473
signal amplitude associated with a fairly broad spectral peak (Ghil and
Mo 1991a, Plaut and Vautard 1994). MTM-based harmonic analysis can
be adapted, by using a sliding window, to follow the slow shift in time of a
sharp line's frequency (Yiou et al. 1991, Birchfield and Ghil1993). When
applied to time series (Flandrin 1993), wavelet analysis seems to provide
an even more natural way of following a quasi-adiabatic or sudden change
in the natural frequency of a climatic oscillator (Meyers et al. 1993, Yiou
et al. 1995). Suitable significance criteria for wavelet analysis results need
to be developed and a tantalizing question (Yiou 1994) is whether dataadaptive wavelet bases, combining in some sense SSA with wavelets, can
be developed, not unlike the way that SSA and MEM turned out to "be
made for each other."
Acknowledgments
It is gratifying to thank our SSA, MEM and MTM collaborators, M. R.
Allen, P. Billant, M. D. Dettinger, N. Jiang, C. Keppenne, M. Kimoto, M.
Mann, J. D. Neelin, C. Penland, G. Plaut, A. R. Robertson, C. M. Strong,
R. Vautard, Y. S. Unal and W. Weibel for the pleasure of working together
and exchanging ideas; we hope that this review gives credit to the joint
work and does not betray their, occasionally different, ideas. Comments
and Fig. 1 from K. Ide, as well as Fig. 12 from R. Vautard, are greatly
appreciated. M.G.'s SSA work is supported by NSF grant ATM90-13217
and P.Y.'s by the French Commissariat a l'Energie Atomique. M.G. is also
indebted to the French Academie des Sciences for the visiting Chair that
provided the necessary leisure for the writing. This is IGPP publication
no. 4607 and LMCE publication no. 00368.
References
Akaike H. (1969) Fitting autoregressive models for prediction. Ann. Inst.
Statist. Math. 21:243-247
Akaike H. (1974) A new look at the statistical model identification. IEEE
Trans. Autom. Control 19:716-723
Allen M. (1992) Interactions Between the Atmosphere and Oceans on Time
Scales of Weeks to Years. PhD thesis St. John's College Oxford
signal amplitude associated with a fairly broad spectral peak (Ghil and
Mo 1991a, Plaut and Vautard 1994). MTM-based harmonic analysis can
be adapted, by using a sliding window, to follow the slow shift in time of a
sharp line's frequency (Yiou et al. 1991, Birchfield and Ghil1993). When
applied to time series (Flandrin 1993), wavelet analysis seems to provide
an even more natural way of following a quasi-adiabatic or sudden change
in the natural frequency of a climatic oscillator (Meyers et al. 1993, Yiou
et al. 1995). Suitable significance criteria for wavelet analysis results need
to be developed and a tantalizing question (Yiou 1994) is whether dataadaptive wavelet bases, combining in some sense SSA with wavelets, can
be developed, not unlike the way that SSA and MEM turned out to "be
made for each other."
Acknowledgments
It is gratifying to thank our SSA, MEM and MTM collaborators, M. R.
Allen, P. Billant, M. D. Dettinger, N. Jiang, C. Keppenne, M. Kimoto, M.
Mann, J. D. Neelin, C. Penland, G. Plaut, A. R. Robertson, C. M. Strong,
R. Vautard, Y. S. Unal and W. Weibel for the pleasure of working together
and exchanging ideas; we hope that this review gives credit to the joint
work and does not betray their, occasionally different, ideas. Comments
and Fig. 1 from K. Ide, as well as Fig. 12 from R. Vautard, are greatly
appreciated. M.G.'s SSA work is supported by NSF grant ATM90-13217
and P.Y.'s by the French Commissariat a l'Energie Atomique. M.G. is also
indebted to the French Academie des Sciences for the visiting Chair that
provided the necessary leisure for the writing. This is IGPP publication
no. 4607 and LMCE publication no. 00368.
References
Akaike H. (1969) Fitting autoregressive models for prediction. Ann. Inst.
Statist. Math. 21:243-247
Akaike H. (1974) A new look at the statistical model identification. IEEE
Trans. Autom. Control 19:716-723
Allen M. (1992) Interactions Between the Atmosphere and Oceans on Time
Scales of Weeks to Years. PhD thesis St. John's College Oxford