Distinct and Predictable U.S. and ROW Equity Market Cycles?

How does the performance of the U.S. stock market compare to that of the aggregated stock markets in the rest of the world over the long run? Is there alternating leadership? To investigate, we use the S&P 500 Index (SP500) as a proxy for the U.S. stock market and the World ex USA Index in U.S. dollars as a proxy for the rest-of-world  equity market(ROW). We consider three ways to relate U.S. and ROW equity returns:

1. Basic return statistics/cumulative performances.
2. Lead-lag analysis between U.S. and ROW annual returns to see whether there is some cycle in the relationship (with the U.S. stock market compared to itself as a control).
3. Sequences of end-of-year high water marks for U.S. and ROW equity markets.

Using annual SP500 and ROW levels during December 1969 (limited by ROW) through December 2024, we find that: