Seasonal adjustment aims to remove predictable seasonal fluctuations and other calendar-related variations from a time series. In the context of economics Hylleberg (1992) defines seasonality  as ``[...] the systematic, although not necessarily regular, intra-year movement caused by the changes of the weather, the calendar, and timing of decisions, directly or indirectly through the production and consumption decisions made by the agents of the economy''.

The removal of seasonal and calendar effects allows analysts, economists, and statisticians to more clearly identify the business cycle and other non-seasonal effects, such as strikes or crises. By adjusting for seasonality, it becomes easier to compare data across different time periods and to make more timely economic assessments and policy decisions. The usual alternative, year-on-year growth-rates, show underlying developments with a time lag of about half a year (cf. Dagum and Mazzi 2018). Moreover, these growth rates may be skewed by  differences in the calendar constellation, for instance a discrepancy in the number of working days between the periods under comparison. To address these issues, seasonal adjustment techniques are employed to provide a more immediate and undistorted view of economic developments.

This dissertation adds to the literature on seasonal adjustment and time series econometrics by introducing contributions in two primary areas. Historically, the development and application of seasonal adjustment methods have predominantly focused on time series data with lower frequencies, such as monthly and quarterly observations. This work, however, develops and analyses methods to seasonally adjust higher frequency time series. Most prominently, a procedure is developed to adjust daily time series. 

The second area of contribution lies in the analysis and enhancement of diagnostic tools that are instrumental in the seasonal adjustment process for both lower and higher frequency time series. This includes the examination and refinement of seasonality tests, which are pivotal in detecting seasonal patterns within the data, as well as unit root tests, which are relevant in many areas of econometrics, and essential for the RegARIMA model based estimation of calendar effects. Collectively, these methodological advancements and diagnostic improvements facilitate more accurate seasonal adjustments.

This thesis contributes to the field of probabilistic forecasting in energy markets through novel methodological developments and empirical applications. The liberalization of energy markets over the past 25 years, combined with the transition towards carbon-neutral energy systems, has created increasingly complex and interconnected markets characterized by high uncertainty from renewable energy sources, demand fluctuations, and geopolitical risks. Traditional point forecasting methods are inadequate for capturing this uncertainty, necessitating probabilistic approaches that enable better risk management and decision-making.
The thesis makes several methodological contributions to the field of probabilistic online learning. First, we introduce CRPS learning, a novel aggregation method that combines probabilistic forecasts using flexible weight functions across quantiles rather than static weights. This approach accounts for varying forecast performance within different parts of the predictive distribution. Second, we extend this framework to multivariate settings, developing a method that exploits dependencies between combination weights of marginal distributions using penalized splines. Third, we propose a regularized probabilistic online learning algorithm that combines online coordinate descent with the framework of generalized additive models for location, scale, and shape (GAMLSS), enabling direct prediction of distributional parameters in high-dimensional settings.
The thesis also addresses specific forecasting challenges in energy markets through three empirical applications. We develop probabilistic forecasting models for day-ahead and month-ahead natural gas prices, accounting for heavy tails and asymmetric effects while considering the influence of European Emission Allowances (EUA) prices. We propose a multivariate VECM-Copula-GARCH model to jointly forecast EUA, natural gas, coal, and oil prices, capturing long-term equilibrium relations, conditional heteroscedasticity, and time-varying dependence structures through one-step estimation. Additionally, we explore the prediction of high-resolution electricity peak demand from low-resolution data using both statistical and machine learning approaches.
Complementing these methodological and empirical contributions, we address the computational challenges of implementing probabilistic forecasting methods by developing an R package for benchmarking C++ code. This tool provides overlapping and nested timers with OpenMP support and nanosecond-level precision, facilitating the development of efficient implementations for online learning algorithms.
The proposed methods are particularly well-suited for streaming data applications in energy markets, where models must update rapidly with new observations. Through simulation studies and empirical applications using real energy market data, we demonstrate the practical utility and superior performance of our approaches compared to established benchmarks. This work advances both the theoretical understanding of probabilistic forecasting and its practical implementation in energy market applications, contributing to more informed decision-making in an increasingly uncertain energy landscape.

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