## 3 Research Objectives and Methodology
### Methodology Used  
Given the complexity of the relationship between renewable energy sources (RES) and electricity price development, as well as the diversity of market and system factors (e.g., consumption flexibility, cross-border interconnections, seasonality of demand), a multi-level methodological strategy was chosen in this paper. This strategy combines quantitative time series processing, multiple regression analyses, correlation modelling, and segmentation approaches based on the identification of threshold effects. The analysis also includes cross-country comparisons, taking into account structural differences in power systems.  
The analysis is based on historical data for selected Central and Western European countries, with high temporal resolution (15 min and hourly data) on electricity prices, wind and solar generation, residual load, meteorological variables (sun, wind, temperature),and consumption. The data have been aggregated into daily and monthly profiles, allowing intraday, seasonal, and inter-annual effects to be examined.  
In the first stage, basic statistical indicators of prices were calculated, including mean, minimum, maximum, and standard deviation. These metrics were also evaluated in year-on-year and month-on-month comparisons. Subsequently, a multi-year regression analysis was performed to model the evolution of electricity prices in relation to daily RES production. Regression models were built for individual years and for several combinations of input variables (Solar, Wind, Wind + Solar), while R\({}^{2}\) values were also evaluated as an indicator of the quality of the models and their predictive ability.  
An important part of the methodology was a segmentation analysis of the occurrence of negative prices depending on the level of RES production. The generation was divided into output bins and, for each bin, the probability of negative prices was determined, thus identifying the so-called threshold effects. For this purpose, rule schemes were also created to formulate conditions leading to a high probability of extreme prices (e.g., \"on a summer weekend when generation > X MW, the probability of negative prices is Y%\"). These rules were derived from empirical distributions without the use of machine learning.  
Furthermore, correlation matrices between the variables (wind generation, solar generation, residual load, and price) have been calculated--both for the whole period and for individual years--allowing the assessment of the temporal stability of the relationships. The cross-country comparative analysis was based on a comparison of volatilities, outliers and correlations between countries with different levels of demand flexibility, storage technologies, and interconnections with neighbouring markets.  
The entire analytical apparatus has been implemented in an environment that supports transparency, replicability, and a high degree of parameterisation, allowing for easy extension of the analyses to other variables or countries. A summary overview of the analytical tools used, their research objective, outputs, and assignment to each hypothesis tested is presented in Table 2.