A two-sample test for comparison of long memory parameters

TL;DR

This paper develops a two-sample test to compare long memory parameters in time series, using ratios of rescaled variance statistics, with an adaptive bandwidth choice to improve robustness and accuracy.

Contribution

It introduces a novel two-sample test for long memory parameters that accounts for dependence and adaptively selects bandwidth, enhancing test reliability.

Findings

The test performs well in simulations across various fractional and ARMA parameters.

Adaptive bandwidth selection improves test size accuracy.

The method is applicable to both independent and dependent samples.

Abstract

We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in [Giraitis L., Leipus, R., Philippe, A., 2006. A test for stationarity versus trends and unit roots for a wide class of dependent errors. Econometric Theory 21, 989--1029]. The two samples have the same length and can be mutually independent or dependent. In the latter case, the test statistic is modified to make it asymptotically free of the long-run correlation coefficient between the samples. To diminish the sensitivity of the test on the choice of the bandwidth parameter, an adaptive formula for the bandwidth parameter is derived using the asymptotic expansion in [Abadir, K., Distaso, W., Giraitis, L., 2009. Two estimators of the long-run variance: Beyond short memory. Journal of Econometrics 150, 56--70]. A simulation study shows that the above choice of bandwidth leads to a good size of our comparison test for most values of fractional and ARMA parameters of the simulated series.