Auto-Correlation Functions and Solar Cycle Predictability

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Starting from the traditional definition of auto-correlation function we can introduce a new quantity, based on the wavelet formalism, called local wavelet auto-correlation function, which contains more information about the correlation properties on a given signal on different scales. The application of this formalism to the temporal variations of solar activity, from the monthly time series of sunspot numbers, allows to derive some interesting information about the correlation properties of different periodicities present in the signal and in particular the correlation characteristics of the main 11 years Schwabe cycle. The scale selectivity, allowed by the local wavelet auto-correlation function, can give interesting information about the range of reliable predictions reachable through deterministic predictive models.