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Register a new userTime series models with infinite-order partial copula dependence
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Stationary and ergodic time series can be constructed using an s-vine decomposition based on sets of bivariate copula functions. The extension of such processes to infinite copula sequences is considered and shown to yield a rich class of models that generalizes Gaussian ARMA and ARFIMA processes to allow both non-Gaussian marginal behaviour and a non-Gaussian description of the serial partial dependence structure. Extensions of classical causal and invertible representations of linear processes to general s-vine processes are proposed and investigated. A practical and parsimonious method for parameterizing s-vine processes using the Kendall partial autocorrelation function is developed. The potential of the resulting models to give improved statistical fits in many applications is indicated with an example using macroeconomic data.
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An approach to modelling volatile financial return series using stationary d-vine copula processes combined with Lebesgue-measure-preserving transformations known as v-transforms is proposed. By developing a method of stochastically inverting v-transforms, models are constructed that can describe both stochastic volatility in the magnitude of price movements and serial correlation in their directions. In combination with parametric marginal distributions it is shown that these models can rival and sometimes outperform well-known models in the extended GARCH family.
In recent biomedical scientific problems, it is a fundamental issue to integratively cluster a set of objects from multiple sources of datasets. Such problems are mostly encountered in genomics, where data is collected from various sources, and typically represent distinct yet complementary information. Integrating these data sources for multi-source clustering is challenging due to their complex dependence structure including directional dependency. Particularly in genomics studies, it is known that there is certain directional dependence between DNA expression, DNA methylation, and RNA expression, widely called The Central Dogma. Most of the existing multi-view clustering methods either assume an independent structure or pair-wise (non-directional) dependency, thereby ignoring the directional relationship. Motivated by this, we propose a copula-based multi-view clustering model where a copula enables the model to accommodate the directional dependence existing in the datasets. We conduct a simulation experiment where the simulated datasets exhibiting inherent directional dependence: it turns out that ignoring the directional dependence negatively affects the clustering performance. As a real application, we applied our model to the breast cancer tumor samples collected from The Cancer Genome Altas (TCGA).
An important problem in analysis of neural data is to characterize interactions across brain regions from high-dimensional multiple-electrode recordings during a behavioral experiment. Lead-lag effects indicate possible directional flows of neural information, but they are often transient, appearing during short intervals of time. Such non-stationary interactions can be difficult to identify, but they can be found by taking advantage of the replication structure inherent to many neurophysiological experiments. To describe non-stationary interactions between replicated pairs of high-dimensional time series, we developed a method of estimating latent, non-stationary cross-correlation. Our approach begins with an extension of probabilistic CCA to the time series setting, which provides a model-based interpretation of multiset CCA. Because the covariance matrix describing non-stationary dependence is high-dimensional, we assume sparsity of cross-correlations within a range of possible interesting lead-lag effects. We show that the method can perform well in realistic settings and we apply it to 192 simultaneous local field potential (LFP) recordings from prefrontal cortex (PFC) and visual cortex (area V4) during a visual memory task. We find lead-lag relationships that are highly plausible, being consistent with related results in the literature.
This paper studies the extreme dependencies between energy, agriculture and metal commodity markets, with a focus on local co-movements, allowing the identification of asymmetries and changing trend in the degree of co-movements. More precisely, starting from a non-parametric mixture copula, we use a novel copula-based local Kendalls tau approach to measure nonlinear local dependence in regions. In all pairs of commodity indexes, we find increased co-movements in extreme situations, a stronger dependence between energy and other commodity markets at lower tails, and a V-type local dependence for the energy-metal pairs. The three-dimensional Kendalls tau plot for upper tails in quantiles shows asymmetric co-movements in the energy-metal pairs, which tend to become negative at peak returns. Therefore, we show that the energy market can offer diversification solutions for risk management in the case of extreme bull market events.
Proper scoring rules are commonly applied to quantify the accuracy of distribution forecasts. Given an observation they assign a scalar score to each distribution forecast, with the the lowest expected score attributed to the true distribution. The energy and variogram scores are two rules that have recently gained some popularity in multivariate settings because their computation does not require a forecast to have parametric density function and so they are broadly applicable. Here we conduct a simulation study to compare the discrimination ability between the energy score and three variogram scores. Compared with other studies, our simulation design is more realistic because it is supported by a historical data set containing commodity prices, currencies and interest rates, and our data generating processes include a diverse selection of models with different marginal distributions, dependence structure, and calibration windows. This facilitates a comprehensive comparison of the performance of proper scoring rules in different settings. To compare the scores we use three metrics: the mean relative score, error rate and a generalised discrimination heuristic. Overall, we find that the variogram score with parameter p=0.5 outperforms the energy score and the other two variogram scores.
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