Recent Developments in Nonlinear Cointegration with - download pdf or read online

By Gilles Dufrénot

ISBN-10: 1441952764

ISBN-13: 9781441952769

ISBN-10: 1475736150

ISBN-13: 9781475736151

This booklet is an introductory exposition of alternative issues that emerged within the literature as unifying issues among fields of econometrics of time sequence, particularly nonlinearity and nonstationarity. Papers on those subject matters have exploded during the last twenty years, yet they're hardly ex­ amined jointly. there's, definitely, numerous arguments that justify this type of separation. yet there also are solid purposes that encourage their mix. those people who are reluctant to a mixed research may perhaps argue that nonlinearity and nonstationarity improve non-trivial difficulties, so their mix doesn't stimulate curiosity in regard to plausibly elevated problems. This argument can, in spite of the fact that, be balanced via different ones of an monetary nature. A main proposal, this day, is nonstationary sequence shows chronic deviations from its long-run parts (either deterministic or stochastic trends). those power deviations are modelized in numerous methods: unit root versions, fractionally built-in procedures, types with shifts within the time pattern, and so forth. even if, there are various different behaviors inherent to nonstationary strategies, that aren't mirrored in linear types. for example, fiscal variables with mix distributions, or strategies which are state-dependent, endure episodes of adjusting dynamics. In versions with a number of long-run equi­ libria, the relocating from an equilibrium to a different occasionally implies hys­ teresis. additionally, it really is identified that yes shocks can switch the commercial basics, thereby decreasing the prospect that an preliminary place is re-established after a surprise (irreversibility).

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Extra info for Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance

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2 Bilinear models: definition, estimation and identification Definition and stationarity property. 27) k=l 1=1 where we assume {ct} rv iid(O, a;). Before discussing the estimation of such processes, some conditions are needed to ensure their existence, stationarity and invertibility. The conditions for the existence of bilinear models have been studied in several papers. For the Markovian representations, the reader can consult Bhaskara Rao et al. (1983), Pham (1985), Guegan (1987), Guegan and Pham (1989).

Things are different when dt contains parameters that have to be estimated. The Dickey-Fuller and Phillips-Perron tests are no longer asymptotically equivalent to members of the PT family. To estimate (3, one does the regression of Yo on Zo and performs the usual ADF test using the residual series ytd = ¥t - /3' Zt in place of ¥t. 99) i=l When d t is only a constant, critical values and asymptotic power are those of the conventional Dickey-Fuller t-statistic. In the linear trend case, things are different and one has to use the critical values tabulated by Elliott et ai.

Dickey and Fuller (1979) have shown that to account for time dependence in the innovations, the basic three models can be augmented with, say, p lags of ~Yt. Then one can compute the t-statistic of p (or equivalently ¢) which follows the same asymptotic distribution as those reported in the simple case, that is in the case where ct is a white noise process. This gives rise to the so-called Augmented Dickey-Fuller tests (ADF). 74). As in the simple DF test, the null hypothesis of the ADF test is: p = 1.

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Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance by Gilles Dufrénot


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