# The data file NILE.TSM consists of the annual minimum water levels of the Nile river as measured at…

Annual Minimum Water Levels; NILE.TSM

The data file NILE.TSM consists of the annual minimum water levels of the Nile river as measured at the Roda gauge near Cairo for the years 622-871. These values are plotted in Figure 10.11 with the corresponding sample autocorrelations shown in Figure 10.12. The rather slow decay of the sample autocorrelation function suggests the possibility of a fractionally inter grated model for the mean-corrected series

*Y _{t}*=

*X*− 1119.

_{t}The ARMA model with minimum (exact) AICC value for the mean-corrected

series {*Y _{t}*} is found, using Model>Estimation>Auto fit, to be

*Y _{t}*= −

*.*323

*Y*

_{t}_{−1}−

*.*060

*Y*

_{t}_{−2}+

*.*633

*Y*

_{t}_{−3}+

*.*069

*Y*

_{t}_{−4}+

*.*248

*Y*

_{t}_{−5}

+ *Z _{t} *+

*.*702

*Z*

_{t}_{−1}+

*.*350

*Z*

_{t}_{−2}−

*.*419

*Z*

_{t}_{−3}

*,*

Figure 10-12 The sample correlation function of the data in Figure 10.11.