Automatic detection of parsimony for heteroskedastic time series processes

Abstract

The paper proposes a new multiple-representation geno-mathematical algorithm for coping with ill-conditioned time series processes through competing nonlinear model formulations. Extensive testing and comparisons to a rigorous statistical time series package indicate that the geno-mathematical search-machine is effective and robust for modelling complicated time series. The new algorithm is used to model a representative set of global asset returns. The diagnostic tests prove that the ARCH-effects of the dif®cult nonlinear processes are annihilated completely in both full and reduced model variants. IntroductionThe present study considers a technique for automatic generation of parsimonious representations for autoregressive conditionally heteroskedastic (ARCH) processes. The topic is important, since numerous economic time series exhibit ARCH-related features. At the same time, the commercially available statistical program packages leave the model speci®cation task to the researcher. Any beautiful theoretical model works as expected with simulated data, when based exactly on the theoretical assumptions. However, when confronted with observed data, the theoretical models usually have to be modi®ed in some suitable way, to cope with unexpected anomalies. Needless to say, estimation of complicated nonlinear time series processes with observed data requires ± almost without exception ± extensive and time consuming testing of numerous alternative model speci®cations, before the ultimate choice can be made. Much of this (non) systematic search can be left to the computer, given suitable software. The empirical researcher should be able to devote his energy to creative work in model speci®cation and interpretation of robust estimation results instead of time-consuming tampering with unreliable statistical packages that frequently produce core dump when applied to ill-conditioned time series.Such packages induce an inherent slow-down of research and require attention on completely irrelevant aspects from a time series modelling viewpoint.Our study represents the intersection of two important research domains: modelling of nonlinear ([X]ARCH) time series and geno-mathematical programming. Our objective is to design and implement a search machine, in which the features of a newly developed genetic hybrid algorithm (O È stermark 1999b, 2001b) are combined with classical maximum likelihood estimation of ARCH-processes. The geno-mathematical programming system has been extensively tested and compared to other techniques in, e.g. O È stermark (1999c, 2000, 2001a).In O È stermark (2001b) we applied a neuro-genetic hybrid algorithm (NGHA) to a dif®cult econometric problem arising from the dynamics of global asset returns. Following Engle (1987a), we initially subjected the global returns database to factor analysis, giving three distinct factors (O È stermark 1997). The time series of the factors were modelled by some rigorous autoregressive conditional heteroskedastic (ARCH)-models suggested in the literature: the self-excit...