Semiparametric stationarity tests based on adaptive multidimensional increment ratio statistics

TL;DR

This paper develops and validates semiparametric stationarity tests based on adaptive multidimensional increment ratio statistics, applicable to a broad class of Gaussian processes, with practical applications to economic data analysis.

Contribution

It introduces new stationarity and nonstationarity tests using the increment ratio estimator, with proven CLT and applicability to diverse Gaussian processes.

Findings

Tests accurately distinguish stationarity from nonstationarity.

The proposed methods outperform traditional tests like ADF and PP.

Applications to economic data demonstrate practical utility.

Abstract

In this paper, we show that the adaptive multidimensional increment ratio estimator of the long range memory parameter defined in Bardet and Dola (2012) satisfies a central limit theorem (CLT in the sequel) for a large 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 computed, tests of stationarity or nonstationarity distinguishing the assumptions $d<0.5$ and $d \geq 0.5$ are constructed. These tests are also consistent tests of unit root. Simulations done on a large benchmark of short memory, long memory and non stationary processes show the accuracy of the tests with respect to other usual stationarity or nonstationarity tests (LMC, V/S, ADF and PP tests). Finally, the estimator and tests are applied to log-returns of famous economic data and to their absolute value power laws.