Statistical Modeling of the Temperatures in the Northern Hemisphere Using Fractional Integration Techniques

The temperatures in the Northern Hemisphere from 1854 to 1999 have been analyzed in this article by means of a testing procedure that permits one to consider fractional degrees of integration. The tests are valid under general forms of serial correlation and deterministic trends and do not require estimation of the fractional differencing parameter. The results show that the series follows a fractionally integrated process with the order of integration higher than zero and thus implying long memory behavior. The series was decomposed into four different subsamples, and it was observed that the degree of dependence between the observations substantially increased during the twentieth century.

[1]  Tom M. L. Wigley,et al.  A Bivariate Time Series Approach to Anthropogenic Trend Detection in Hemispheric Mean Temperatures , 2003 .

[2]  David I. Harvey,et al.  Unit roots and double smooth transitions , 2002 .

[3]  P. Stott,et al.  Origins and estimates of uncertainty in predictions of twenty-first century temperature rise , 2002, Nature.

[4]  J. Stock,et al.  Macroeconomic Forecasting Using Diffusion Indexes , 2002 .

[5]  Donald B. Percival,et al.  Interpretation of North Pacific Variability as a Short- and Long-Memory Process* , 2001 .

[6]  Luis A. Gil-Alana,et al.  A fractionally integrated exponential model for UK unemployment , 2001 .

[7]  Lajos Horváth,et al.  Change-Point Detection in Long-Memory Processes , 2001 .

[8]  L. Gil-Alana,et al.  Testing Stochastic Cycles in Macroeconomic Time Series , 2001 .

[9]  David I. Harvey,et al.  Modelling global temperature trends using cointegration and smooth transitions , 2001 .

[10]  L. Gil‐Alana.  Mean reversion in the real exchange rates , 2000 .

[11]  F. Diebold,et al.  Long Memory and Regime Switching , 2000 .

[12]  L. Gil‐Alana.  Testing of Seasonal Fractional Integration in UK and Japanese Consumption and Income , 2000 .

[13]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[14]  Xiaogu Zheng,et al.  Structural Time Series Models and Trend Detection in Global and Regional Temperature Series , 1999 .

[15]  M. Taqqu,et al.  Estimating long-range dependence in the presence of periodicity: An empirical study , 1999 .

[16]  R. J. Bhansali,et al.  On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes , 1998 .

[17]  Richard L. Smith,et al.  Anthropogenic influence on the autocorrelation structure of hemispheric-mean temperatures , 1998, Science.

[18]  M. Taqqu,et al.  Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation , 1997 .

[19]  Walter Willinger,et al.  Proof of a fundamental result in self-similar traffic modeling , 1997, CCRV.

[20]  Murad S. Taqqu,et al.  Some long‐run properties of rainfall records in Italy , 1996 .

[21]  P. Robinson,et al.  Testing of unit root and other nonstationary hypotheses in macroeconomic time series , 1996 .

[22]  Jan Beran,et al.  Testing for a change of the long-memory parameter , 1996 .

[23]  Richard T. Baillie,et al.  Long memory processes and fractional integration in econometrics , 1996 .

[24]  B. Mandelbrot,et al.  A CLASS OF MICROPULSES AND ANTIPERSISTENT FRACTIONAL BROWNIAN MOTION , 1995 .

[25]  P. Robinson.  Gaussian Semiparametric Estimation of Long Range Dependence , 1995 .

[26]  Henry L. Gray,et al.  Selecting a Model for Detecting the Presence of a Trend , 1995 .

[27]  P. Robinson.  Log-Periodogram Regression of Time Series with Long Range Dependence , 1995 .

[28]  P. Robinson.  Efficient Tests of Nonstationary Hypotheses , 1994 .

[29]  Mark W. Watson,et al.  Estimating Deterministic Trends in the Presence of Serially Correlated Errors , 1994, Review of Economics and Statistics.

[30]  Tim Bollerslev,et al.  Cointegration, Fractional Cointegration, and Exchange Rate Dynamics , 1994 .

[31]  P. Robinson.  Semiparametric Analysis of Long-Memory Time Series , 1994 .

[32]  Henry L. Gray,et al.  Global warming and the problem of testing for trend in time series data , 1993 .

[33]  John W. Galbraith,et al.  Inference about trends in global temperature data , 1992 .

[34]  Peter Schmidt,et al.  LM Tests for a Unit Root in the Presence of Deterministic Trends , 1992 .

[35]  K. Briffa,et al.  Global Surface Air Temperature Variations During the Twentieth Century: Part 1, Spatial, Temporal and Seasonal Details , 1992 .

[36]  D. Nychka,et al.  Climate spectra and detecting climate change , 1992 .

[37]  P. Bloomfield.  Trends in global temperature , 1992 .

[38]  J. Hansen,et al.  Global surface air temperatures: update through 1987 , 1988 .

[39]  J. Hansen,et al.  Global trends of measured surface air temperature , 1987 .

[40]  A. Raftery,et al.  Space-time modeling with long-memory dependence: assessing Ireland's wind-power resource. Technical report , 1987 .

[41]  J. Hosking.  Modeling persistence in hydrological time series using fractional differencing , 1984 .

[42]  C. Granger.  Some properties of time series data and their use in econometric model specification , 1981 .

[43]  C. Granger.  Long memory relationships and the aggregation of dynamic models , 1980 .

[44]  Bridger M. Mitchell,et al.  Estimating the Autocorrelated Error Model with Trended Data: Further Results, , 1980 .

[45]  M. Taqqu.  Weak convergence to fractional brownian motion and to the rosenblatt process , 1975, Advances in Applied Probability.

[46]  R. K. Adenstedt,et al.  On Large-Sample Estimation for the Mean of a Stationary Random Sequence , 1974 .

[47]  P. Bloomfield.  An exponential model for the spectrum of a scalar time series , 1973 .

[48]  U. Grenander,et al.  Statistical analysis of stationary time series , 1958 .

[49]  H. Hurst,et al.  A Suggested Statistical Model of some Time Series which occur in Nature , 1957, Nature.

[50]  Crowley,et al.  Atmospheric science: Methane rises from wetlands , 2011, Nature.

[51]  David B. Stephenson,et al.  Is the North Atlantic Oscillation a random walk , 2000 .

[52]  William R. Parke.  What is Fractional Integration? , 1999, Review of Economics and Statistics.

[53]  Marcus J. Chambers,et al.  Long Memory and Aggregation in Macroeconomic Time Series , 1998 .

[54]  Richard L. Smith,et al.  Regression in Long-Memory Time Series , 1996 .

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

[56]  R. Smith.  Long-range dependence and global warming , 1992 .

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

[58]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[59]  P. Robinson,et al.  Statistical inference for a random coefficient autoregressive model , 1978 .

[60]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .