Semiparametric tests for the order of integration in the possible presence of level breaks

TY - JOUR

T1 - Semiparametric tests for the order of integration in the possible presence of level breaks

AU - Iacone, Fabrizio

AU - Nielsen, Morten Ørregaard

AU - Taylor, A.M. Robert

PY - 2022/4

Y1 - 2022/4

N2 - Lobato and Robinson developed semiparametric tests for the null hypothesis that a series is weakly autocorrelated, or I(0), about a constant level, against fractionally integrated alternatives. These tests have the advantage that the user is not required to specify a parametric model for any weak autocorrelation present in the series. We extend this approach in two distinct ways. First, we show that it can be generalized to allow for testing of the null hypothesis that a series is (Formula presented.) for any δ lying in the usual stationary and invertible region of the parameter space. The second extension is the more substantive and addresses the well-known issue in the literature that long memory and level breaks can be mistaken for one another, with unmodeled level breaks rendering fractional integration tests highly unreliable. To deal with this inference problem, we extend the Lobato and Robinson approach to allow for the possibility of changes in level at unknown points in the series. We show that the resulting statistics have standard limiting null distributions, and that the tests based on these statistics attain the same asymptotic local power functions as infeasible tests based on the unobserved errors, and hence there is no loss in asymptotic local power from allowing for level breaks, even where none is present. We report results from a Monte Carlo study into the finite-sample behavior of our proposed tests, as well as several empirical examples.

AB - Lobato and Robinson developed semiparametric tests for the null hypothesis that a series is weakly autocorrelated, or I(0), about a constant level, against fractionally integrated alternatives. These tests have the advantage that the user is not required to specify a parametric model for any weak autocorrelation present in the series. We extend this approach in two distinct ways. First, we show that it can be generalized to allow for testing of the null hypothesis that a series is (Formula presented.) for any δ lying in the usual stationary and invertible region of the parameter space. The second extension is the more substantive and addresses the well-known issue in the literature that long memory and level breaks can be mistaken for one another, with unmodeled level breaks rendering fractional integration tests highly unreliable. To deal with this inference problem, we extend the Lobato and Robinson approach to allow for the possibility of changes in level at unknown points in the series. We show that the resulting statistics have standard limiting null distributions, and that the tests based on these statistics attain the same asymptotic local power functions as infeasible tests based on the unobserved errors, and hence there is no loss in asymptotic local power from allowing for level breaks, even where none is present. We report results from a Monte Carlo study into the finite-sample behavior of our proposed tests, as well as several empirical examples.

KW - Conditional heteroscedasticity

KW - Fractional integration

KW - Lagrange multiplier testing principle

KW - Level breaks

KW - Local Whittle likelihood

KW - Spurious long memory

U2 - 10.1080/07350015.2021.1876712

DO - 10.1080/07350015.2021.1876712

M3 - Journal article

SN - 0735-0015

VL - 40

SP - 880

EP - 896

JO - Journal of Business and Economic Statistics

JF - Journal of Business and Economic Statistics

IS - 2

ER -