Unit Root Testing and Estimation in Nonlinear ESTAR Models with Normal and Non-Normal Errors

Abstract

Exponential Smooth Transition Autoregressive (ESTAR) models can capture non-linear adjustment of the deviations from equilibrium conditions which may explain the economic behavior of many variables that appear non stationary from a linear viewpoint. Many researchers employ the Kapetanios test which has a unit root as the null and a stationary nonlinear model as the alternative. However this test statistics is based on the assumption of normally distributed errors in the DGP. Cook has analyzed the size of the nonlinear unit root of this test in the presence of heavy-tailed innovation process and obtained the critical values for both finite variance and infinite variance cases. However the test statistics of Cook are oversized. It has been found by researchers that using conventional tests is dangerous though the best performance among these is a HCCME. The over sizing for LM tests can be reduced by employing fixed design wild bootstrap remedies which provide a valuable alternative to the conventional tests. In this paper the size of the Kapetanios test statistic employing hetroscedastic consistent covariance matrices has been derived and the results are reported for various sample sizes in which size distortion is reduced. The properties for estimates of ESTAR models have been investigated when errors are assumed non-normal. We compare the results obtained through the fitting of nonlinear least square with that of the quantile regression fitting in the presence of outliers and the error distribution was considered to be from t-distribution for various sample sizes.

Causal Links Between Ict, Hdi, and Economic Growth: Evidence From Mena

“…The MENA countries are stationary at all levels for GDP only, while there were stationary at the first level. These results can be accepted to support that the data for the three categories of countries are stationary and there will be no 2 nd difference for the unit root test (Khalil, et al, 2016). So it shows the existence of a long-run relationship between the variables used in the model that leads to the application of Pedroni and Kao cointegration tests.…”