Practical methods of tracking of nonstationary time series applied to real-world data

In this paper, we discuss some practical implications for implementing adaptable network algorithms applied to non-stationary time series problems. Two real world data sets, containing electricity load demands and foreign exchange market prices, are used to test several different methods, ranging from linear models with fixed parameters, to non-linear models which adapt both parameters and model order on-line. Training with the extended Kalman filter, we demonstrate that the dynamic model-order increment procedure of the resource allocating RBF network (RAN) is highly sensitive to the parameters of the novelty criterion. We investigate the use of system noise for increasing the plasticity of the Kalman filter training algorithm, and discuss the consequences for on-line model order selection. The results of our experiments show that there are advantages to be gained in tracking real world non-stationary data through the use of more complex adaptive models.

Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Concentrations and d13C compositions of n-alkanes, n-alcohols, n-alkanoic acids in a 34-month time series of suspended sediments from the outflow of the Congo River

The concentrations, distributions, and stable carbon isotopes (d13C) of plant waxes carried by fluvial suspended sediments contain valuable information about terrestrial ecosystem characteristics. To properly interpret past changes recorded in sedimentary archives it is crucial to understand the sources and variability of exported plant waxes in modern systems on seasonal to inter-annual timescales. To determine such variability, we present concentrations and d13C compositions of three compound classes (n-alkanes, n-alcohols, n-alkanoic acids) in a 34-month time series of suspended sediments from the outflow of the Congo River. We show that exported plant-dominated n-alkanes (C25-C35) represent a mixture of C3 and C4 end members, each with distinct molecular distributions, as evidenced by an 8.1 ± 0.7 per mil (±1Sigma standard deviation) spread in d13C values across chain-lengths, and weak correlations between individual homologue concentrations (r = 0.52-0.94). In contrast, plant-dominated n-alcohols (C26-C36) and n-alkanoic acids (C26-C36) exhibit stronger positive correlations (r = 0.70-0.99) between homologue concentrations and depleted d13C values (individual homologues average <= -31.3 per mil and -30.8 per mil, respectively), with lower d13C variability across chain-lengths (2.6 ± 0.6 per mil and 2.0 ± 1.1 per mil, respectively). All individual plant-wax lipids show little temporal d13C variability throughout the time-series (1 Sigma <= 0.9 per mil), indicating that their stable carbon isotopes are not a sensitive tracer for temporal changes in plant-wax source in the Congo basin on seasonal to inter-annual timescales. Carbon-normalized concentrations and relative abundances of n-alcohols (19-58% of total plant-wax lipids) and n-alkanoic acids (26-76%) respond rapidly to seasonal changes in runoff, indicating that they are mostly derived from a recently entrained local source. In contrast, a lack of correlation with discharge and low, stable relative abundances (5-16%) indicate that n-alkanes better represent a catchment-integrated signal with minimal response to discharge seasonality. Comparison to published data on other large watersheds indicates that this phenomenon is not limited to the Congo River, and that analysis of multiple plant-wax lipid classes and chain lengths can be used to better resolve local vs. distal ecosystem structure in river catchments.

Gaussian Process Kernels for Cross-Spectrum Analysis in Electrophysiological Time Series

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.

Tourism time series forecast

In this chapter four combinations of input features and the feedforward, cascade forward and recurrent architectures are compared for the task of forecast tourism time series. The input features of the ANNs consist in the combination of the previous 12 months, the index time modeled by two nodes used to the year and month and one input with the daily hours of sunshine (insolation duration). The index time features associated to the previous twelve values of the time series proved its relevance in this forecast task. The insolation variable can improved results with some architectures, namely the cascade forward architecture. Finally, the experimented ANN models/architectures produced a mean absolute percentage error between 4 and 6%, proving the ability of the ANN models based to forecast this time series. Besides, the feedforward architecture behaved better considering validation and test sets, with 4.2% percentage error in test set.

Change-point detection in environmental time series based on the informational approach

In this study, the Schwarz Information Criterion (SIC) is applied in order to detect change-points in the time series of surface water quality variables. The application of change-point analysis allowed detecting change-points in both the mean and the variance in series under study. Time variations in environmental data are complex and they can hinder the identification of the so-called change-points when traditional models are applied to this type of problems. The assumptions of normality and uncorrelation are not present in some time series, and so, a simulation study is carried out in order to evaluate the methodology’s performance when applied to non-normal data and/or with time correlation.