xv
14.3.4 Spectral Properties . . . . . . . . . . . . . .
266
14.3.5 Choice of the Embedding Dimension . . . .
266
14.3.6 Estimating Time and Space-Time Patterns
267
14.4 Climatic Applications of SSA . . . . . . . . . . . .
268
14.4.1 The Analysis of Intraseasonal Oscillations .
268
14.4.2 Empirical Long-Range Forecasts Using MSSA Predictors275
14.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .. 278
15 Multivariate Statistical Modeling: POP-Model as a First Order Approximation
281
by JIN-SONG VON STORCH
15.1 Introduction . . . . . . . . . . . .
281
15.2 The Cross-Covariance Matrix
and the Cross-Spectrum Matrix .
15.3 Multivariate AR(l) Process
and its Cross-Covariance
and Cross-Spectrum Matrices . . . . . . . . .
15.3.1 The System Matrix A and its POPs .
15.3.2 Cross-Spectrum Matrix in POP-Basis:
Its Matrix Formulation . . . . . . . .
15.3.3 Cross-Spectrum Matrix in POP-Basis:
Its Diagonal Components . . . . . . .
15.3.4 Eigenstructure of Cross-Spectrum Matrix
at a Frequency Interval: Complex EOFs .
15.3.5 Example. . . . . . . . . . . . . . . . . . .
15.4 Estimation of POPs and Interpretation Problems
15.5 POPs as Normal Modes . . . . . . . . . . . . . .
References
Ab breviations
Index
284
285
286
286
288
289
292
295
296
299
329
331