Abstract The surface drifting buoys, or drifters, of the Global Drifter Program (GDP) are predominantly tracked by Argos positioning system, providing drifter locations with O (100 m) errors at nonuniform temporal intervals, an average interval 1.2 h since January 2005. This data set is thus a rich and global source information on high‐frequency small‐scale oceanic processes, yet still relatively understudied because challenges associated its large size sampling characteristics. A...

The Whittle likelihood is a widely used and computationally efficient pseudolikelihood. However, it known to produce biased parameter estimates with finite sample sizes for large classes of models. We propose method debiasing second-order stationary stochastic processes. debiased can be computed in the same |${O}(n\log n)$| operations as standard approach. demonstrate superior performance our simulation studies application large-scale oceanographic dataset, where both cases approach reduces...

Summary The paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely drifting satellite-tracked instruments. time series proposed are used to summarize large multivariate data sets and infer important physical parameters inertial oscillations other processes. Non-stationary methods employed account spatiotemporal variability each trajectory. Because large, we construct computationally efficient through use frequency domain modelling estimation,...

Abstract. Stochastic processes exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm), with spectral slope at high frequencies being associated degree of small-scale roughness or fractal dimension. However, a broad class real-world signals have high-frequency slope, like fBm, but plateau vicinity zero frequency. This low-frequency plateau, it is shown, implies that temporal integral process exhibits diffusive behavior, dispersing...

We propose a simple stochastic process for modeling improper or noncircular complex-valued signals. The is natural extension of autoregressive process, extended to include widely linear term. This can then capture elliptical, as opposed circular, oscillations in bivariate signal. order one and more parsimonious than alternative approaches the literature. provide conditions stationarity, derive form covariance relation sequence this model. describe how parameter estimation be efficiently...

A dataset of sea surface temperature (SST) estimates is generated from the observations drifting buoys NOAA's Global Drifter Program. Estimates SST at regular hourly time steps along drifter trajectories are obtained by fitting to a mathematical model representing simultaneously diurnal variability with three harmonics daily frequency, and low-frequency first degree polynomial. Subsequent non-diurnal SST, anomalies, total as their sum, provided respective standard uncertainties. This...

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, single complex-valued or analytic signals known the rotary components. Each representation has unique advantages depending on system interest and application goals. In this paper, we provide joint framework for all representations in context frequency-domain stochastic modeling. This allows us to extend many established statistical procedures time series representations....

We provide a novel methodology for computing the most likely path taken by drifters between arbitrary fixed locations in ocean. also an estimate of travel time associated with this path. Lagrangian pathways and times are practical value not just understanding surface velocities, but modelling transport ocean-borne species such as planktonic organisms, floating debris plastics. In particular, estimated can be used to compute distance, which is often more informative than Euclidean distance...

This paper proposes a novel multiscale estimator for the integrated volatility of an Itô process in presence market microstructure noise (observation error). The structure observed is represented frequency by frequency, and concept ratio introduced to quantify bias realized due observation error. estimated from single sample path, frequency-by-frequency correction procedure proposed, which simultaneously reduces variance. We extend method include correlated errors provide implied time-domain...

Abstract Welch’s method provides an estimator of the power spectral density that is statistically consistent. This achieved by averaging over periodograms calculated from overlapping segments a time series. For finite-length series, while variance decreases as number increases, magnitude estimator’s bias increases: bias-variance trade-off ensues when setting segment number. We address this issue providing novel for debiasing maintains computational complexity and asymptotic consistency,...

Wind-generated waves are often treated as stochastic processes. There is particular interest in their spectral density functions, which expressed some parametric form. Such functions used inputs when modelling structural response or other engineering concerns. Therefore, accurate and precise recovery of the parameters such a form, from observed wave records, important. Current techniques known to struggle with recovering certain parameters, especially peak enhancement factor tail decay. We...

This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods multivariate processes from the circulant embedding literature. method can be performed in $\mathcal{O}(n\log_2 n)$ operations, where $n$ is length of desired sequence. exact, except when eigenvalues prescribed matrices are negative. We evaluate performance empirically, and provide a practical example guaranteed to exact all...

Revenue management strongly relies on accurate forecasts. Thus, when extraordinary events cause outlier demand, revenue systems need to recognise this and adapt both forecast controls. Many passenger transport service providers, such as railways airlines, control the sale of tickets through management. State-of-the-art in these industries rely analyst expertise identify demand online (within booking horizon) offline (in hindsight). So far, little research focuses automating evaluating...

Accelerometry data has been widely used to measure activity and the circadian rhythm of individuals across health sciences, in particular with people advanced dementia. Modern accelerometers can record continuous observations on a single individual for several days at sampling frequency order one hertz. Such rich lengthy sets provide new opportunities statistical insight, but also pose challenges selecting from wide range possible summary statistics, how calculation such statistics should be...

We provide a computationally and statistically efficient method for estimating the parameters of stochastic covariance model observed on regular spatial grid in any number dimensions. Our proposed method, which we call Debiased Spatial Whittle likelihood, makes important corrections to well-known likelihood account large sources bias caused by boundary effects aliasing. generalize approach flexibly allow significant volumes missing data including those with lower-dimensional substructure,...

Abstract Bike-sharing is a popular component of sustainable urban mobility. It requires anticipatory planning, e.g. station locations and inventory, to balance expected demand capacity. However, external factors such as extreme weather or glitches in public transport, can cause deviate from baseline levels. Identifying outliers keeps historic data reliable improves forecasts. In this paper we show how be identified by clustering stations applying functional depth analysis. We apply our...

Abstract Buoy data in the form of multivariate time series are routinely recorded at many locations world’s oceans. Such can help characterise ocean wavefield by modelling frequency-direction spectrum. State-of-the-art methods for estimating parameters such models do not make use full spatiotemporal content buoy observations due to unnecessary assumptions and smoothing. We explain how debiased Whittle likelihood be used jointly estimate all spectra directly from series. apply method North...

Plankton seascape genomics studies have revealed different trends from large-scale weak differentiation to microscale structures. Previous underlined the influence of environment and on species adaptation. However, these generally focused a few single species, sparse molecular markers, or local scales. Here, we investigated genomic plankton at macro-scale in holistic approach using Tara Oceans metagenomic data together with reference-free computational method.We reconstructed FST-based 113...

Many sequential decision making problems require an agent to balance exploration and exploitation maximise long-term reward. Existing policies that address this tradeoff typically have parameters are set a priori control the amount of exploration. In finite-time problems, optimal values these highly dependent on problem faced. paper, we propose adapting performed on-line, as information is gathered by agent. To end introduce novel algorithm, e-ADAPT, which has no free parameters. The...

We propose a new class of univariate non‐stationary time series models, using the framework modulated series, which is appropriate for analysis rapidly evolving as well observations with missing data. extend our techniques to bivariate that are isotropic. Exact inference often not computationally viable analysis, and so we an estimation method based on Whittle likelihood, commonly adopted pseudo‐likelihood. Our procedure shown be consistent under standard assumptions, having considerably...

A comprehensive methodology is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. also show to allow outliers which are typical in GPS signals. effectiveness of our methods on trajectory obtained oceanographic floating instruments known as drifters.