CHAOTIC FORECASTING OF DISCHARGE TIME SERIES: A CASE STUDY1

ABSTRACT: This paper considers the problem of forecasting the discharge time series of a river by means of a chaotic approach. To this aim, we first check for some evidence of chaotic behavior in the dynamic by considering a set of different procedures, namely, the phase portrait of the attractor, the correlation dimension, and the largest Lyapunov exponent. Their joint application seems to confirm the presence of a nonlinear deterministic dynamic of chaotic type. Second, we consider the so‐called nearest neighbors predictor and we compare it with a classical linear model. By comparing these two predictors, it seems that nonlinear river flow modeling, and in particular chaotic modeling, is an effective method to improve predictions.     

STATISTICAL CONSIDERATIONS ON THE RANDOMNESS OF ANNUAL MAXIMUM DAILY RAINFALL1

ABSTRACT: Annual maximum daily rainfall data from nine stations throughout the southern slopes of the Eastern Italian Alps with record length of 67–68 years have been analyzed with the aim of verifying if their internal structure justifies the assumption of independence and identical distribution, or the “White noise hypothesis.” The approach is to consider the hypothesis H₀ of white noise as the intersection of several sub-hypotheses, each concerning one of the characteristics of a white noise process. To this end the nine series were subjected to various statistical tests regarding randomness, independence, change-points, and predictability. The results are examined first individually and then globally. They indicate that in eight of the nine considered time series the “white noise hypothesis” was rejected.