## 1 Introduction
Another study found that the average and median values of PLR for mono-Si installed before 2000 were, respectively, \(-0.7\%\) per year and \(-0.5\%\) per year, whereas the values for thin-film technologies installed after 2000 were higher at \(-1.5\%\) per year and \(-1\%\) per year, respectively [6]. Although the PLR is often used to quantify the performance change at the module level based on laboratory or outdoor test conditions [9], the indicator can also be applied on the PV system level [10; 11; 12]. PLR is calculated using the following general steps:  
* Reading in available input data;
* Data filtering;
* Selection of performance metric;
* Possible correction and data aggregation;
* Application of the statistical method to calculate the final PLR. In this work, two different raw data irradiance sources, namely measured irradiance and clear sky modeled irradiance [7], are tested and two different methodologies were used to calculate PLR. A study in Cyprus [9] found that the annual PLR of mc-Si was \(-0.64\%\)/year, with \(-0.62\%\)/year for mc-Si, and \(-1.78\%\)/year for thin-film systems. Although the study uses quite a small sample size, it could indicate that the PLR value of thin-film is nearly three-fold of the PLR value of c-Si PV systems in warm climates. Unlike the calculation of PR, which is basically straightforward, the calculation of PLR does not follow a pre-determined procedure. To estimate the PLR of a PV system, a performance metric must be selected and calculated first. After possible correction and aggregation steps, a statistical method is applied to extract the performance trend. Many methods decompose the metric time-series into their components. Using additive decomposition, the sum of the components at each point of time is the same as the value of the data at that specific time as represented by Equation (1) [13]. \[\text{y}_{\text{t}}\text{=}\text{S}_{\text{t}}\text{+}\text{T}_{\text{t}}\text {+}\varepsilon_{\text{t}} \tag{1}\]  
where \(\text{y}_{\text{t}}\) is the data, \(\text{S}_{\text{t}}\) is the seasonal component, \(\text{T}_{\text{t}}\) is the trend-cycle component, and \(\varepsilon_{\text{t}}\) is the remainder, all at period t. The \"seasonality\" component is a repeated pattern observed between regular intervals due to seasonal factors such as the time of the day or the month of the year. Seasonality in weather data related to PV systems shows the regular variation in the environmental conditions such as the irradiance, the spectral content, the angle of incidence (\(\theta\)), the ambient temperature (\(\text{T}_{\text{amb}}\)), and wind speed (\(\
u\)) [14]. Seasonality affects both c-Si and thin-film technologies, although c-Si technologies are more dependent on temperature changes and spectral effects [15]. The \"trend\" component shows the overall increasing or decreasing slope of the metric over time. The \"remainder\" component is the activity that is not explained by the trend or the seasonal value. The remainder is also expressed as the \"error\", \"residual\", or \"irregular\" component. The time-series are sequence of observations recorded at regular time intervals. They contain information about the inherent nature of the measured phenomenon, such as the physical world, which displays interesting movements over longer periods. Understanding time-series can also be used as a basis for forecasting the future characteristics of the measured phenomenon. Time-series can contain features such as autocorrelation and periodic movements, stationarity and nonstationarity, volatility, seasonality, trends, and other common features [16]. In this work, we will focus on seasonality and trend features of the time-series. Various statistical models are used to extract the components of time-series. The most commonly used methods are moving averages (either moving average smoothing or weighted moving averages), X11 method, SEATS decomposition, or Seasonal and Trend decomposition using Locally weighted scatterplot smoothing (STL decomposition) [13].