of nonlinear time series
Carlo Novara, Mario Milanese · 2001
In this paper a nonlinear prediction method based on a Set Mcmbcrship approach is proposcd. Such method does not need any assumption about the functional form of thc model used for prcdiction, but uses only some information on its regularity. At thc contrary, most of the existing prediction methods need the choicc of a model structure and this choicc is usually thc result of heuristic searches. Thcsc searches may be quite time consuming, and lead only to approximatc modcl structurcs, whosc crrors may be responsible of bad propagation of prediction errors, especially for the multi-step ahcad prediction. Moreovcr, the mcthod proposed in this papcr assumcs only that the noisc is boundcd, in contrast with statistical approaches, which rcly on assumptions such as stationarity, crgodicity, uncorrelation, typc of distribution, etc. The validity of these assumptions may be difficult to be rcliably tested in many applications, whcrc scrics of short lcngth are availablc, and is ccrtainly lost in prcscncc of approximatc modeling. Thc effectivcncss of thc method is tcsted on simulated data and real word data (Wolf Sunspot Numbers scries), comparing thc obtained prcdiction pcrformanccs with thosc obtained by mcthods bascd on neural networks and on statistical models.