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Following is the general form of ADRL model of co-integration or UECM;
We follow the general-to-specific procedure by Hendry and Ericsson (1991) to obtain the parsimonious UECM by dropping sequentially the insignificant first difference variables.
The financial development equation is estimated using three different time-series estimators, that is, the VECM, UECM, and DOLS approaches.
To test the long-run relationship, Ordinary Least Square (OLS) method has been used and results of Un-restricted Error Correction Model (UECM) / long run results have been reported in Table 2.
The Unrestricted Error Correction Models (UECMs) to explain the defense-debt relationship for Pakistan and India are given below respectively:
Bound testing ARDL model or Unrestricted Error Correction Model (UECM)
To test for cointegration in model (2) by the bounds test, the following conditional Unrestricted Error Correction Model (UECM), is constructed
The first step in ARDL approach is to examine the LR relationship among the interested variables by carrying out familiar F-statistic on the differenced variables components of 'Unrestricted Error Correction Model' (UECM) for the joint significance of the coefficients of lagged level of the variables.
In the ARDL model, as a first step, the LR relationship among variables is carried out by calculating partial `F' test on the first differenced part of Unrestricted Error Correction Model (UECM) of equations (3) and (4).
(3) The unrestricted error-correction model (UECM) is written as:
The bounds approach to cointegration also seems to combine short run dynamics with long run equilibrium path having long run information following unrestricted error correction model (UECM).
To apply the bounds test for cointegration, the Unrestricted Error Correction Model (UECM) representation of double log money demand function: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] takes the following form:
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