Techniques of Linear Prediction for Systems with Periodic Statistics

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Abstract
Many parameters that measure climatic variability have nonstationary statistics, that is, they depend strongly on the phase of the annual cycle. In this case normal statistical analysis techniques based on time-invariant models are inappropriate. Generalized methods accounting for seasonal nonstationarity (phase averaged or cyclostationary models) have been developed to treat such data. The methods are applied to the problem of predicting El Niño off South America. It is shown that El Niños may be predicted up to a year in advance with considerably more confidence and accuracy using phase-averaged models than with time-invariant models. In a second application surface air temperature anomalies are predicted over North America from Pacific Ocean sea surface temperatures. Again, the phase-averaged models consistently outperform models based on standard statistical procedures. Abstract Many parameters that measure climatic variability have nonstationary statistics, that is, they depend strongly on the phase of the annual cycle. In this case normal statistical analysis techniques based on time-invariant models are inappropriate. Generalized methods accounting for seasonal nonstationarity (phase averaged or cyclostationary models) have been developed to treat such data. The methods are applied to the problem of predicting El Niño off South America. It is shown that El Niños may be predicted up to a year in advance with considerably more confidence and accuracy using phase-averaged models than with time-invariant models. In a second application surface air temperature anomalies are predicted over North America from Pacific Ocean sea surface temperatures. Again, the phase-averaged models consistently outperform models based on standard statistical procedures.

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