The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling...

By using a symbolic method, known in the literature as the classical umbral calculus, the trace of a non-central Wishart random matrix is represented as the convolution of the traces of its central component and of a formal variable matrix. Thanks to this representation, the moments of this...

Let {X(t),t∈Z} be a stationary time series with a.e. positive spectrum. Two consequences of that the bispectrum of {X(t),t∈Z} is real-valued but nonzero are: (1) if {X(t),t∈Z} is also linear, then it is reversible; (2) {X(t),t∈Z} cannot be causal linear. A corollary of the first...

<Para ID="Par1">Motivated by a roundoff problem, we derive new expressions for cumulants of a random variable distributed uniformly on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$0,1, \ldots , n-1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>. Their computational efficiency over a known expression is discussed. Copyright Springer-Verlag Berlin Heidelberg 2015

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling...

In this paper, we propose a kernel-type estimator for the local characteristic function of locally stationary processes. Under weak moment conditions, we prove joint asymptotic normality for local empirical characteristic functions. For time-varying linear processes, we establish a central limit...

We consider parameter estimation for time-dependent locally stationary long-memory processes. The asymptotic distribution of an estimator based on the local infinite autoregressive representation is derived, and asymptotic formulas for the mean squared error of the estimator, and the...