POPs and MOPs

 Principal oscillation pattern (POP) analysis fits a first order multivariate autoregressive model to a reduced subset of the variables of a complex system. It has been shown in the past that important modes of complex systems can be detected through the POP technique. In this note two problems with this method will be addressed. Firstly, the POP analysis may face difficulties if the reduced system is of higher order in time than first. An example from linear equatorial wave dynamics is given to illustrate this point. Autoregressive models of higher order (MOP-models) are shown to provide a partial solution in such situations but are not fully satisfactory either. Nonlinearity may cause problems as well. A nonlinear low-order model is used to discuss this point. Both the POP and the MOP scheme are applied without data reduction. The MOP approach is superior to the POP technique in that it detects oscillating patterns which elude the POP analysis. The results suggest that the MOP analysis may be a valuable extension of the POP approach. Received: 29 July 1998 / Accepted: 10 February 1999