The following analysis is included in Mitchell, T. P., and J. M. Wallace, 2001: The instrumental record of ENSO: 1840s to 2000. Submitted to J. Climate. (PDF file)
The following is a plot of the cold tongue index (CTI) which shows ENSO variability for 1875-2000. The CTI is the average SST anomaly for a broad region of the central and eastern equatorial Pacific Ocean, and the global-mean SST anomaly is removed for every month of the record.
In the following the CTI is shown plotted in two different ways: as above without annotation, and with the time series running backwards in time and the 25-year segments reordered. The latter presentation has the same character as the original time series.
The figures entitled "one," "two,", ..., "six" are the same game played with two other ENSO indices, and again with the CTI. "one" and "two" uses a (dynamical) ENSO index constructed from 6 tropical indices (winds, SLP, and rainfall); "three" and "four" are based on the average of four pressure records in the eastern Indian Ocean (EIPI); and "five" and "six" are the CTI analysis repeated. The dynamical ENSO index uses variables that exhibit a simple dynamical relationship in the ENSO cycle: winds in the tropics tend to be down gradient, and changes in moisture convergence are related to rainfall fluctuations. The even numbered analyses are the original time series, and the odd numbered analyses are with time running backwards and the 25-year segments rearranged. The CTI has had a portion of global-warming signal removed (for each month), and the EIPI and dynamical ENSO have not had this step performed to them.