An Application of Low-Order Arma and Garch Models for Sea Level Fluctuations

The paper presents the analysis of geographically-dependent irregular sea level fluctuations, often referred to as residual terms around deterministic signals, carried out by means of stochastic low-order autoregressive moving average (ARMA) and generalised autoregressive conditional heteroscedastic (GARCH) models. The gridded sea level anomaly (SLA) time series from TOPEX/Poseidon (T/P) and Jason-1 (J-1) satellite altimetry, commencing on 10th January 1993 and finishing on 14th July 2003, has been examined. The aforementioned models, limited to low-orders being combinations of 0,1 and 2, have been fitted to the SLA data. The root mean square and the Shapiro-Wilk test for the normal distribution have been used to calculate statistics of the residuals from these models. It has been found that autoregressive (AR) models as well as ARMA ones serve well the purpose of adequate modelling irregular sea level fluctuations, with a successful fit in some patchy bits of the equatorial Pacific. In contrast, GARCH models have been shown to be rather inaccurate, specifically in the vicinity of the tropical Pacific, in the North Pacific and in the equatorial Indian Ocean. The pattern of the Tropical Instability Waves (TIWs) has been noticed in the statistics of AR and ARMA model residuals indicating that the dynamics of these waves cannot be captured by the aforementioned linear stochastic processes.