This paper uses the logistic smooth transition GARCH model to study the time-varying volatility of the USS?P 500 index. In the LSTGARCH specification, the parameters are function of some information variables that help capturing the conditional return volatility. Tests of standard GARCH models are provided. Forecast comparisons with the GJR model are proposed, showing an overwhelming predominance of the LSTGARCH model.

The aim of this paper is to present recent contributions extending the classical concept of cointegration to non-linear cases. Thus, we look at a joint study of non-stationary and non-linear phenomena and offer a complete presentation of theoretical developments involving the concepts of integration, memory and non-linear cointegration. Within this framework we look at the methods available to express the non-linear cointegration concept: non-linear error correction models, tools developed from information theory and the concepts of mixed time series and time series with strong dependence. The article also gives a brief overview of empirical literature.

Grandmont [7] was among the first to study the possibility of self-sustaining cycles in the overlapping generations models. In his paper, the origin of these cycles is the conflict between the substitution effect and the income effect due to variations of relative prices. Grandmont’s approach has been criticized on empirical basis: income effects in the model are too large compared to their values in real life. Our paper, conversely, provides some theoretical arguments that explains why cyclical and complex paths cannot be ruled out. In this view, we examine the problem of endogenous fluctuations in pure exchange economies from the viewpoint of macroeconomic theories of consumption and saving.

Cet article présente une étude empirique relative aux dynamiques non-linéaires sur données à haute fréquence. Les séries de cotation utilisées sont celles du Dollar contre le Mark sur le marché londonien durant l'année 1994. Nous montrons que le caractère leptokurtique et asymétrique des distributions peut s'expliquer par la présence de non-linéarités dans la moyenne ou dans la variance conditionnelle des taux de rendement. Nous utilisons le test KPSS et le test du bispectre qui paraissent bien adaptés à nos séries. La composante non-linéaire de la variance conditionnelle est décrite par des processus IGARCH avec loi de Student sur les résidus. Nous estimons en outre des modèles bilinéaires qui révèlent la présence de composantes non-linéaires dans la moyenne conditionnelle. This paper presents an empirical study of non-linear dynamics in high frequency data. We use quotations of the Dollar/Mark exchange rates on the London market during the year 1994. We show that lepto-kurtic and asymmetric distributions in several rates of return are due to the presence of stochastic nonlinearities in either the conditional variance or the conditional mean. Tests such as the KPSS for stationarity and the bispectrum for linearity perform well to our data. Two kinds of models are proposed to model both the volatility and the instability of exchange rates. We first estimate IGARCH processes with Student distributions for the residuals. We also build bilinear models to exhibit non-linear patterns in the conditional mean of the series.