In meteorology, identification of teleconnections between climatic phenomena plays an important role in the validation of atmospheric models which are used for weather and climate prediction, as well as the development of future climate scenarios. To evaluate the connectivity between climatic phenomena, correlation analysis is often used, but this type of analysis may lead to oversimplified relationships, which does not imply causality between different scales of time. In this work, Partial Directed Coherence (PDC) and kernel nonlinear Partial Directed Coherence (knPDC) were used to infer the influence between atmospheric compartments (atmosphere and ocean), allowing the detection of linear and nonlinear connections, respectively, between variables representative of important climatic variability modes. Teleconnections patterns were divided into two groups of climatological indicators, from 1950 to 2018, available from the National Oceanic and Atmospheric Administration (NOAA). The first group comprises the El Nino-Southern Oscillation (ENSO), Atlantic Multidecadal Oscillation (AMO), Pacific Decadal Oscillation (PDO) and Atlantic Interhemispheric SST Gradient (AITG) and the second, Antarctic Oscillation (AAO), PDO, Pacific-South American (PSA) and Sunspot Number (SPI). Causality analysis suggests that ENSO causes AMO and AITG causes PDO, highlighting the nonlinear relations ENSO→PDO and ENSO→AITG. Furthermore, we observe the influences PDO→AITG and PDO→AAO, evidencing the energy transfer from the Pacific to the Atlantic Ocean. Also, PDC and knPDC techniques results suggest that some indices have nonlinear interaction, emphasizing the use of nonlinear machine learning techniques, e.g., deep learning, that can capture these variations.