Nonlinearity and fractional integration in the US dollar/euro exchange rate

Burcu Kiran

doi:10.2298/pan1203325k

Abstract

This paper examines the nonlinear behavior and the fractional integration property of the US dollar/euro exchange rate over the period from January 1999 to August 2010 by extending the procedure of Peter M. Robinson (1994) to the case of nonlinearity. First, using the approach developed by Mehmet Caner and Bruce E. Hansen (2001), we investigate the possible presence of nonlinearity in the series through the estimation of a two-regime threshold autoregressive model. After finding nonlinearity, we also allow for disturbances to be fractionally integrated based on the different versions of Robinson (1994) tests. The findings show that the US dollar/euro exchange rate follows a stationary process with a weak evidence for long memory.

Highlights

Robinson Tests Under the Case of NonlinearityTo examine the time series behavior, we take into account the possible nonlinearity and fractional integration properties of the US dollar/euro exchange rate in the same analysis following Caporale and Gil-Alana (2007)
Following this result, which gives a strong support to the existence of a threshold effect in the US dollar/euro exchange rate, we estimate two-regime threshold autoregressive (TAR) model for m = 1 using least squares estimation method
These findings show that the US dollar/euro exchange rate follows a stationary process, and there is a weak evidence of long memory only for white noise disturbances

Summary

Robinson Tests Under the Case of Nonlinearity

To examine the time series behavior, we take into account the possible nonlinearity and fractional integration properties of the US dollar/euro exchange rate in the same analysis following Caporale and Gil-Alana (2007) For this purpose, the nonlinearity is investigated using a TAR model that allows to derive endogenous threshold effects, and the fractional integration property is determined using different versions of the Robinson (1994) tests. We use a two-regime TAR model suggested by Caner and Hansen (2001) that allows to derive endogenous threshold effects in the series, instead of Eq (1). Recent work by Caner and Hansen (2001) presents some new results on the TAR model introduced by Howell Tong (1978) They develop new tests for threshold effects and estimate the threshold parameter. After finding a threshold effect in the data, we apply Robinson (1994) tests to the residuals obtained from the TAR model in the second step of the analysis

Data and Empirical Results

Nonlinearity Test Results and TAR Model Estimations

Conclusions