Testing Equality of Autocorrelation Coefficients in Two Independent Time Series Using Empirical Likelihood

The present paper considers an empirical likelihood approach for testing equality of autocorrelation coefficients in two independent stationary time series. In the time domain, a two-sample blockwise empirical likelihood method is constructed for weakly dependent data. In the frequency domain, a two-sample frequency-domain empirical likelihood test is introduced using spectral moment restrictions for autocorrelation. Under suitable regularity conditions, the corresponding profiled empirical likelihood statistics converge to chi-square limits under the null hypothesis. To improve small-sample performance, a bootstrap Bartlett-type calibration is proposed for the profiled two-sample frequency-domain statistic. The finite-sample behavior of the proposed procedures is examined in a Monte Carlo study covering AR, ARMA, and ARFIMA models with both Gaussian and asymmetric heavy-tailed innovations. The results show that the frequency-domain empirical likelihood procedure provides reliable size control in the short-memory models considered and remains competitive in mild long-memory settings, while the benchmark procedures are more sensitive to parametric misspecification or block-length choice. The simulation study shows that the bootstrap Bartlett-type calibration improves performance in smaller samples. An empirical application to squared Nikkei 225 returns provides evidence of higher short-run volatility persistence during the COVID-19 regime than in the pre-pandemic period.