10-year sp500 returns periodic cycle?

Yesterday, analyzing the 10 and 15-year annualized rolling returns of the S&P 500, I noticed a strong correlation with a sinusoid (in the model composed of three sinusoids of harmonic frequencies with fixed phase plus a further correction for the drawdown peak) of a 35.5-36.5 year period. With Monte Carlo simulations, it turns out that a correlation this strong with a simple sinusoid with $R\^2 > 0.7$ (attached photo) cannot be due to chance ($p < 0.01$, taking into account both autocorrelation through Newey-West and sample bias, besides having run a test on 1000 different scrambles with block bootstrapping). Therefore, it probably reflects real economic cycles. Whether this is predictive is pure speculation; it remains only interesting to understand what growth a model of the kind discounts. Actually, at a glance, it seems that the market is slightly ahead on the start of what is the "peak" estimated by the 10-year return model (so 2016-2026 returns will be similar to 2019-2029 etc. and we are around a maximum) and we can assume a worst case scenario that we are 4 years in advance with respect to the cycle . Therefore, from these returns (and past price data starting from 2016) I created two price charts: one derived from the rolling returns as predicted, and a pessimistic but perhaps more realistic one anticipating them by 4 years (for which the 10 year return on the window ending in year 2027 in the pessimistic model is equal the one predicted by the periodic "fitted" model for the year 2031). With this data, the model predicts a heavy slowdown or recession between 2033 and 2037 (depending on the anticipation or not), however, before that we get to have another 6-10 years of annualized returns similar to those of the last 15 years (15% annualized average with net dividends which are taxed 26%).