Embedding reconstruction methodology for short time series – application to large El Niño events

• Main Authors: H. F. Astudillo, F. A. Borotto, R. Abarca-del-Rio
• Format: Article
• Language: English
• Published: Copernicus Publications 2010-12-01
• Series: Nonlinear Processes in Geophysics
• Online Access: http://www.nonlin-processes-geophys.net/17/753/2010/npg-17-753-2010.pdf

We propose an alternative approach for the embedding space reconstruction method for short time series. An <i>m</i>-dimensional embedding space is reconstructed with a set of time delays including the relevant time scales characterizing the dynamical properties of the system. By using a maximal predictability criterion a <i>d</i>-dimensional subspace is selected with its associated set of time delays, in which a local nonlinear blind forecasting prediction performs the best reconstruction of a particular event of a time series. An locally unfolded <i>d</i>-dimensional embedding space is then obtained. The efficiency of the methodology, which is mathematically consistent with the fundamental definitions of the local nonlinear long time-scale predictability, was tested with a chaotic time series of the Lorenz system. When applied to the Southern Oscillation Index (SOI) (observational data associated with the El Niño-Southern Oscillation phenomena (ENSO)) an optimal set of embedding parameters exists, that allows constructing the main characteristics of the El Niño 1982–1983 and 1997–1998 events, directly from measurements up to 3 to 4 years in advance.