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Aperiodic variability is a characteristic feature of young stars, massive stars, and active galactic nuclei. With the recent proliferation of time domain surveys, it is increasingly essential to develop methods to quantify and analyze…
This paper presents a new method for modelling periodic signals having an aperiodic trend, using the method of variable projection. It is a major extension to the IEEE-standard 1057 by permitting the background to be time varying;…
I introduce a general, Bayesian method for modelling univariate time series data assumed to be drawn from a continuous, stochastic process. The method accommodates arbitrary temporal sampling, and takes into account measurement…
For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the…
Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates…
The problem of denoising a one-dimensional signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. For example, in the time domain, an astronomical object may exhibit a smoothly…
Radio observations of the neutral hydrogen signal from the Cosmic Dawn and Epoch of Reionisation have helped to provide constraints on the properties of the first stars and galaxies. Since this global 21-cm cosmological signal from the…
The problem of estimating trend and seasonal variation in time-series data has been studied over several decades, although mostly using single time series. This paper studies the problem of estimating these components from functional data,…
We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…
Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…
Astronomical time series often have non-uniform sampling in time, or irregular cadences, with long gaps separating clusters of observations. Some of these data sets are also explicitly non-Gaussian with respect to the expected model fit, or…
The development of robust generative models for highly varied non-stationary time series data is a complex yet important problem. Traditional models for time series data prediction, such as Long Short-Term Memory (LSTM), are inefficient and…
A Bayesian method of moments/instrumental variable (BMOM/IV) approach is developed and applied in the analysis of the important mean and multiple regression models. Given a single set of data, it is shown how to obtain posterior and…
New time-series analysis tools are needed in disciplines as diverse as astronomy, economics and meteorology. In particular, the increasing rate of data collection at multiple wavelengths requires new approaches able to handle these data.…
We propose a voxel-wise general linear model with autoregressive noise and heteroscedastic noise innovations (GLMH) for analyzing functional magnetic resonance imaging (fMRI) data. The model is analyzed from a Bayesian perspective and has…
We develop a generalization of correlated trend-cycle decompositions that avoids prior assumptions about the long-run dynamic characteristics by modelling the permanent component as a fractionally integrated process and incorporating a…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…
Big spatio-temporal datasets, available through both open and administrative data sources, offer significant potential for social science research. The magnitude of the data allows for increased resolution and analysis at individual level.…
A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…