For a process with stationary first differences necessary and sufficient conditions for the variance of the process to be unbounded are given. An example shows that the variance of an integrated process -- while being unbounded -- need not diverge to infinity. Sufficient conditions for the...

The performance of a kernel HAC estimator depends on the accuracy of the estimation of the normalized curvature, an unknown quantity in the optimal bandwidth represented as the spectral density and its derivative. This paper proposes to estimate it with a general class of kernels. The AMSE of...

Ng and Perron (2001) designed a unit root test which incorporates the properties of DF-GLS and Phillips Perron test. Ng and Perron claim that the test performs exceptionally well especially in the presence of negative moving average. However, the performance of test depends heavily on the choice...

For a wide class of second-order stationary spatial processes on a lattice, the statistical properties of the maximum Gaussian pseudo-likelihood estimators are studied. The estimators are natural as they imitate the theoretical prototypes of spatial best linear prediction. Under certain...

The Fourier estimator of Malliavin and Mancino depends on both sample size and a so-called cutting frequency. The latter controls the number of Fourier coefficients to be included, and it also determines how the Fourier estimator responds to market microstructure noise. By examining the finite...

The time-dependent projection operator technique according to Willis and Picard (Phys. Rev. A 9 (1974) 1343) offers a unique quantum statistical description of two interacting subsystems. The technique is used here to go beyond the standard quantum master equation (QME) for a small system...

Ecologists have observed that environmental noise affects population variance in the logistic equation for one-species growth. Interactions between deterministic and stochastic dynamics in a one-dimensional system result in increased variance in species population density over time. Since...

High-dimensional time series may well be the most common type of dataset in the so-called “big data” revolution, and have entered current practice in many areas, including meteorology, genomics, chemometrics, connectomics, complex physics simulations, biological and environmental research,...

Motivated by a recent paper of Caiado et al. (2009), we investigate testing problems for spectral densities of time series with unequal sample sizes. We thereby focus on analyzing their mathematical properties and illustrate our results in a small simulation study.