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In asteroseismology, the observed time series often suffers from incomplete time coverage due to gaps. The presence of periodic gaps may generate spurious peaks in the power spectrum that limit the analysis of the data. Various methods have…
Context: A fraction of active galactic nuclei (AGN) show dramatic X-ray spectral changes on the day-to-week time scales associated with variation in the line of sight of the cold absorber. Aims: We intend to model the polarization…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…
Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…
The advent of integral field data has revolutionised the study of galaxy evolution. A key component of this is dynamical modelling methods which have allowed for crucial insights to be made from kinematic data. Despite this importance, most…
We study the biasing relation between dark-matter halos or galaxies and the underlying mass distribution, using cosmological $N$-body simulations in which galaxies are modelled via semi-analytic recipes. The nonlinear, stochastic biasing is…
Temporal analysis of X-ray binaries and Active Galactic Nuclei have shown that hard X-rays react to variation of soft ones after a time delay. The opposite trend, or soft lag, has only been seen in a few rare Quasi-periodic Oscillations in…
Short-term variability of X-ray spectra has been reported for several Active Galactic Nuclei. Significant X-ray flux variations are observed within time scales down to 10^4 -- 10^5 seconds. We discuss short variability time scales in the…
Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the…
A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the…
Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process…
RXTE ASM count rates from the X-ray pulsar Her X-1 began falling consistently during the late months of 2003. The source is undergoing another state transition similar to the anomalous low state of 1999. This new event has triggered…
The normalized excess variance is a popular method used by many authors to estimate the variability of active galactic nuclei (AGNs), especially in the X-ray band. We show that this estimator is affected by the cosmological time dilation,…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
Modern observatories are designed to deliver increasingly detailed views of astrophysical signals. To fully realize the potential of these observations, principled data-analysis methods are required to effectively separate and reconstruct…
Jet precession is sometimes invoked to explain asymmetries in radio galaxy (RG) jets and "X/S/Z-shape" radio galaxies, caused by the presence of a binary black hole companion to the source active galactic nucleus (AGN) or by accretion…
Long-period variability in luminous red giants has several promising applications, all of which require models able to accurately predict pulsation periods. Linear pulsation models have proven successful in reproducing the observed periods…
This work develops application techniques for stochastic modelling of Active Galactic Nuclei (AGN) variability as a probe of accretion disk physics. Stochastic models, specifically Continuous Auto-Regressive Moving Average (CARMA) models,…
Galaxy evolution is driven by spatially distributed processes with varying timescales. Integral field spectroscopy provides spatially-resolved information about these processes. Nevertheless, disentangling these processes, which are related…