH på dygnsobservationer, och det är enbart när månadsobservationer används som säsongen kan elimineras med S-ARIMA. Därefter kan observerat volatilitetskluster i variansen modelleras med traditionell GARCH. Dygnsobservationer kan modelleras med SETAR och GARCH då tröskeltekniken fångar upp större delen av säsongsberoendet.
Resultatet som framkommer är att det går att eliminera beroendestrukturen och uppnå approximativt vitt brus i processen för valda modeller. Det går dock inte att särskilja någon direkt skillnad i modellval mellan de fyra älvarna trots olik omfattning på vattenföringen och geografiskt läge. Modellering av månadsdata verkar inte återspegla vattenföringens struktur på ett högupplöst sätt, utan snarare observeras en utslätningseffekt och simpla modeller är tillräckligt för att uppnå vitt brus. Modellering av dygnsdata ger en mer komplicerad struktur där SETAR i vissa lägen har svårt att reagera på snabba förändringar i processen, vilket lämnar ett behov av en bättre integrerad modell för att effektivt separera älvarnas komplicerade beroendestruktur. (Less)
Please use this url to cite or link to this publication:
author
Pedersen, Dennis LU and Bengtsson, Henrik LU
supervisor
organization
course
STAH11 20152
year
type
M2 - Bachelor Degree
subject
keywords
ARMA, GARCH, SETAR, tröskeleffekter, oreglerade älvar, vattenföring
language
Swedish
id
8865612
date added to LUP
2016-03-22 13:53:50
date last changed
2016-03-22 13:53:50
@misc{8865612,
  abstract     = {This paper studies the possibility to model the water flows of four Swedish unregulated rivers between 1980-2015 with ARMA, GARCH and SETAR models. By examining the amount of water that flows through the river and what the dependence in the process looks like in general, a further understanding for effects on for example wildlife and climate changes can be developed. The process of the time series is treated as an additive process, where components of dependence can be eliminated one by one until only white noise remains. The initial distribution of the observations is fairly symmetrical after a logarithmic transformation, although it is not normally distributed, but rather multimodal. The rivers are situated in the northern parts of Sweden, which induces heavy seasonal patterns when the water freezes as well as the ice and snow melts. These seasonal patterns make it problematic to apply the ARMA+GARCH on daily observations, and it is only when monthly observations are used that the seasonality can be eliminated with S-ARIMA. After that, the observed volatility clustering in the variance can be modeled using traditional GARCH. Daily observations can be modeled using SETAR and GARCH since the threshold technique captures the majority of the seasonal patterns.
The conclusive results are that it is possible to eliminate the structural dependence and achieve approximate white noise in the process with the selected models. Though it is difficult to distinguish any difference in the parameter choosing between the four rivers despite large differences in water volume and geographical location. Modeling with monthly observations does not seem to reflect the structure of the water flows in a highly detailed resolution, but rather, it tends to indicate a smoothening effect that generates simple models with white noise. Modeling with daily observations gives a more complex structure, where SETAR in some cases is incapable of reacting to the quick changes in the process. This leaves a desire for a better integrated model to efficiently separate the complex dependence structure in the river water flows.},
  author       = {Pedersen, Dennis and Bengtsson, Henrik},
  keyword      = {ARMA,GARCH,SETAR,tröskeleffekter,oreglerade älvar,vattenföring},
  language     = {swe},
  note         = {Student Paper},
  title        = {Tidsseriemodellering av fyra oreglerade älvars vattenföring - En explorativ studie med GARCH- och Tröskelteknik},
  year         = {2016},
}