Limitations of instantaneous water quality sampling in surface-water catchments: Comparison with near-continuous phosphorus time-series data.

The validity of load estimates from intermittent, instantaneous grab sampling is dependent on adequate spatial coverage by monitoring networks and a sampling frequency that re?ects the variability in the system under study. Catchments with a ?ashy hydrology due to surface runoff pose a particular challenge as intense short duration rainfall events may account for a signi?cant portion of the total diffuse transfer of pollution from soil to water in any hydrological year. This can also be exacerbated by the presence of strong background pollution signals from point sources during low flows. In this paper, a range of sampling methodologies and load estimation techniques are applied to phosphorus data from such a surface water dominated river system, instrumented at three sub-catchments (ranging from 3 to 5 km2 in area) with near-continuous monitoring stations. Systematic and Monte Carlo approaches were applied to simulate grab sampling using multiple strategies and to calculate an estimated load, Le based on established load estimation methods. Comparison with the actual load, Lt, revealed signi?cant average underestimation, of up to 60%, and high variability for all feasible sampling approaches. Further analysis of the time series provides an insight into these observations; revealing peak frequencies and power-law scaling in the distributions of P concentration, discharge and load associated with surface runoff and background transfers. Results indicate that only near-continuous monitoring that re?ects the rapid temporal changes in these river systems is adequate for comparative monitoring and evaluation purposes. While the implications of this analysis may be more tenable to small scale ?ashy systems, this represents an appropriate scale in terms of evaluating catchment mitigation strategies such as agri-environmental policies for managing diffuse P transfers in complex landscapes.

Genetic Algorithm Search for Predictive Patterns in Multidimensional Time Series

Based on an algorithm for pattern matching in character strings, we implement a pattern matching machine that searches for occurrences of patterns in multidimensional time series. Before the search process takes place, time series are encoded in user-designed alphabets. The patterns, on the other hand, are formulated as regular expressions that are composed of letters from these alphabets and operators. Furthermore, we develop a genetic algorithm to breed patterns that maximize a user-defined fitness function. In an application to financial data, we show that patterns bred to predict high exchange rates volatility in training samples retain statistically significant predictive power in validation samples.

NON-GAUSSIAN STATISTICS OF OIL PRICING TIME-SERIES: A CASE STUDY

The stochastic nature of oil price fluctuations is investigated over a twelve-year period, borrowing feedback from an existing database (USA Energy Information Administration database, available online). We evaluate the scaling exponents of the fluctuations by employing different statistical analysis methods, namely rescaled range analysis (R/S), scale windowed variance analysis (SWV) and the generalized Hurst exponent (GH) method. Relying on the scaling exponents obtained, we apply a rescaling procedure to investigate the complex characteristics of the probability density functions (PDFs) dominating oil price fluctuations. It is found that PDFs exhibit scale invariance, and in fact collapse onto a single curve when increments are measured over microscales (typically less than 30 days). The time evolution of the distributions is well fitted by a Levy-type stable distribution. The relevance of a Levy distribution is made plausible by a simple model of nonlinear transfer. Our results also exhibit a degree of multifractality as the PDFs change and converge toward to a Gaussian distribution at the macroscales.

Nonlinear time series prediction based on a power-law noise model

In this paper we investigate the influence of a power-law noise model, also called noise, on the performance of a feed-forward neural network used to predict time series. We introduce an optimization procedure that optimizes the parameters the neural networks by maximizing the likelihood function based on the power-law model. We show that our optimization procedure minimizes the mean squared leading to an optimal prediction. Further, we present numerical results applying method to time series from the logistic map and the annual number of sunspots demonstrate that a power-law noise model gives better results than a Gaussian model.

Temporal extension of Laplacian Eigenmaps for unsupervised dimensionality reduction of time series

A novel non-linear dimensionality reduction method, called Temporal Laplacian Eigenmaps, is introduced to process efficiently time series data. In this embedded-based approach, temporal information is intrinsic to the objective function, which produces description of low dimensional spaces with time coherence between data points. Since the proposed scheme also includes bidirectional mapping between data and embedded spaces and automatic tuning of key parameters, it offers the same benefits as mapping-based approaches. Experiments on a couple of computer vision applications demonstrate the superiority of the new approach to other dimensionality reduction method in term of accuracy. Moreover, its lower computational cost and generalisation abilities suggest it is scalable to larger datasets. © 2010 IEEE.

