Copulas and time series with long-ranged dependencies

Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: Application to financial returns

We construct a two-tailed peaks-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating extreme gains and losses within the daily log-returns of the S&P 500 equity index. We find that the arrivals of extreme losses and gains are described by a common conditional intensity to which losses contribute twice as much as gains. However, the contribution of the former decays almost five times more quickly than that of the latter. We attribute these asymmetries to the different reactions of market traders to extreme upward and downward movements of asset prices: an example of negativity bias, wherein trauma is more salient than euphoria.

Mixture Kernel Density Estimation and Remedied Correlation Matrix on the EEG-Based Copula Model for the Assessment of Visual Discomfort

Since electroencephalogram (EEG) signals can directly provide information on changes in brain activity due to behaviour changes, how to assess visual discomfort through EEG signals attracts researchers’ attention. However, previous assessments based on time-domain EEG features lack sufficient consideration of the dependence among EEG signals, which may affect the discrimination to visual discomfort. Although the copula model can explore the dependence among variables, the EEG-based copula models still have the following deficiencies: (1) the methods ignoring the fine-grained information hidden in EEG signals could make the estimated marginal density function improper, and (2) the approaches neglecting the pseudo-correlation among data may inappropriately estimate the correlation matrix parameter of the copula density function. The mixture kernel density estimation (MKDE) and remedied correlation matrix (RCM) on the EEG-based copula model are proposed to mitigate the mentioned shortcomings. The simulation experiments show that MKDE can not only better estimate the marginal density function but also explore fine-grained information. The RCM can be closer to the real correlation matrix parameter. With the favourable quality of the proposed EEG-based model, it is used to extract time-domain EEG features to assess visual discomfort further. To our best knowledge, the extracted features present better discrimination to visual discomfort compared with the features extracted by the state-of-the-art method.

Significance of trends in long-term correlated records

We study the distribution P(x;α,L) of the relative trend x in long-term correlated records of length L that are characterized by a Hurst exponent α between 0.5 and 1.5. The relative trend x is the ratio between the strength of the trend Δ in the record measured by linear regression and the standard deviation σ around the regression line. We consider L between 400 and 2200, which is the typical length scale of monthly local and annual reconstructed global climate records. Extending previous work by Lennartz and Bunde [S. Lennartz and A. Bunde, Phys. Rev. E 84, 021129 (2011)] we show explicitly that x follows the Student's t distribution P∝[1+(x/a)2/l]-(l+1)/2, where the scaling parameter a depends on both L and α, while the effective length l depends, for α below 1.15, only on the record length L. From P we can derive an analytical expression for the trend significance S(x;α,L)=∫(-x)xP(x';α,L)dx' and the border lines of the 95% significance interval. We show that the results are nearly independent of the distribution of the data in the record, holding for Gaussian data as well as for highly skewed non-Gaussian data. For an application, we use our methodology to estimate the significance of central west Antarctic warming.