The author gratefully acknowledges financial support from the Ministerio de Ciencia y Tecnología (ECO2008-03035 ECON Y FINANZAS, Spain) and from a PIUNA Project at the University of Navarra. Comments from two anonymous referees and the editor of the journal are gratefully acknowledged.
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Though not explicitly mentioned, ut in (5) admits an infinite AR representation, implying that ut can be expressed in terms of all its past history.
These processes were introduced by Granger (1980, 1981) and Hosking (1981), and they were justified in terms of the aggregation of individual heterogeneous AR(1) processes by Robinson (1978) and Granger (1980).
Seasonal dummy variables were not considered given the lack of systematic patterns in the monthly observations (see Fig. 2).
These two models [(8b) and (8c)] may look inappropriate in view of the correlogram and periodogram of the data. However, in these two plots displayed in Fig. 1, seasonality may be obscuring other important features of the data.
Some authors eliminate trends in the data by using techniques such as wavelets (Arneodo et al. 1996) or detrended fluctuation analysis (DFA; Bunde et al. 2003a). See also Yue et al. (2010) for applications of these techniques in precipitation.
Note, however, that Gaussianity is not a requirement in this procedure with a moment condition of only order 2 required.
Performing AR(1) models for each month, the estimated parameters were −0.03, −0.05, 0.27, 0.03, 0.08, 0.06, 0.12. −0.07, 0.05, 0.08, −0.00, and 0.10, clearly showing a distinct pattern across months.
As earlier mentioned, though long-range persistence exists in temperature, its evidence is weak in rainfall data.