Persistence and long run co-movements across stock market prices

This paper investigates long memory, persistence and co-movements in the most representative stock markets from all over the world. We look at seven stock market indices from Europe, Asia and North America, first individually, by looking at the order of integration of the series from a fractional point of view and comparing different sampling periods (daily, weekly and monthly) for the time period 2009-2020. Then, co-movements across the series are examined by looking at the differences between them. The results indicate that all the individual series are highly persistent, with orders of integration close to 1 in most cases; evidence of a small degree of mean reversion is found in the two American indices (S&P500 and Dow Jones) and, generally, lower orders of integration are found at lower sampling frequencies. Focusing on the co-movements across the series, we observe a reduction in the degree of persistence in the one-by-one differential comparison of the series. Even though the differencing parameter is small compared with what we should have obtained under standard cointegration, this factor still shows long-memory as it ranges in the interval (0.5, 1) in the majority of cases; and appears to be greater when comparing markets from the same geographic region, showing evidence that the convergence process between the stocks is slower between markets of the same continents.