Abstract
As the field of study expands, or as the number of observations in a sample increases, data observed at discrete points is generally assumed to be sampled from an underlying real function. As the number of observation points increases, those observations are likely to be sampled from a real-valued function. In this case, the derived data will be examples of a functional structure. We analyzed the daily average temperature data at 65 discrete points in 18 cities in Turkey's Black Sea Region. Fourier basis functions were used as a basis function approach because the temperature data had a periodic structure. The data were then transformed into a continuous function using the basis function and roughness penalty approach. Functional data were obtained using the roughness penalty approach. The generalized cross-validation method was used to determine the smoothing parameter of the variable (temperature variable). Finally, smoothed functional principal components analysis was applied to the functional data. In this way, changes in temperature functions, which seem hard to tackle, were evaluated on the same graph using the mean function generated for the principal component function and using the functions and the mean function obtained using the principal component function.