Nonlinear Financial Econometrics: Markov Switching Models, Persistence and Nonlinear Cointegration by Greg N. Gregoriou & Razvan Pascalau

Author:Greg N. Gregoriou & Razvan Pascalau
Language: eng
Format: epub
Publisher: Palgrave Macmillan
Published: 2011-06-14T16:00:00+00:00

where the union is taken over all persistence decay patterns. A transformation g belongs in space Eb.t. (0) if and only if predictor E[g(Xt+h)|Zt] to infinity.

In Section 3, we noted that a regular, stationary process is such that Eb.t.(0)is equal to the set of all scalar functions. In general, this space is strictly smaller, and the behavior of some transformations of a process can resemble the behavior of a stationary process, while the behavior of other transformations may look nonstationary. This leads to the following definition of nonlinear integration.

Definition 7.2. If g belongs in Eb.t.(0), the transformed process is nonlinearly integrated of order 0 (NLI(0)). If g does not belong in Eb.t.(0), the transformed process is NLI (nonlinearly integrated).

The above definition of nonlinear integration is used in the sequel to define nonlinear cointegration.

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