The extended finite Fourier transformation is an effective mathematical method for analyzing time series data with vector values. In this study, the transformation is applied to (n + m) time series data, and the approximations obtained are used to create usable features for further analysis. This technique could be useful in the field of climate science, where missing data can be a significant challenge. Researchers may more accurately analyses climate data using the extended finite Fourier transformation, even when some observations are missing at random. This can lead to a better understanding of climate patterns and trends over time, which is necessary for forecasting future changes and developing effective mitigation policies. Overall, the extended finite Fourier transformation is an interesting development in the field of time series analysis, with several possible applications in a variety of fields. We should expect even more spectacular developments in the coming years as academics continue to explore its powers and perfect its methodologies.