Forecasting and Granger Modelling with Non-linear Dynamical Dependencies

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the reproducing kernel Hilbert space and develop a method for learning prediction functions that accommodate such non-linearities. The method not only learns the predictive function but also the matrix-valued kernel underlying the function search space directly from the data. Our approach is based on learning multiple matrix-valued kernels, each of those composed of a set of input kernels and a set of output kernels learned in the cone of positive semi-definite matrices. In addition to superior predictive performance in the presence of strong non-linearities, our method also recovers the hidden dynamic relationships between the series and thus is a new alternative to existing graphical Granger techniques.Comment: Accepted for ECML-PKDD 201

Temporal aggregation of seasonally near-integrated processes

We investigate the implications that temporally aggregating, either by average sampling or systematic (skip) sampling, a seasonal process has on the integration properties of the resulting series at both the zero and seasonal frequencies. Our results extend the existing literature in three ways. First, they demonstrate the implications of temporal aggregation for a general sea- sonally integrated process with S seasons. Second, rather than only considering the aggregation of seasonal processes with exact unit roots at some or all of the zero and seasonal frequen- cies, we consider the case where these roots are local-to-unity such that the original series is near-integrated at some or all of the zero and seasonal frequencies. These results show, among other things, that systematic sampling, although not average sampling, can impact on the non- seasonal unit root properties of the data; for example, even where an exact zero frequency unit root holds in the original data it need not necessarily hold in the systematically sampled data. Moreover, the systematically sampled data could be near-integrated at the zero frequency even where the original data is not. Third, the implications of aggregation on the deterministic kernel of the series are explored

Measuring and Modeling Risk Using High-Frequency Data

Measuring and modeling financial volatility is the key to derivative pricing, asset allocation and risk management. The recent availability of high-frequency data allows for refined methods in this field. In particular, more precise measures for the daily or lower frequency volatility can be obtained by summing over squared high-frequency returns. In turn, this so-called realized volatility can be used for more accurate model evaluation and description of the dynamic and distributional structure of volatility. Moreover, non-parametric measures of systematic risk are attainable, that can straightforwardly be used to model the commonly observed time-variation in the betas. The discussion of these new measures and methods is accompanied by an empirical illustration using high-frequency data of the IBM incorporation and of the DJIA index

Correlations and forecast of death tolls in the Syrian conflict

The Syrian armed conflict has been ongoing since 2011 and has already caused thousands of deaths. The analysis of death tolls helps to understand the dynamics of the conflict and to better allocate resources and aid to the affected areas. In this article, we use information on the daily number of deaths to study temporal and spatial correlations in the data, and exploit this information to forecast events of deaths. We found that the number of violent deaths per day in Syria varies more widely than that in England in which non-violent deaths dominate. We have identified strong positive auto-correlations in Syrian cities and non-trivial cross-correlations across some of them. The results indicate synchronization in the number of deaths at different times and locations, suggesting respectively that local attacks are followed by more attacks at subsequent days and that coordinated attacks may also take place across different locations. Thus the analysis of high temporal resolution data across multiple cities makes it possible to infer attack strategies, warn potential occurrence of future events, and hopefully avoid further deaths

On directed information theory and Granger causality graphs

Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory includes measures such as the transfer entropy, and that it is the adequate information theoretic framework needed for neuroscience applications, such as connectivity inference problems.Comment: accepted for publications, Journal of Computational Neuroscienc