Autore: Grillenzoni, Carlo
Titolo: Forecasting unstable and non-stationary time series
Periodico: European University Institute of Badia Fiesolana (Fi). Department of Economics - Working papers
Anno: 1993 - Fascicolo: 1 - Pagina iniziale: 1 - Pagina finale: 27

Many of the time series encountered in social and economic applications are asymptotically unstable and intrinsically non-stationary, i.e. satisfy difference equations with roots greater than one (in modulus) and with time-varying coefficients. Time series modeling developed by Box & Jenkins (1976) solves these problems by imposing on data two groups of stationarity transformations : differencing and exponential (Box-Cox). Owing to a generalization of the Jensen inequality, these transformations are not optimal from the forecasting viewpoint and, sometimes, they may be entirely arbitrary. In this paper it is shown that there are no practical and methodological obstacles in modeling time series with unstable roots and changing coefficients. Paradoxically, instability has useful consequences for conventional least squares estimators since it improves their speed of convergence in probability. This property, named super-consistency, was thoroughly analyzed by statisticians in the '50 and in this paper it is investigated by means of recursive estimators applied to simulated data. Next, the effectiveness of adaptive recursive estimators in tracking time-varying unstable roots is shown in the context of an application to the airline data-set of Box-Jenkins. This framework is proper for forecasting time series with trends, cycles and seasonalities whose patterns change over time. Since it does not assume a-priori dynamics for such components, it may be used as a non-parametric alternative to the structured models of Harrison-Harvey.




Testo completo: http://hdl.handle.net/1814/442

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