Approximate Models and Error Analysis

Exogenous disturbances affect time series variables in complex and varied ways. Their relationships are usually only approximately captured by models. In the frequency domain, rational transfer functions of the models are best viewed as approximations to more complex rational, or possibly irrational, transfer functions. In the time domain, finite-dimensional state space (innovation) models merely approximate dynamic phenomena of greater complexity that cannot be conveniently captured. Model builders can only hope to reproduce some salient features of actual dynamics by judicious choice of the dimension and the values of model system matrices, and by analyzing the consequences of adding (deleting) a time series from the data vector, or of retaining (dropping) correlations between some of the data components.