A previous post described the use of proxy records of ENSO to fit the Southern Oscillation Index Model (SOIM). This model fit used one specific set of data that featured a disconnected record of coral measurements from the past 1000 years, see Cobb .
As the focus of this post, another set of data (the Unified ENSO Proxy set) is available as an ensemble record of various proxy measurements since 1650 -- giving an unbroken span of over 300 years to apply a SOIM fit . This ensemble features 10 different sets, which includes the Cobb coral as a subset.
To fit over this long a time span is quite a challenge as it assumes that the time series is stationary over this interval. The data has a resolution of only one year, in comparison to the monthly data previously used, so it may not have the temporal detail as the other sets, yet still worthy of investigation. (an interactive version is available here).
One of the long-standing theories in climate science has to do with the topic of atmospheric tides. Similar to the more-familiar concept of ocean tides, these can be measured as regular fluctuations in wind, temperature, density and pressure throughout the atmosphere, with the effect more pronounced at higher altitudes as the lower density requires less energy to create an impact. The on-going theory states that the 24-hour solar cycle is the greatest contributor to the periodic atmospheric tidal effect . Note that the theory appears to have (at least partially) originated with the famed AGW skeptic Richard Lindzen.
Yet some recent research appears to be challenging these ideas of a principally solar influence, especially in regards to features that obviously don't match the periods expected of the solar cycle . The counter theory is that of it being a lunar (gravitational) origin rather than a solar (thermal) origin. This is all based on the rich detail in the data available from length-of-day measurements  and the credible fits of the countervailing theory to that data.
If the impact of this effect is real, it likely has repercussions on how I look at the source of the Quasi-biennial Oscillation (QBO) forcing and of the El Nino Southern Oscillation (ENSO) forcing.