Related papers: Copula-based algorithm for generating bursty time …
Long-term temporal correlations observed in event sequences of natural and social phenomena have been characterized by algebraically decaying autocorrelation functions. Such temporal correlations can be understood not only by heterogeneous…
Temporal sequences of discrete events that describe natural and social processes are often driven by non-Poisson dynamics. In addition to a heavy-tailed interevent time distribution, which primarily captures the deviation from a Poisson…
Multivariate time series (MTS) data often include a heterogeneous mix of non-Gaussian distributional features (asymmetry, multimodality, heavy tails) and data types (continuous and discrete variables). Traditional MTS methods based on…
Temporal correlations in the time series observed in various systems have been characterized by the autocorrelation function. Such correlations can be explained by heavy-tailed interevent time distributions as well as by correlations…
Comprehensive characterization of non-Poissonian, bursty temporal patterns observed in various natural and social processes is crucial to understand the underlying mechanisms behind such temporal patterns. Among them bursty event sequences…
Characterizing bursty temporal interaction patterns of temporal networks is crucial to investigate the evolution of temporal networks as well as various collective dynamics taking place in them. The temporal interaction patterns have been…
Long-term temporal correlations in time series in a form of an event sequence have been characterized using an autocorrelation function (ACF) that often shows a power-law decaying behavior. Such scaling behavior has been mainly accounted…
Joint modelling of longitudinal and time-to-event data is usually described by a joint model which uses shared or correlated latent effects to capture associations between the two processes. Under this framework, the joint distribution of…
Human social interactions tend to vary in intensity over time, whether they are in person or online. Variable rates of interaction in structured populations can be described by networks with the time-varying activity of links and nodes. One…
The visibility graph (VG) algorithm and its variants have been extensively studied in the time series analysis as they transform the time series into the network of nodes and links, enabling to characterize the time series in terms of…
An approach to the modelling of volatile time series using a class of uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe the relationship between quantiles of the stationary distribution of the…
The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2011) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random…
In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time…
In the copula-based approach to univariate time series modeling, the finite dimensional temporal dependence of a stationary time series is captured by a copula. Recent studies investigate how copula-based time series models can be…
Many time series applications require access to multi-step forecast trajectories in the form of sample paths. Recently, time series foundation models have leveraged multi-step lookahead predictions to improve the quality and efficiency of…
We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility…
We present a simple stochastic algorithm for generating multiplicative processes with multiscaling both in space and in time. With this algorithm we are able to reproduce a synthetic signal with the same space and time correlation as the…
The Multiplicative Error Model (Engle (2002)) for nonnegative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with nonnegative support. A multivariate extension allows…
Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical…
Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty…