How long is the memory of the US stock market?

The Efficient Market Hypothesis (EMH), one of the most important hypothesis in financial economics, argues that return rates have no memory (correlation) which implies that agents cannot make abnormal profits in financial markets, due to the possibility of arbitrage operations. With return rates for the US stock market, we corroborate the fact that with a linear approach, return rates do not show evidence of correlation. However, linear approaches might not be complete or global, since return rates could suffer from nonlinearities. Using detrended cross-correlation analysis and its correlation coefficient, a methodology which analyzes long-range behavior between series, we show that the long-range correlation of return rates only ends in the 149th lag, which corresponds to about seven months. Does this result undermine the EMH?

Do Global CO2 Emissions from Fossil-Fuel Consumption Exhibit Long Memory? A Fractional Integration Analysis

In this article we use an autoregressive fractionally integrated moving average approach to measure the degree of fractional integration of aggregate world CO2 emissions and its five components – coal, oil, gas, cement, and gas flaring. We find that all variables are stationary and mean reverting, but exhibit long-term memory. Our results suggest that both coal and oil combustion emissions have the weakest degree of long-range dependence, while emissions from gas and gas flaring have the strongest. With evidence of long memory, we conclude that transitory policy shocks are likely to have long-lasting effects, but not permanent effects. Accordingly, permanent effects on CO2 emissions require a more permanent policy stance. In this context, if one were to rely only on testing for stationarity and non-stationarity, one would likely conclude in favour of non-stationarity, and therefore that even transitory policy shocks