🤖 AI Summary
This study addresses the challenge of distinguishing between long memory and nonstationarity, both of which induce slow decay in sample autocovariances and are often confounded by existing stationarity tests—either by ignoring long memory or suffering from size distortions near the boundary. To resolve this, the paper proposes a frequency-domain test based on comparing periodograms across different time segments. By deriving the asymptotic distribution as a weighted sum of independent chi-squared variables, the method effectively discriminates between long-memory and nonstationary processes at their boundary. Integrating spectral analysis, periodogram-based evaluation, and asymptotic theory, the approach demonstrates superior empirical size control and testing power over competing methods in numerical experiments.
📝 Abstract
Distinguishing long memory behaviour from nonstationarity can be very difficult as in both cases the sample autocovariance function decays very slowly. Available stationarity tests either do not include long memory or fare poorly in terms of empirical size, especially near the boundary between long memory and nonstationarity. We propose a testing procedure based on evaluating periodograms at different epochs. Limiting distributions established here are easily tractable as sum of weighted independent $χ^2$ random variables. Moreover, numerical studies are provided to show that the proposed approach seems to outperform existing methods.