Like I said, there is no way to test for how well it will extrapolate, because actual QBO values prior to 1953 will never be known. And the values for the future won't be known for some time to come :)
I can do something like take parts of the known QBO time-series as a training interval and use it to evaluate other parts, but that is a trade-off and judgment call. The trade-off is that a smaller training interval will have less information content than a longer interval. IOW, TINSTAAFL
Here is another recent paper "The validity of long-term prediction of quasi-biennial oscillation (QBO) as a proof of the exact seasonal synchronization of the equatorial stratospheric QBO cycle"
The author claims that QBO cycles are either 24, 30, or 36 months long, or on 2, 2.5, or 3 year seasonal boundaries. If the average cycle length is 28 months or 2.333 years, a bit of discrete combinatorial math will show that a set of months that are portioned out as
5c24, 2x30, and 2x36, will compose 9x2.333 cycles, which is a 21 year repeat period.
This gives the correct mean as well
(5x24, 2x30, and 2x36)/(5+2+2) = 28
It might be worthwhile to test this out. Of course, one would want to use as long an interval as possible to order the sequence.
Another grouping to consider is
(2+2+3) + (2+2.5+2.5) + (2+2+3)
This generates boundaries on 7 year cycles plus the 21 year cycle to maintain the 2.33 year average.