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.

[1]  Clive W. J. Granger,et al.  Developments in the study of cointegrated economic variables , 2001 .

[2]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[3]  Fallaw Sowell.  Maximum likelihood estimation of stationary univariate fractionally integrated time series models , 1992 .

[4]  S. Johansen,et al.  Statistical Analysis of Global Surface Air Temperature and Sea Level Using Cointegration Methods , 2011 .

[5]  S. Rahmstorf.  Response to Comments on "A Semi-Empirical Approach to Projecting Future Sea-Level Rise" , 2007, Science.

[6]  W. Landman.  Climate change 2007: the physical science basis , 2010 .

[7]  W. Palma.  Long-Memory Time Series: Theory and Methods , 2007 .

[8]  J. Dolado,et al.  A Fractional Dickey–Fuller Test for Unit Roots , 2002 .

[9]  J. Houghton,et al.  Climate Change 2013 - The Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change , 2014 .

[10]  Corinne Le Quéré,et al.  Climate Change 2013: The Physical Science Basis , 2013 .

[11]  Ying-Wong Cheung,et al.  A Fractional Cointegration Analysis of Purchasing Power Parity , 1993 .

[12]  A. Mackay.  Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change , 2008 .

[13]  Wen-Jen Tsay,et al.  The spurious regression of fractionally integrated processes , 2000 .

[14]  N. White,et al.  Sea-Level Rise from the Late 19th to the Early 21st Century , 2011 .

[15]  Michael E. Mann,et al.  Climate over past millennia , 2004 .

[16]  P. Jones,et al.  Uncertainty estimates in regional and global observed temperature changes: A new data set from 1850 , 2006 .

[17]  Wilfredo Palma,et al.  Long-memory time series , 2007 .

[18]  S. Grassi,et al.  The statistical relation of sea-level and temperature revisited , 2013 .

[19]  J. Hansen,et al.  GLOBAL SURFACE TEMPERATURE CHANGE , 2010 .

[20]  Katsumi Shimotsu,et al.  EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND , 2009, Econometric Theory.

[21]  Makiko Sato,et al.  A closer look at United States and global surface temperature change , 2001 .

[22]  Aslak Grinsted,et al.  Reconstructing sea level from paleo and projected temperatures 200 to 2100AD , 2009 .

[23]  J. Palutikof,et al.  Climate change 2007 : impacts, adaptation and vulnerability , 2001 .

[24]  Robert J. Nicholls,et al.  Sea‐level scenarios for evaluating coastal impacts , 2014 .

[25]  Anny Cazenave,et al.  The rate of sea-level rise , 2014 .

[26]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[27]  Roberto Roson,et al.  Economy-wide Estimates of the Implications of Climate Change: Sea Level Rise , 2004 .

[28]  K. Holmgren,et al.  Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data , 2005, Nature.

[29]  Glenn D. Rudebusch,et al.  On the Power of Dickey-Fuller Tests against Fractional Alternatives , 1991, Business Cycles.

[30]  Peter C. B. Phillips,et al.  Exact Local Whittle Estimation of Fractional Integration , 2002 .

[31]  S. Rahmstorf,et al.  Global sea level linked to global temperature , 2009, Proceedings of the National Academy of Sciences.

[32]  M. Galeotti,et al.  On the Robustness of Robustness Checks of the Environmental Kuznets Curve Hypothesis , 2008 .

[33]  S. Jevrejeva,et al.  Nonlinear trends and multiyear cycles in sea level records , 2006 .

[34]  Katsumi Shimotsu.  Exact local Whittle estimation of fractionally cointegrated systems , 2012 .

[35]  Comment on "A Semi-Empirical Approach to Projecting Future Sea-Level Rise" , 2007, Science.

[36]  N. White,et al.  A 20th century acceleration in global sea‐level rise , 2006 .

[37]  S. Johansen,et al.  Statistical Analysis of Global Surface Air Temperature and Sea Level Using Cointegration Methods , 2011 .

[38]  A. Cameron,et al.  Microeconometrics: Methods and Applications , 2005 .

[39]  Anny Cazenave,et al.  Causes for contemporary regional sea level changes. , 2013, Annual review of marine science.

[40]  S. Jevrejeva,et al.  Comment on "A Semi-Empirical Approach to Projecting Future Sea-Level Rise" , 2007, Science.

[41]  Other,et al.  Working Group II Contribution to the Intergovernmental Panel on Climate Change Fourth Assessment Report: Climate Change 2007: Climate Change Impacts, Adaptation and Vulnerability: Summary for Policymakers , 2007 .

[42]  Vincent R. Gray.  Climate Change 2007: The Physical Science Basis Summary for Policymakers , 2007 .