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. Next, PARMA models (autoregressive moving average models with periodically varying parameters) are introduced as models for periodically correlated series. Finally, trend estimation with periodically correlated series is explored.