Is the Observed Persistence Spurious? A Test for Fractional Integration Versus Short Memory and Structural Breaks

Abstract

Although it is commonly accepted that most macroeconomic variables are nonstationary, it is often difficult to identify the source of the non-stationarity. In particular, it is well-known that integrated and short memory models containing trending components that may display sudden changes in their parameters share some statistical properties that make their identification a hard task. The goal of this paper is to extend the classical testing framework for I(1) versus I(0)+ breaks by considering a a more general class of models under the null hypothesis: non-stationary fractionally integrated (FI) processes. A similar identification problem holds in this broader setting which is shown to be a relevant issue from both a statistical and an economic perspective. The proposed test is developed in the time domain and is very simple to compute. The asymptotic properties of the new technique are derived and it is shown by simulation that it is very well-behaved in finite samples. To illustrate the usefulness of the proposed technique, an application using inflation data is also provided. * I would like to thank Jushan Bai and Manuel Domínguez for his very useful comments. I acknowledge financial support from the Spanish Ministry of Education through grants SEC2003-04429 and SEC2003-04476 and also from the Barcelona Economics Program of CREA.

Uporczywość inflacji i jej komponentów – badanie empiryczne dla Polski

“…Uwzgl dnianie potencjalnych zmian strukturalnych w szeregach czasowych in acji w trakcie badania jej uporczywo ci ma powa ny wp yw na uzyskane wyniki. Mayoral (2006) i Dolado, Gonzalo, Mayoral (2006), pokazali, e pewne cechy stacjonarnych szeregów czasowych zawieraj cych zmiany strukturalne, w tym m.in. podobna struktura autokorelacyjna szeregów czasowych, mog wyst pi równie w przypadku szeregów czasowych zintegrowanych u amkowo i dlatego procesy te mog by ze sob mylone.…”

Modelling Ireland's Exchange Rates: From EMS to EMU

“…For example, Diebold and Inoue (2001) and Perron and Qu (2004) investigate the effects of nonlinearity on the estimation of the fractional integration parameter, while Hsu (2001) and Krämmer and Sibbertsen (2002) examine the impact of long memory on estimates and tests of structural change. Other recent work by Dolado, et al (2005), Gil-Alana (2004 and Mayoral (2005) has devised new test procedures for fractionality and/or nonlinearity. However, in most cases the form of the nonlinearity needs to be known.…”

The Persistence of Inflation in OECD Countries: A Fractionally Integrated Approach

“…15 Next, we test for FI versus short memory (I(0)). To this end, a point-optimal test recently proposed by Mayoral (2004b) has been implemented and the results are presented in Table 1 5 The FDF invariant regression that has been run is equal to ∆y t = α 1 τ t−1 (d) + φ∆ d y t−1 + P k j=1 ψ j ∆y t−j + a t and a number of lags of ∆y t equal to two was chosen according to the BIC criterion. The coefficient α 1 is associated to the deterministic components (a constant, see Dolado et al (2003)).…”

“…The asymptotic distribution of this statistic (scaled by T 1−2d ) is not standard and critical values can be found in Mayoral (2004b) for the case where u t is i.i.d. When u t is a general linear short memory process, a nonparametric correction should be introduced using any of the standard techniques available in the literature (see Mayoral (2004b)).…”

“…When u t is a general linear short memory process, a nonparametric correction should be introduced using any of the standard techniques available in the literature (see Mayoral (2004b)). …”