Related papers: Gradual changes in functional time series
Methods for detecting structural changes, or change points, in time series data are widely used in many fields of science and engineering. This chapter sketches some basic methods for the analysis of structural changes in time series data.…
We propose a Bayesian hierarchical model to simultaneously estimate mean based changepoints in spatially correlated functional time series. Unlike previous methods that assume a shared changepoint at all spatial locations or ignore spatial…
We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behaviour. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate…
We study the problem of quickest detection of a change in the mean of an observation sequence, under the assumption that both the pre- and post-change distributions have bounded support. We first study the case where the pre-change…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
We present a functional data analysis approach for studying time-dependent, continuous glucose monitoring data with repeated measures for each individual in an experiment. After scaling the glucose concentration curves to the interval [0,…
Environmental data often take the form of a collection of curves observed sequentially over time. An example of this includes daily pollution measurement curves describing the concentration of a particulate matter in ambient air. These…
It is commonly required to detect change points in sequences of random variables. In the most difficult setting of this problem, change detection must be performed sequentially with new observations being constantly received over time.…
We analyze the occurrence and the values of record-breaking temperatures in daily and monthly temperature observations. Our aim is to better understand and quantify the statistics of temperature records in the context of global warming.…
We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series $p$ is large in relation to the length of time series $n$. Our first step performs an…
Researchers are often interested in examining between-individual differences in within-individual processes. If the process under investigation is tracked for a long time, its trajectory may show a certain degree of nonlinearity, so that…
We aim to develop simultaneous inference tools for the mean function of functional data from sparse to dense. First, we derive a unified Gaussian approximation to construct simultaneous confidence bands of mean functions based on the…
Particulate matter data now include various particle sizes, which often manifest as a collection of curves observed sequentially over time. When considering 51 distinct particle sizes, these curves form a high-dimensional functional time…
Many natural systems undergo critical transitions, i.e. sudden shifts from one dynamical regime to another. In the climate system, the atmospheric boundary layer can experience sudden transitions between fully turbulent states and…
A new statistical approach is presented to study the thermal instability process of optically thin unmagnetized plasma. In this approach the time evolution of mass distribution function over temperature is calculated. This function…
As contemporary software-intensive systems reach increasingly large scale, it is imperative that failure detection schemes be developed to help prevent costly system downtimes. A promising direction towards the construction of such schemes…
We consider the problem of detecting abrupt changes (i.e., large jump discontinuities) in the rate function of a point process. The rate function is assumed to be fully unknown, non-stationary, and may itself be a random process that…
Climate change is a massive multidimensional shift. Temperature shifts, in particular, have important implications for urbanization, agriculture, health, productivity, and poverty, among other things. While much research has documented…
We address the problem of detecting a change in the distribution of a high-dimensional multivariate normal time series. Assuming that the post-change parameters are unknown and estimated using a window of historical data, we extend the…
Methodology is proposed to uncover structural breaks in functional data that is "fully functional" in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break…