| Abstract: | The non‐stationary Functional Series time‐dependent autoregressive moving average (TARMA) modelling and simulation of earthquake ground motion is considered. Full Functional Series TARMA models, capable of modelling both resonances and antiresonances, are examined for the first time via a novel mixed parametric/non‐parametric estimation scheme, and critical comparisons with pure TAR and recursive ARMA (RARMA)‐recursive maximum likelihood (RML) adaptive filtering type modelling are made. The study is based upon two California ground motion signals: a 1979 El Centro accelerogram and a 1994 Pacoima Dam accelerogram. A systematic analysis, employing various functional subspaces and model orders, leads to two Haar function based models: a TARMA(2,4)8 model for the El Centro case and a TARMA(6,2)10 model for the Pacoima Dam case. Both models are formally validated and their simulation (synthesis) capabilities are demonstrated via Monte Carlo experiments focusing on important time domain signal characteristics. The Functional Series TAR/TARMA models are shown to achieve parsimony, as well as superior accuracy and simulation capabilities, over their RARMA counterparts. Copyright © 2001 John Wiley & Sons Ltd. |
