The memory of ENSO revisited by a 2-factor Gegenbauer process

This article specifies a multi-factor long memory process, namely Gegenbauer process, particularly adapted for data with slow damping correlations and cyclical patterns, and explores the use of this representation in the inter-annual climate variability range capture by indices of the El Niño Southern Oscillation (ENSO). The empirical results suggest that sea surface temperature (SST) indices are stationary long memory processes. It is found that the indices in the eastern and central Pacific exhibit different dynamics. The variability of the eastern equatorial Pacific SST indices (Niño 1 − 2 and Niño 3) is characterized by a large component of long-memory behaviour associated with the quasi-biennial and the semi-annual frequency. In contrast, the variability of the central Pacific SST indices (Niño 3.4 and Niño 4) is characterized by a large component of long-memory behaviour associated with the annual and the semi-annual frequency. These results are consistent with recent studies that suggest that ENS0 SST anomalies in the equatorial Pacific can be considered to consist of two processes. The use of Gegenbauer processes can be considered as an alternative competitive procedure in the analysis of cyclical long memory climatological time series from a different time series perspective.