Related papers: Autocorrelation functions for point-process time s…
Perception is one of the key abilities of autonomous mobile robotic systems, which often relies on fusion of heterogeneous sensors. Although this heterogeneity presents a challenge for sensor calibration, it is also the main prospect for…
We consider a one-dimensional vehicular network where the time headway (time difference between successive vehicles as they pass a point on the roadway) follows the shifted-exponential distribution. We show that neglecting the impact of…
Classical anomaly detection is principally concerned with point-based anomalies, those anomalies that occur at a single point in time. Yet, many real-world anomalies are range-based, meaning they occur over a period of time. Motivated by…
Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…
The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of…
Complex systems such as protein conformational fluctuations and supercooled liquids exhibit a long relaxation time and are considered to posses multiple relaxation times. We analytically obtain the exact correlation function for stochastic…
Continuously-observed event occurrences, often exhibit self- and mutually-exciting effects, which can be well modeled using temporal point processes. Beyond that, these event dynamics may also change over time, with certain periodic trends.…
We develop a framework especially suited to the autocorrelation properties observed in financial times series, by borrowing from the physical picture of turbulence. The success of our approach as applied to high frequency foreign exchange…
Many astrophysical phenomena are time-varying, in the sense that their intensity, energy spectrum, and/or the spatial distribution of the emission suddenly change. This paper develops a method for modeling a time series of images. Under the…
The purpose of this paper is to give an overview of the time series forecasting problem based on similarity of trajectories. Various methodologies are introduced and studied, and detailed discussions on hyperparameter optimization, outlier…
Fluctuations in nuclear collisions can be measured as a function of momentum-space binning scale over a scale interval bounded by detector two-track resolution and acceptance. Fluctuation scale dependence is related to two-particle…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient…
This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a…
We describe the impact of the intra-day activity pattern on the autocorrelation function estimator. We obtain an exact formula relating estimators of the autocorrelation functions of non-stationary process to its stationary counterpart.…
Spreading processes on graphs arise in a host of application domains, from the study of online social networks to viral marketing to epidemiology. Various discrete-time probabilistic models for spreading processes have been proposed. These…
The observable outputs of many complex dynamical systems consist in time series exhibiting autocorrelation functions of great diversity of behaviors, including long-range power-law autocorrelation functions, as a signature of interactions…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…