Testing Fractional Integration in Time Series with Artificial Neural Network

This paper initiates a non-linear fractional unit root test also known as autoregressive neural network–fractional integration (ARNN–FI) test. The test is based on a new multilayer perceptron of a neural network process which is applied in Yaya et al. (2021). Further, to investigate the properties of the proposed test, a Monte Carlo simulation experiment was carried out. The simulation results revealed that, as the number of observations increases, size and power distortions would disappear in three alternative fractional unit root tests, i.e. the Robinson test (Robinson, 1994), the Alana–Yaya (AY) test (Gil-Alana and Yaya, 2020) and the proposed ARNN–FI test. We further applied the three tests on the unemployment rates of four European countries, wherein we find from the former two tests that unemployment rates in the considered countries are non-mean-reverting, while the ARNN–FI test indicates mean-reversion in the situation of Portugal and the United Kingdom