Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.

An econometric analysis of international tourism demand in Hong Kong : a cointegration and error correction approach

The purpose of this study is to develop econometric models to better understand the economic factors affecting inbound tourist flows from each of six origin countries that contribute to Hong Kong’s international tourism demand. To this end, we test alternative cointegration and error correction approaches to examine the economic determinants of tourist flows to Hong Kong, and to produce accurate econometric forecasts of inbound tourism demand. Our empirical findings show that permanent income is the most significant determinant of tourism demand in all models. The variables of own price, weighted substitute prices, trade volume, the share price index (as an indicator of changes in wealth in origin countries), and a dummy variable representing the Beijing incident (1989) are also found to be important determinants for some origin countries. The average long-run income and own price elasticity was measured at 2.66 and – 1.02, respectively. It was hypothesised that permanent income is a better explanatory variable of long-haul tourism demand than current income. A novel approach (grid search process) has been used to empirically derive the weights to be attached to the lagged income variable for estimating permanent income. The results indicate that permanent income, estimated with empirically determined relatively small weighting factors, was capable of producing better results than the current income variable in explaining long-haul tourism demand. This finding suggests that the use of current income in previous empirical tourism demand studies may have produced inaccurate results. The share price index, as a measure of wealth, was also found to be significant in two models. Studies of tourism demand rarely include wealth as an explanatory forecasting long-haul tourism demand. However, finding a satisfactory proxy for wealth common to different countries is problematic. This study indicates with the ECM (Error Correction Models) based on the Engle-Granger (1987) approach produce more accurate forecasts than ECM based on Pesaran and Shin (1998) and Johansen (1988, 1991, 1995) approaches for all of the long-haul markets and Japan. Overall, ECM produce better forecasts than the OLS, ARIMA and NAÏVE models, indicating the superiority of the application of a cointegration approach for tourism demand forecasting. The results show that permanent income is the most important explanatory variable for tourism demand from all countries but there are substantial variations between countries with the long-run elasticity ranging between 1.1 for the U.S. and 5.3 for U.K. Price is the next most important variable with the long-run elasticities ranging between -0.8 for Japan and -1.3 for Germany and short-run elasticities ranging between – 0.14 for Germany and -0.7 for Taiwan. The fastest growing market is Mainland China. The findings have implications for policies and strategies on investment, marketing promotion and pricing.

Causality in crude oil prices

Economic media inform on prices of three well established crude oil benchmarks: Brent, WTI and Dubai Fateh. The relevance of these is however declining with their low output - motivating investigation of the pricing dynamics. We apply Granger causality tests to study the price dependencies of 32 crude oils. The aim is to establish what crudes are setting the prices and what crudes are just following the general market trends. The investigation is performed globally as well as for different quality, geographical and organisational segments. The results indicate that crude oil price analysts should follow at least four different crudes that are good price indicators. WTI and Brent still lead the market, but they are not the only crude prices worth paying attention to. In particular, Russian Urals drives global prices in a significant way, and Iran Seri Kerir is a significant price setter within OPEC. Dubai Fateh does not display any significant influence as a price setter, which confirms the lack of dominant benchmark within the segment of medium quality crudes.

Monetary variability and monetary variables in the Franc zone

Failure to detect or account for structural changes in economic modelling can lead to misleading policy inferences, which can be perilous, especially for the more fragile economies of developing countries. Using three potential monetary policy instruments (Money Base, M0, and Reserve Money) for 13 member-states of the CFA Franc zone over the period 1989:11-2002:09, we investigate the magnitude of information extracted by employing data-driven techniques when analyzing breaks in time-series, rather than the simplifying practice of imposing policy implementation dates as break dates. The paper also tests Granger's (1980) aggregation theory and highlights some policy implications of the results.

Causality in crude oil prices

Crude oil markets witness growing disparity between the quality of crudes supplied and demanded in the market. The market share of low-quality crudes is increasing due to the depletion of old fields and increasing demand. This is unnerving the practitioners and affecting the relevance of the traditional benchmark crudes due to the lack of lower quality benchmarks (Montepeque, 2005). In this article, we apply Granger causality tests to study the price dependence of 32 crudes in order to establish which crudes drive other prices and which ones simply follow general market trends. Our results indicate that some of the old benchmarks are still relevant while others can be disregarded. Our results also interestingly show that the low-quality Mediterranean Russian Urals crude, introduced in the late 1990s, has emerged recently as a significant driver of global prices. © 2011 Taylor & Francis.