Long-Range Dependence and Sea Level Forecasting

Ali Ercan, M. Levent Kavvas, Rovshan K. Abbasov

This study shows that the Caspian Sea level time series possess long range dependence even after removing linear trends, based on analyses of the Hurst statistic, the sample autocorrelation functions, and the periodogram of the series. Forecasting performance of ARMA, ARIMA, ARFIMA and Trend Line-ARFIMA (TL-ARFIMA) combination models are investigated. The forecast confidence bands and the forecast updating methodology, provided for ARIMA models in the literature, are modified for the ARFIMA models. Sample autocorrelation functions are utilized to estimate the differencing lengths of the ARFIMA models. The confidence bands of the forecasts are estimated using the probability densities of the residuals without assuming a known distribution. There are no long-term sea level records for the region of Peninsular Malaysia and Malaysia’s Sabah-Sarawak northern region of Borneo Island. In...