Complexity and predictability of the monthly Western Mediterranean Oscillation index

The complexity, predictability and predictive instability of the Western Mediterranean Oscillation index ( WeMOi ) at monthly scale, years 1856–2000, are analysed from the viewpoint of monofractal and multifractal theories. The complex physical mechanism is quantified by: (1) the Hurst exponent, H , of the rescaled range analysis; (2) correlation and embedding dimensions, μ * and d E , together with Kolmogorov entropy, κ , derived from the reconstruction theorem; and (3) the critical Hölder exponent, α o , the spectral width, W , and the asymmetry of the multifractal spectrum, f ( α ). The predictive instability is described by the Lyapunov exponents, λ , and the Kaplan–Yorke dimension, D KY , while the self‐affine character is characterized by the Hausdorff exponent, H a . Relationships between the exponent β , which describes the dependence of the power spectrum S ( f ) on frequency f , and the Hurst and Hausdorff exponents suggest fractional Gaussian noise ( fGn ) as a right simulation of empiric WeMOi . Comparisons are made with monthly North‐Atlantic Oscillation and Atlantic Multidecadal Oscillation indices. The analysis is complemented with an ARIMA (p,1,0) autoregressive process, which yields a more accurate prediction of WeMOi than that derived from fGn simulations.