Related papers: Locally stationary long memory estimation
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…
Most time series observed in practice exhibit time-varying trend (first-order) and autocovariance (second-order) behaviour. Differencing is a commonly-used technique to remove the trend in such series, in order to estimate the time-varying…
The paper deals with a question of robustness of inferences, carried out on a continuous-time stationary process contaminated by a small trend, to this departure from stationarity. We show that a smoothed periodogram approach to parameter…
For stationary time series, it is common to use the plots of partial autocorrelation function (PACF) or PACF-based tests to explore the temporal dependence structure of such processes. To our best knowledge, such analogs for non-stationary…
Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this…
In this paper, we show that the central limit theorem (CLT) satisfied by the data-driven Multidimensional Increment Ratio (MIR) estimator of the memory parameter d established in Bardet and Dola (2012) for d $\in$ (--0.5, 0.5) can be…
Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…
In order to interpret and explain the physiological signal behaviors, it can be interesting to find some constants among the fluctuations of these data during all the effort or during different stages of the race (which can be detected…
This paper develops a general asymptotic theory of series estimators for spatial data collected at irregularly spaced locations within a sampling region $R_n \subset \mathbb{R}^d$. We employ a stochastic sampling design that can flexibly…
While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…
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.…
This article develops nonparametric cointegrating regression models with endogeneity and semi-long memory. We assume that semi-long memory is produced in the regressor process by tempering of random shock coefficients. The fundamental…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
This paper analyzes the limit properties of the empirical process of $\alpha$-stable random variables with long range dependence. The $\alpha$-stable random variables are constructed by non-linear transformations of bivariate sequences of…
The success of large-scale models in recent years has increased the importance of statistical models with numerous parameters. Several studies have analyzed over-parameterized linear models with high-dimensional data, which may not be…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
Classical spectral methods are subject to two fundamental limitations: they only can account for covariance-related serial dependencies, and they require second-order stationarity. Much attention has been devoted lately to quantile-based…
Most machine learning methods assume fixed probability distributions, limiting their applicability in nonstationary real-world scenarios. While continual learning methods address this issue, current approaches often rely on black-box models…
This paper considers the estimation and testing of a class of locally stationary time series factor models with evolutionary temporal dynamics. In particular, the entries and the dimension of the factor loading matrix are allowed to vary…