Testing fractional unit roots with non-linear smooth break approximations using Fourier functions.

Area of Science:

• Econometrics
• Time Series Analysis

Background:

• Fractional integration is a key concept in time series analysis.
• Non-linear dynamics are prevalent in many economic time series.

Purpose of the Study:

• To develop and validate a testing procedure for fractional orders of integration.
• To accommodate non-linear terms approximated by Fourier functions.

Main Methods:

• Development of a new test statistic.
• Asymptotic distribution theory (standard normal).
• Monte Carlo simulations for finite sample performance.

Main Results:

• The proposed test statistic follows an asymptotic standard normal distribution.
• Monte Carlo experiments demonstrate good finite sample properties.
• The procedure is effective in analyzing real-world economic data.

Conclusions:

• The new testing procedure is a valuable tool for analyzing fractional integration in the presence of non-linearities.
• The method is robust and applicable to various economic time series datasets.