Related papers: Testing second order dynamics for autoregressive p…
In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the $L^2$-distance between the square of the regression function…
This paper is devoted to the off-line multiple change-point detection in a semiparametric framework. The time series is supposed to belong to a large class of models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),... models where…
This paper considers the statistical inference of the class of asymmetric power-transformed $\operatorname{GARCH}(1,1)$ models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity…
We propose a new sequential procedure to detect change in the parameters of a process $ X= (X_t)_{t\in \Z}$ belonging to a large class of causal models (such as AR($\infty$), ARCH($\infty$), TARCH($\infty$), ARMA-GARCH processes). The…
This paper considers an augmented double autoregressive (DAR) model, which allows null volatility coefficients to circumvent the over-parameterization problem in the DAR model. Since the volatility coefficients might be on the boundary, the…
We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for…
We propose a general class of INteger-valued Generalized AutoRegressive Conditionally Heteroscedastic (INGARCH) processes by allowing time-varying mean and dispersion parameters, which we call time-varying dispersion INGARCH (tv-DINGARCH)…
Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a…
Multivariate locally stationary functional time series provide a flexible framework for modeling complex data structures exhibiting both temporal and spatial dependencies while allowing for time-varying data generating mechanism. In this…
Time series observations are ubiquitous in astronomy, and are generated to distinguish between different types of supernovae, to detect and characterize extrasolar planets and to classify variable stars. These time series are usually…
In this paper, we consider subgeometric (specifically, polynomial) ergodicity of univariate nonlinear autoregressions with autoregressive conditional heteroskedasticity (ARCH). The notion of subgeometric ergodicity was introduced in the…
We propose a new asymptotic test to assess the stationarity of a time series' mean that is applicable in the presence of both heteroscedasticity and short-range dependence. Our test statistic is composed of Gini's mean difference of local…
In this paper, a concurrent learning based adaptive observer is developed for a class of second-order linear time-invariant systems with uncertain system matrices. The developed technique yields an exponentially convergent state estimator…
We propose a novel algorithm for testing the hypothesis of nonstationarity in complex-valued signals. The implementation uses both the bootstrap and the Fast Fourier Transform such that the algorithm can be efficiently implemented in…
Time series of counts are frequently analyzed using generalized integer-valued autoregressive models with conditional heteroskedasticity (INGARCH). These models employ response functions to map a vector of past observations and past…
A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and $\beta$-mixing solution is established under a mild assumption on the density of the underlying independent process. We give…
Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are…
In modern interdisciplinary research, manifold time series data have been garnering more attention. A critical question in analyzing such data is ``stationarity'', which reflects the underlying dynamic behavior and is crucial across various…
Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs) appear in a wide spectrum of applications such as chemical reactors, concentration flows, and biological systems. A large number of these applications require the…
Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at…