We propose a heteroskedasticity‐robust locally best invariant (LBI) statistic to test the hypothesis of a unit root against the alternative of an explosive root associated with speculative bubbles. Compared to existing alternatives such as Dickey‐Fuller type tests, the LBI statistic has a...

Ridge regression is a popular method for dense least squares regularization. In this article, ridge regression is studied in the context of VAR model estimation and inference. The implications of anisotropic penalization are discussed, and a comparison is made with Bayesian ridge‐type...

A new and flexible class of ARMA‐like (autoregressive moving average) models for nominal or ordinal time series is proposed, which are characterized by using so‐called weighting operators and are, thus, referred to as weighted discrete ARMA (WDARMA) models. By choosing an appropriate type of...

Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low‐dimensional observations, it becomes challenging for more intricate objects, such as multi‐variate functions. Here, the covariance can be so complex that just saving a...

Estimating parameters of functional ARMA, GARCH and invertible processes requires estimating lagged covariance and cross‐covariance operators of Cartesian product Hilbert space‐valued processes. Asymptotic results have been derived in recent years, either less generally or under a strict...

Using ‘working’ assumptions on conditional third and fourth moments of errors, we propose a method of moments estimator that can have improved efficiency over the popular Gaussian quasi‐maximum likelihood estimator (GQMLE). Higher‐order moment assumptions are not needed for consistency...

In this article, we derive (local) orthogonality graphs for the popular continuous‐time state space models, including in particular multivariate continuous‐time ARMA (MCARMA) processes. In these (local) orthogonality graphs, vertices represent the components of the process, directed edges...

For a spatiotemporal process {Xj(s,t)∣s∈S,t∈T}j=1,…,n, where S denotes the set of spatial locations and T the time domain, we consider the problem of testing for a change in the sequence of mean functions {μj(s,t)∣s∈S,t∈T}j=1,…,n. In contrast to most of the literature, we are...

The autocovariance and cross-covariance functions naturally appear in many time series procedures (e.g. autoregression or prediction). Under assumptions, empirical versions of the autocovariance and cross-covariance are asymptotically normal with covariance structure depending on the second- and...

We represent the dynamic relation among variables in vector autoregressive (VAR) models as directed graphs. Based on these graphs, we identify so‐called strongly connected components. Using this graphical representation, we consider the problem of variable choice. We use the relations among...