Semiparametric stationarity and fractional unit roots tests based on data-driven multidimensional increment ratio statistics

TL;DR

This paper extends the CLT for the multidimensional increment ratio estimator to a broader class of Gaussian fractionally integrated processes, enabling robust semiparametric stationarity and fractional unit root testing with high accuracy.

Contribution

It introduces data-driven MIR-based tests for stationarity and fractional unit roots applicable to processes with memory parameter d in (-0.5, 1.25), improving robustness and efficiency.

Findings

MIR estimator shows high accuracy across various processes.

MIR tests outperform traditional stationarity and unit root tests.

Asymptotic variance estimation enables reliable hypothesis testing.

Abstract

In this paper, we show that the central limit theorem (CLT) satisfied by the data-driven Multidimensional Increment Ratio (MIR) estimator of the memory parameter d established in Bardet and Dola (2012) for d $\in$ (--0.5, 0.5) can be extended to a semiparametric class of Gaussian fractionally integrated processes with memory parameter d $\in$ (--0.5, 1.25). Since the asymptotic variance of this CLT can be estimated, by data-driven MIR tests for the two cases of stationarity and non-stationarity, so two tests are constructed distinguishing the hypothesis d \textless{} 0.5 and d $\ge$ 0.5, as well as a fractional unit roots test distinguishing the case d = 1 from the case d \textless{} 1. Simulations done on numerous kinds of short-memory, long-memory and non-stationary processes, show both the high accuracy and robustness of this MIR estimator compared to those of usual semiparametric estimators. They also attest of the reasonable efficiency of MIR tests compared to other usual stationarity tests or fractional unit roots tests. Keywords: Gaussian fractionally integrated processes; semiparametric estimators of the memory parameter; test of long-memory; stationarity test; fractional unit roots test.