Advances and Applications in Statistics
Volume 37, Issue 1, Pages 73 - 94
(November 2013)
|
|
BOOTSTRAP DETERMINATION OF THE CO-INTEGRATION RANK WITH UNKNOWN LAG ORDER IN VAR MODEL: APPLICATION ON EGYPT’S IMPORTS FROM THE MAIN CROPS
Mahmoud M. Alderiny
|
Abstract: In this paper, bootstrap approach was applied to determine co-integration rank in VAR model with unknown lag order. The empirical VAR model includes deterministic components and taking into account three time series which reflect Egypt ’s import values from the main crops (lentils, wheat and maize). The available data collected from (FAO) publication in period 1976-2010 and SAS program was used to obtain the results of unit root tests as well as bootstrapping determination of the co-integration rank for empirical VAR model. The values of ADF test statistics proved that the above mentioned time series are stationary at the first differences and integrated of order one then there exists a co-integrating vector The bootstrap estimates for modified Akaike’s information criterion MAIC in the case of generation bootstrap samples from disturbances of unrestricted empirical VEC model are generally lower than the same estimates in the case of generation bootstrap samples from disturbances of restricted model, also in both of the two cases, the values of MAIC computed under initial bootstrapping values equal normal values, no difference more than the same values MAIC computed under initial values equal zeros. According to the rule of minimization (MAIC), the appropriate lag order of VECM is 1 at rank = 0 and 3 at ranks = 1, 2 so when the bootstrap samples are generated from disturbances of unrestricted model. But when the bootstrap samples are generated from disturbances of restricted model, the appropriate lag order of VECM is 2 at rank = 0 and 3 at ranks = 1, 2. The case in which the bootstrap samples drawn from disturbances of unrestricted model with lag order equal 1, bootstrapping estimates for p-value indicated that the series above are co-integrated with rank 1 at significance level 5%, but these series co-integrated with rank 2 at significance level 20%. The other case, bootstrap samples drawn from disturbances of restricted model with lag order equal 2, the series are co-integrated with rank 1 at significance level 30%. So three vector error corrected models can be suggested for empirical model and bootstrap estimates for its parameters are calculated. |
Keywords and phrases: bootstrapping, Gaussian VAR model, error correction model, deterministic component, co-integration rank, maximum likelihood estimation, trace tests, likelihood ratio test, i.i.d. bootstrap, information criteria, unit root test. |
|
Number of Downloads: 363 | Number of Views: 1420 |
|