Long-Range Dependence and Sea Level Forecasting by Ali Ercan M. Levent Kavvas & Rovshan K. Abbasov

Author:Ali Ercan, M. Levent Kavvas & Rovshan K. Abbasov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.3)

where L is the differencing length. In order to estimate the differencing length L for the Caspian Sea level data, the sample ACFs of the residuals were compared for various differencing lengths L for periods from 1837 to 1977, to 1995 and to 2009, respectively. For illustration the sample ACFs of the residuals, together with two standard error limits (), are depicted for various differencing lengths (L = 40, 60, 80 100, 120, 130, 135, 140, 145 years) for 1837–2009 period in Fig. 4.9. The differencing lengths that minimize the magnitude of the sample ACF of the residuals are estimated as 110 years for 1837–1977 period, and 140 years for 1837–1995 and 1837–2009 periods. After applying fractional differencing, a first order AR model was fitted by the least squares estimation method to the residuals. The AR coefficients are estimated as 0.9999, 0.9525 and 0.9773 for 1837–1977, 1837–1995, and 1837–2009 periods, respectively. The standardized lower bound zp− is estimated as −1.75, −1.53, −2.66; and the standardized upper bound zp+ is estimated as 1.86, 2.23, 2.15 for ARFIMA models for 1837–1977, 1837–1995, and 1837–2009 periods, respectively. Residuals of the ARFIMA models pass the portmanteau lack of fit test that was applied to the first 15 sample autocorrelations, and the cumulative periodogram test using 5 % Kolmogorov-Smirnov limits.

Fig. 4.9Sample ACF of residuals for differencing lengths of 40, 60, 80 100, 120, 130, 135, 140, 145 years for the period 1837–2009

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