Universität zu Köln

Liebl, Dominik (2013). Contributions to Functional Data Analysis with Applications to Modeling Time Series and Panel Data. PhD thesis, Universität zu Köln.

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Abstract

In Chapter 1 we propose a new perspective on modeling and forecasting electricity spot prices. Our approach is motivated by the data-generating process of electricity spot prices, which is well described what is called the merit order model. The merit order model is a micro economic model based on the assumption that spot prices on electricity exchanges are determined by the marginal generation costs of the last power plant that is required to cover the demand. The resulting merit order curve reflects the increasing generation costs of the installed power plants. Correspondingly, we suggest interpreting hourly electricity spot prices as noisy discretization points of smooth price functions. These price functions are modeled by a functional factor model (FFM) for which we discuss a two-step estimation procedure. The first step is a classical pre-smoothing step in order to estimate the single price functions from the noisy discretization points. The second step then aims for a robust estimation of a finite set of common basis functions from the pre-smoothed price functions. In doing this, we carefully consider the issue of finding an optimal smoothing parameter. The presentation of our functional factor model concludes with an extensive forecast study which compares our FFM with alternative time series models that have been successfully applied in the literature on electricity spot prices. The forecast study clearly confirms the superior power of our functional factor model and the use of price functions as underlying structures of electricity spot prices in general. A slightly modified version of Chapter 1 is forthcoming as a single-authored article in "The Annals of Applied Statistics"; see Liebl (2013). Chapter 2 further discusses the problem of modeling electricity spot prices. On the one hand, we extend the concept of price function introduced in Chapter 1 using covariables. On the other hand, we focus on a generally deeper theoretical consideration of the involved multivariate nonparametric regression model, which is used as a tool for FPCA. We extend existing theoretical results with respect to FPCA for sparse functional data by considering the asymptotic bias and variance of the multivariate local linear estimator of the mean and the covariance functions. Here, we carefully consider the effects of between-correlations, which are caused by the time series context, and the effects of within-correlations, which are caused by the functional nature of the data. In order to demonstrate the usefulness of our model we analyze the effects of Germany's nuclear moratorium on March 14, 2011. This event describes a natural experiment, since in the course of Germany's nuclear moratorium on March 14, 2011, eight nuclear power plants were phased out [Nestle (2012)]. The data set analyzed in Chapter 2 covers exactly one year before and one year after Germany's nuclear power phase-out. We apply our model separately to these two time spans in order to contrast the different market situations. In Chapter 3 we pick up the successful application of FDA within the literature on panel data models. Recent panel data models allow us to control for complex unobserved heterogeneity effects by the incorporation of latent factor models. This new kind of panel data models extends the classical concept of individual random (scalar) effects to random processes or random functions [see, e.g., Bai, Kao and Ng (2009), Bai (2009), and Kneip, Sickles and Sond (2012)]. Even though this class of panel models is of high relevance for practical problems such as stochastic frontier analysis, they are still rarely applied in the empirical literature. Our implementation of these methods in the statistical software package of phtt provides a first step towards facilitating their application. As the estimation procedure of Kneip, Sickles and Sond (2012) involves nonparametric smoothing methods, the choice of a reliable procedure to find an optimal smoothing parameter is most important for implementing the estimation procedure in a statistical software package. We consider this problem and suggest to use the technique of ``parameter-cascading'' in order to approximate an upper bound for the optimal smoothing parameter [see also Cao and Ramsay (2010)]. The final optimal smoothing parameter lies somewhere between this approximated upper bound and zero. Knowledge of this interval allows for a robust implementation of the computationally costly cross validation criterion. A slightly modified version of Chapter 3 is accepted as a co-authored article for the "Journal of Statistical Software"; see Bada and Liebl (2013).

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Liebl, Dominik liebl@statistik.uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-53021
Date:	2013
Language:	English
Faculty:	Faculty of Management, Economy and Social Sciences
Divisions:	Faculty of Management, Economics and Social Sciences > Economics > Econometrics and Statistics > Professorship for Economic and Social Statistics
Subjects:	Social sciences Economics Natural sciences and mathematics
Uncontrolled Keywords:	Keywords Language Functional Data Analysis English Time Series English Panel Data English
Date of oral exam:	21 August 2013
Referee:	Name Academic Title Mosler, Karl Prof. Dr. Kneip, Alois Prof. Dr Bettzüge, Marc Oliver Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/5302