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.

The impact of a PCR assay for candidemia on antifungal drug prescribing in critical care: an interrupted time series pilot study.

Objective To evaluate the feasibility of conducting a definitive study to assess the impact of introducing a rapid PCR-based test for candidemia on antifungal drug prescribing. Method Prospective, single centre, interrupted time series study consisting of three periods of six months' duration. The assay was available during the second period, during which the PCR assay was available for routine use by physicians Monday–Friday with guaranteed 24-h turnaround time. For each period total antifungal drug use, expressed as treatment-days, was recorded and an adjustment was made to exclude estimated use for proven candidemia. Also, during the intervention period, antifungal prescribing decisions for up to 72 h after each PCR result became available were recorded as either concordant or discordant with that result. Results While overall antifungal use remained relatively stable throughout, after adjustment for candidemia, there was a 38% reduction in use following introduction of the PCR test; however, this was nonsignificant at the 95% level. During the intervention period overall concordance between the PCR result and prescribing decisions was 84%. Conclusions The PCR assay for candidemia was requested, prescribing decisions were generally concordant with the results produced and there was an apparent decrease in antifungal prescription, although this was sustained even after withdrawal of the intervention; these findings should be more thoroughly evaluated in a larger trial.

Pointwise universal trigonometric series

A series $S_a=\sum\limits_{n=-\infty}^\infty a_nz^n$ is called a {\it pointwise universal trigonometric series} if for any $f\in C(\T)$, there exists a strictly increasing sequence $\{n_k\}_{k\in\N}$ of positive integers such that $\sum\limits_{j=-n_k}^{n_k} a_jz^j$ converges to $f(z)$ pointwise on $\T$. We find growth conditions on coefficients allowing and forbidding the existence of a pointwise universal trigonometric series. For instance, if $|a_n|=O(\e^{\,|n|\ln^{-1-\epsilon}\!|n|})$ as $|n|\to\infty$ for some $\epsilon>0$, then the series $S_a$ can not be pointwise universal. On the other hand, there exists a pointwise universal trigonometric series $S_a$ with $|a_n|=O(\e^{\,|n|\ln^{-1}\!|n|})$ as $|n|\to\infty$.

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.

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.

NHS Inquiries: A Time Series Analysis

This article provides a time series analysis of NHS public inquiries and inquiries related to health against the background of recent policy changes which are centralizing hazardous incident investigations within agencies such as the Healthcare Commission.