The basis of the ENSO model is the forcing derived from the long-period cyclic lunisolar gravitational pull of the moon and sun. There is some thought that ENSO shows [teleconnections](https://en.wikipedia.org/wiki/Teleconnection) to other oceanic behaviors. The primary oceanic dipoles are ENSO and AMO for the Pacific and Atlantic. There is also the PDO for the mid-northern-latitude of the Pacific, which has a pattern distinct from ENSO. So the question is: Are these connected through interactions or do they possibly share a common-mode mechanism through the same lunisolar forcing mechanism?
Based on tidal behaviors, it is known that the gravitational pull varies geographically, so it would be understandable that ENSO, AMO, and PDO would demonstrate distinct time-series signatures. In checking this, you will find that the correlation coefficient between any two of these series is essentially zero, regardless of applied leads or lags. Yet the underlying component factors (the lunar Draconic, lunar Anomalistic, and solar modified terms) may *potentially* emerge with only slight variations in shape, with differences only in relative amplitude. This is straightforward to test by fitting the basic ENSO model to AMO and PDO by allowing the parameters to vary.
The following figure is the result of fitting the model to ENSO, AMO, and PDO and then comparing the constituent factors.
First, note that the same parametric model fits each of the time series arguably well. The Draconic factor underling both the ENSO and AMO model is almost perfectly aligned, indicated by the red starred graph, with excursions showing a CC above 0.99. All of the rest of the CC's in fact are above 0.6.
The upshot of this analysis is two-fold. First to consider how difficult it is to fit any one of these time series to a minimal set of periodically-forced signals. Secondly that the underlying signals are not that different in character, only that the combination in terms of a [Laplace's tidal equation weighting](https://agu.confex.com/agu/fm18/preliminaryview.cgi/Paper415478.html) are what couples them together via a common-mode mechanism. Thus, the teleconnection between these oceanic indices is likely an underlying common lunisolar tidal forcing, just as one would suspect from conventional tidal analysis.