Long-Memory and the Sea Level-Temperature Relationship: A Fractional Cointegration Approach

Through thermal expansion of oceans and melting of land-based ice, global warming is very likely contributing to the sea level rise observed during the 20th century. The amount by which further increases in global average temperature could affect sea level is only known with large uncertainties due to the limited capacity of physics-based models to predict sea levels from global surface temperatures. Semi-empirical approaches have been implemented to estimate the statistical relationship between these two variables providing an alternative measure on which to base potentially disrupting impacts on coastal communities and ecosystems. However, only a few of these semi-empirical applications had addressed the spurious inference that is likely to be drawn when one nonstationary process is regressed on another. Furthermore, it has been shown that spurious effects are not eliminated by stationary processes when these possess strong long memory. Our results indicate that both global temperature and sea level indeed present the characteristics of long memory processes. Nevertheless, we find that these variables are fractionally cointegrated when sea-ice extent is incorporated as an instrumental variable for temperature which in our estimations has a statistically significant positive impact on global sea level.