Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance

Abstract

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Nonlinear Cointegration Analysis Based on Support Vector Machines and Its Application to the Connection between Financial Markets

“…Zhang et al (1999) employed a neural network to test the existence of nonlinear cointegration relation and discussed its feasibility [5]. But, the neural network is still flawed to the discriminate analysis of nonlinear cointegration because of its well-known limitations.…”

“…But, the neural network is still flawed to the discriminate analysis of nonlinear cointegration because of its well-known limitations. Here, the ε-SVR will be applied to overcome these limitations and the specific steps are expressed as follows according to the definition [5][11]:…”

“…But, discriminate analysis of whether the relations are nonlinear cointegration constitutes the key step in the nonlinear cointegration test. So far, most literatures concern the test, such as Dufrénot and Mignon (2002) [5], Chang and Park (2003) [6], Lieberman and Phillips (2008) [7], Choi and Saikkonen (2010) [8], etc. These methods can be divided into two categories, that is, the parametric approach and the nonparametric one.…”

“…Grange and Hallman (1991) pioneered the nonlinear transform of variables, socalled nonparametric alternating conditional expectation algorithm, which only demands distribution hypothesis weakly and can thus tackle various nonlinear transform [9]. Dufrénot and Mignon (2002) and Zhang et al (2008) employed neural network technology in succession to cope with parameter estimation of the nonlinear cointegration relations by taking advantage of its good approximation capability of the nonlinear cointegration functions [5] [11].…”

Structure non-linéaire du taux de change et une proposition de modélisation

“…Ensuite, Anderson (1997) a proposé une extension de ces modèles où l'ajustement est plutôt lisse contrairement au modèle de Balke et Fomby (1997) où l'ajustement est brutal. Par suite à ces travaux, les modèles de cointégration à seuil ont fait l'objet de plusieurs analyses empiriques tels que ceux de Escribano (1997), Michael, Peel et Taylor (1997), Dufrénot et Mignon (2002), Sarantis (1999), ainsi que Rothman, Van Dijk et Franses (2001) et Dufrénot et al (2003). Ces travaux ont appliqué les modèles de cointégration à seuil aux différents marchés pour tenir compte des dynamiques non linéaire, dont les sources ont été discutées plus haut (coûts de transaction, hétérogénéité des investisseurs).…”