On the Robustness of Ljung-Box and McLeod-Li Q Tests: A Simulation Study

In financial time series analysis, serial correlations and the volatility clustering effect of asset returns are commonly checked by Ljung-Box and McLeod-Li Q tests and filtered by ARMA-GARCH models. However, this simulation study shows that both the size and power performance of these two tests are not robust to heavily tailed data. Further, these Q tests may reject processes without ARMA-GARCH structures simply because of nonlinearity and conditionally heteroskedastic higher-order moments. These results imply that, to avoid misleading interpretations on time series data, these two tests should be used with care in practical applications.ARMA-GARCH

Uniqueness theorems for meromorphic mappings sharing hyperplanes in general position

The purpose of this article is to study the uniqueness problem for meromorphic mappings from $\mathbb{C}^{n}$ into the complex projective space $\mathbb{P}^{N}(\mathbb{C}).$ By making using of the method of dealing with multiple values due to L. Yang and the technique of Dethloff-Quang-Tan respectively, we obtain two general uniqueness theorems which improve and extend some known results of meromorphic mappings sharing hyperplanes in general position.Comment: 10 page

Characterizing Intermittency of 4-Hz Quasi-periodic Oscillation in XTE J1550-564 using Hilbert-Huang Transform

We present the time-frequency analysis results based on the Hilbert-Huang transform (HHT) for the evolution of a 4-Hz low-frequency quasi-periodic oscillation (LFQPO) around the black hole X-ray binary XTE J1550-564. The origin of LFQPOs is still debated. To understand the cause of the peak broadening, we utilized a recently developed time-frequency analysis, HHT, for tracking the evolution of the 4-Hz LFQPO from XTE J1550 564. By adaptively decomposing the ~4-Hz oscillatory component from the light curve and acquiring its instantaneous frequency, the Hilbert spectrum illustrates that the LFQPO is composed of a series of intermittent oscillations appearing occasionally between 3 Hz and 5 Hz. We further characterized this intermittency by computing the confidence limits of the instantaneous amplitudes of the intermittent oscillations, and constructed both the distributions of the QPO's high and low amplitude durations, which are the time intervals with and without significant ~4-Hz oscillations, respectively. The mean high amplitude duration is 1.45 s and 90% of the oscillation segments have lifetimes below 3.1 s. The mean low amplitude duration is 0.42 s and 90% of these segments are shorter than 0.73 s. In addition, these intermittent oscillations exhibit a correlation between the oscillation's rms amplitude and mean count rate. This correlation could be analogous to the linear rms-flux relation found in the 4-Hz LFQPO through Fourier analysis. We conclude that the LFQPO peak in the power spectrum is broadened owing to intermittent oscillations with varying frequencies, which could be explained by using the Lense-Thirring precession model.Comment: 27 pages, 9 figures, accepted for publication in The Astrophysical Journa