Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models

TY - JOUR

T1 - Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models

AU - Kristensen, Dennis

AU - Rahbek, Anders

PY - 2013/12

Y1 - 2013/12

N2 - We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new(uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full asymptotic theory for estimators and test statistics. The derived asymptotic results prove to be nonstandard compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. This complicates implementation of tests motivating the introduction of bootstrap versions that are simple to compute. A simulation study shows that the finite-sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes.

AB - We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new(uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full asymptotic theory for estimators and test statistics. The derived asymptotic results prove to be nonstandard compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. This complicates implementation of tests motivating the introduction of bootstrap versions that are simple to compute. A simulation study shows that the finite-sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes.

U2 - 10.1017/S0266466613000054

DO - 10.1017/S0266466613000054

M3 - Journal article

SN - 0266-4666

VL - 29

SP - 1238

EP - 1288

JO - Econometric Theory

JF - Econometric Theory

IS - 6

ER -