Progress is being made on long-term nonlinear predictability of ENSO events:

Astudillo, H.F., Abarca-del-Río, R. & Borotto, F.A. (2017), "Long-term potential nonlinear predictability of El Niño–La Niña events", Clim Dyn, 49: 131. doi:10.1007/s00382-016-3330-1

https://rd.springer.com/article/10.1007%2Fs00382-016-3330-1?utm_content=buffer41715&utm_medium=social&utm_source=twitter.com&utm_campaign=bufferAbstract: "We show that the monthly recorded history (1866–2014) of the Southern Oscillation Index (SOI), a descriptor of the El Niño Southern Oscillation (ENSO) phenomenon, can be correctly described as a dynamic system supporting a potential nonlinear predictability well beyond the spring barrier. Long-term predictability is strongly connected to a detailed knowledge about the topology of the attractor obtained by embedding the SOI index in a wavelet base state space. By utilizing the state orbits on the attractor, we show that the information contained in the SOI is sufficient to provide nonlinear attractor information, allowing the detection of predictability for longer than a year: 2, 3, and 4 years in advance throughout the record with an acceptable error. This is possible due to the fact that the lower-frequency variability of the SOI presents long-term positive autocorrelation. Thus, by using complementary methods, we confirm that the reconstructed attractor of the low-frequency part (lower than 1/year) of SOI time series cannot be attributed to stochastic influences. Furthermore, we establish its multifractality. As an example of the capabilities of the methodology, we investigate a few specific El Niño (1972–1973, 1982–1983, 1997–1998) and La Niña (1973–1973, 1988–1989 and 2010–2011) events. Our results indicate that each of these present several equivalent temporal structures over other eras of these 149 years (1866–2014). Accordingly, none of these cases, including extreme events, presents temporal singularity. We conclude that the methodology’s simplicity of implementation and ease of use makes it suitable for studying nonlinear predictability in any area where observations are similar to those describing the ENSO phenomenon."