Climatological Time Series with Periodic Correlation

Abstract

Many climatological time series display a periodic correlation structure. This paper examines three issues encountered when analyzing such time series: detection of periodic correlation, modeling periodic correlation, and trend estimation under periodic correlation. Time series containing monthly observations of stratospheric ozone concentrations, average temperatures, and carbon dioxide concentrations are tested for periodic correlation and analyzed further in the paper. A frequency domain test to detect periodic correlation is first reviewed. This test shows that the ozone and temperature series analyzed have a periodic autocorrelation structure; the carbon dioxide series shows periodicities only through its seasonal mean. Next, PARMA models (autoregressive moving average models with periodically varying parameters) are introduced as models for periodically correlated series. Algorithms for fitting a parsimonious PARMA model to a periodically correlated series are presented. Finally, trend estimation with periodically correlated series is explored with trends being found in the temperature and carbon dioxide series. Least squares and maximum likelihood trend estimation methods are compared.