Testing the Fractional Integration Parameter Revisited: a Fractional Dickey-Fuller Test

TL;DR

This paper critiques the existing fractional Dickey-Fuller test, proposes a new testing procedure for fractional integration, and demonstrates its effectiveness through simulations and real data application.

Contribution

It introduces a novel fractional integration test inspired by the Dickey-Fuller test, improving practical performance over previous methods.

Findings

The new test performs well in size and power in simulations.

It is effectively applied to Nelson and Plosser data.

The existing fractional Dickey-Fuller test is shown to be ineffective.

Abstract

In this paper, in the first step, we show that the fractional Dickey-Fuller test proposed by Dolado et al [10] is useless in practice. In the second step, we propose a new testing procedure for the degree of fractional integration of a time series inspired on the unit root test of Dickey-Fuller [7]. Through a simulation study, we show the good performance of the test in terms of size and power. Finally, in order to show how to use the new testing procedure, the test is applied to the well-known Nelson and Plosser data.