Discussion Papers 2023

CIRJE-F-1216	"Johansen Test with Fourier-Type Smooth Nonlinear Trends in Cointegrating Relations"
Author Name	Takamitsu Kurita and Mototsugu Shintani
Date	June 2023
Full Paper	PDF file
Remarks

Abstract
We develop methodology for testing cointegrating rank in vector autoregressive (VAR) models in the presence of Fourier-type smooth nonlinear deterministic trends in cointegrating relations. The limiting distribution of log-likelihood ratio test statistics is derived and approximated limit quantiles are tabulated. A sequential procedure to select cointegrating rank is evaluated by Monte Carlo simulations. Our empirical application to economic data also demonstrates the usefulness of the proposed methodology in a practical context.
Keywords: Vector autoregressive systems; Smooth nonlinear deterministic trends; Trigonometric functions; Cointegrating rank; Log-likelihood ratio test statistics; Monte Carlo experiments

Abstract

We develop methodology for testing cointegrating rank in vector autoregressive (VAR) models in the presence of Fourier-type smooth nonlinear deterministic trends in cointegrating relations. The limiting distribution of log-likelihood ratio test statistics is derived and approximated limit quantiles are tabulated. A sequential procedure to select cointegrating rank is evaluated by Monte Carlo simulations. Our empirical application to economic data also demonstrates the usefulness of the proposed methodology in a practical context.

Keywords: Vector autoregressive systems; Smooth nonlinear deterministic trends; Trigonometric functions; Cointegrating rank; Log-likelihood ratio test statistics; Monte Carlo experiments