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Determining whether commodity prices (and volatility) are driven by linear stochastic processes or low-dimensional nonlinear deterministic dynamics (“chaos”) is crucial for policymaking, forecasting, production, storage, investment, risk management, and hedging decisions. Previous studies that used Lyapunov exponents and correlation dimensions to identify chaotic structures in price series may be unreliable in practical applications because these methods rely on asymptotic properties that require large, noiseless data which is often not available. We applied nonlinear time series analysis approaches to empirically detect the underlying market dynamics using the daily futures prices of ten agricultural commodities. We used phase space reconstruction to reconstruct the empirical attractor from the observed price series, as well as nonlinear predictive skill and permutation entropy measures to distinguish between linear stochastic and nonlinear deterministic dynamics. We find evidence of low-dimensional nonlinear deterministic dynamics in commodity price series. Our results suggest that the observed volatility is most likely endogenously generated by an inherently unstable market which cannot be expected to self-correct, suggesting the need for government intervention to stabilize prices and reduce volatility. It also suggests that long-term forecasts are unlikely due to the nature of the dynamics, but short-term forecasts may be improved using nonlinear prediction methods. Advisor: Fabio L. Mattos

Adequate understanding of streamflow dynamics is important for a wide range of applications in hydrology and water resources. A basic idea in streamflow studies is to establish connections that generally exist between the different components of the catchment system. Despite the development and applications of numerous approaches, our understanding of the connections in streamflow remains inadequate. The concepts of complex networks offer new avenues for studying connections in complex and dynamically-evolving systems, such as catchments. Applications of the complex networks concepts to streamflow are an emerging area of research. This thesis aims to study the spatial, temporal, and spatio-temporal connections in streamflow using complex networks concepts. Since the construction of the network (i.e., nodes and links) using data is a key step in complex networks-based methods, an improvement to network construction is proposed. Specifically, the phase space reconstruction concept, which allows reconstruction of a single time series in a multi-dimensional phase space to represent the system, is used for constructing the temporal and spatio-temporal streamflow networks. The spatial, temporal, and spatio-temporal connections in streamflow are primarily examined using the clustering coefficient, which quantifies the network’s tendency to cluster. The degree distribution, a measure of the spread in the node degree, is also used to examine the spatial connections. For implementation, monthly streamflow data observed over a period of 53 years from a large network of 639 monitoring stations in the contiguous United States are studied. The influence of the correlation threshold in the spatial analysis and distance threshold in the temporal and spatio-temporal analysis is investigated. Based on the clustering coefficients, the type of network is identified. The clustering coefficients are also interpreted in terms of catchment and flow characteristics. The clustering coefficients for the spatial, temporal, and spatio-temporal connections reveal that the streamflow networks are not purely random networks, but may be small-world or scale-free or some other type. The clustering coefficients also offer reliable interpretations in terms of catchment and flow characteristics, especially about the complexity of network and strength of connections. These outcomes clearly indicate the usefulness of the complex networks-based methods for streamflow analysis.

The recording and analysis of electroencephalography (ECG) plays crucial roles in clinical research and diagnosis. As a result, the development of automatic ECG analysis algorithms has been rapidly growing in recent decades. However, conventional ECG analysis encounters tradeoff between computational cost and performance accuracy. This study aims to develop a series of real-time (online) ECG analysis algorithms that include heartbeat detection and ECG arrhythmia classification. We first propose a novel phase space based method for heartbeat detection that maps the ECG data into a two-dimensional reconstructed attractor. Unlike conventional algorithms, our detector replaces the preprocessing stage with a reconstruction process. This improvement highly reduces the computational cost. Moreover, we introduce a two-dimensional decision mechanism in order to obtain high performance accuracy at the detection stage. For the ECG arrhythmia classification study, an unsupervised classification algorithm referred to as “superparamagnetic clustering” is introduced to ECG analysis field for the first time. Current studies in ECG classification mainly use supervised artificial intelligence methods. The common drawbacks of these classifiers include: they are incapable of discriminating clusters with significant population differences; manual annotation efforts by clinicians/researchers are required in order to form the training sets; the network training procedure is computationally expensive. The proposed arrhythmia ECG classifier overcomes these issues because of the non-parametric configuration of the classifier. Clustering with different desirable discrimination levels could be realized by adjusting the “temperature” parameter. Moreover, this study explicitly involves exploration of the feature selection issue. To ensure the most reliable configuration, an appropriate number of the most significant features should be selected from the candidate pool. A comparative study between principal component analysis (PCA) and genetic algorithm analysis (GA) is conducted with the conclusion that the 10-15 principal components from PCA is the optimal combination for ECG arrhythmia classification. We also study the dynamic interactions between cardiac contraction and respiration using time-frequency analysis tools such as Hilbert and wavelet transforms as well as the recurrence properties of the system. The analysis results show a unidirectional modulation relationship in the cardio-respiratory system as well as the existence of thoracic-abdominal asynchrony during certain periods that include significant clinical events.