Detecting sequence dependent transcriptional pauses from RNA and protein number time series

Background: Evidence suggests that in prokaryotes sequence-dependent transcriptional pauses a?ect the dynamics of transcription and translation, as well as of small genetic circuits. So far, a few pause-prone sequences have been identi?ed from in vitro measurements of transcription elongation kinetics.<br/><br/>Results: Using a stochastic model of gene expression at the nucleotide and codon levels with realistic parameter values, we investigate three di?erent but related questions and present statistical methods for their analysis. First, we show that information from in vivo RNA and protein temporal numbers is su?cient to discriminate between models with and without a pause site in their coding sequence. Second, we demonstrate that it is possible to separate a large variety of models from each other with pauses of various durations and locations in the template by means of a hierarchical clustering and a random forest classi?er. Third, we introduce an approximate likelihood function that allows to estimate the location of a pause site.<br/><br/>Conclusions: This method can aid in detecting unknown pause-prone sequences from temporal measurements of RNA and protein numbers at a genome-wide scale and thus elucidate possible roles that these sequences play in the dynamics of genetic networks and phenotype.

Bandwidth selection by cross-validation for forecasting long memory financial time series

The paper addresses the issue of choice of bandwidth in the application of semiparametric estimation of the long memory parameter in a univariate time series process. The focus is on the properties of forecasts from the long memory model. A variety of cross-validation methods based on out of sample forecasting properties are proposed. These procedures are used for the choice of bandwidth and subsequent model selection. Simulation evidence is presented that demonstrates the advantage of the proposed new methodology.

Learning from time series:Supervised Aggregative Feature Extraction

<p>Many modeling problems require to estimate a scalar output from one or more time series. Such problems are usually tackled by extracting a fixed number of features from the time series (like their statistical moments), with a consequent loss in information that leads to suboptimal predictive models. Moreover, feature extraction techniques usually make assumptions that are not met by real world settings (e.g. uniformly sampled time series of constant length), and fail to deliver a thorough methodology to deal with noisy data. In this paper a methodology based on functional learning is proposed to overcome the aforementioned problems; the proposed Supervised Aggregative Feature Extraction (SAFE) approach allows to derive continuous, smooth estimates of time series data (yielding aggregate local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The SAFE paradigm enjoys several properties like closed form solution, incorporation of first and second order derivative information into the regressor matrix, interpretability of the generated functional predictor and the possibility to exploit Reproducing Kernel Hilbert Spaces setting to yield nonlinear predictive models. Simulation studies are provided to highlight the strengths of the new methodology w.r.t. standard unsupervised feature selection approaches. © 2012 IEEE.</p>

Supervised Aggregative Feature Extraction for Big Data Time Series Regression

In many applications, and especially those where batch processes are involved, a target scalar output of interest is often dependent on one or more time series of data. With the exponential growth in data logging in modern industries such time series are increasingly available for statistical modeling in soft sensing applications. In order to exploit time series data for predictive modelling, it is necessary to summarise the information they contain as a set of features to use as model regressors. Typically this is done in an unsupervised fashion using simple techniques such as computing statistical moments, principal components or wavelet decompositions, often leading to significant information loss and hence suboptimal predictive models. In this paper, a functional learning paradigm is exploited in a supervised fashion to derive continuous, smooth estimates of time series data (yielding aggregated local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The proposed Supervised Aggregative Feature Extraction (SAFE) methodology can be extended to support nonlinear predictive models by embedding the functional learning framework in a Reproducing Kernel Hilbert Spaces setting. SAFE has a number of attractive features including closed form solution and the ability to explicitly incorporate first and second order derivative information. Using simulation studies and a practical semiconductor manufacturing case study we highlight the strengths of the new methodology with respect to standard unsupervised feature extraction approaches.

Error sensitive historical GIS: Identifying areal interpolation errors in time series data

Historical GIS has the potential to re-invigorate our use of statistics from historical censuses and related sources. In particular, areal interpolation can be used to create long-run time-series of spatially detailed data that will enable us to enhance significantly our understanding of geographical change over periods of a century or more. The difficulty with areal interpolation, however, is that the data that it generates are estimates which will inevitably contain some error. This paper describes a technique that allows the automated identification of possible errors at the level of the individual data values.