The North Atlantic is one of the key regions, where low-frequency climate variability is formed. However, despite numerous studies related to this topic, some issues still remains unsolved. One of them is the ambiguous cross-correlation of the North Atlantic sea surface temperature (SST) and the intensity of Atlantic Meridional Overturning Circulation (AMOC). A widely accepted concept suggests that the long-term climate variability is a result of the atmospheric stochastic forcing transformed by the inertial ocean. Existence of negative and positive feedback mechanisms suggests that the long-term North Atlantic dynamics may be considered as a damped stochastically forced oscillator in which both SST and AMOC are the elements of the same process. In this study, we analyze the cross-correlation functions of the main North Atlantic climatic indexes derived from a simple box-like stochastic model. The random forcing simulates the air-sea interface heat fluxes and excites both the SST and the AMOC. Stochastic excitation of the meridional circulation implies the leading AMOC and stochastic forcing of SST implies the leading Atlantic Multidecadal Oscillation (AMO). Connection of the AMOC and AMO indexes depends on the principal oceanic feedbacks and the dissipation intensity.