A. R. Soltani

Inference on periodograms of infinite dimensional discrete time periodically correlated processes

In this work we shall consider two classes of weakly second-order periodically correlated and strongly second-order periodically correlated processes with values in separable Hilbert spaces. The periodogram for these processes is introduced and its statistical properties are studied. In particular, it is proved that the periodogram is asymptotically unbiased for the spectral density of the processes, where the type of the convergence is fully specified.

Classes of power semicircle laws that are randomly weighted average distributions

We give an affirmative answer to the conjecture raised in Soltani and Roozegar [On distribution of randomly ordered uniform incremental weighted averages: divided difference approach. Statist Probab Lett. 2012;82(5):1012–1020] that a certain class of power semicircle distributions, parameterized by n, gives the distributions of the average of n independent and identically Arcsine random variables weighted by the cuts of (0,1) by the order statistics of a uniform (0, 1) sample of size n−1, for each n. Then we establish the central limit theorem for this class of distributions. We also use the Demni [On generalized Cauchy–Stieltjes transforms of some beta distributions. Comm Stoch Anal. 2009;3:197–210] results on the connection between the ordinary and generalized Cauchy or Stieltjes transforms, and introduce new classes of randomly weighted average distributions.

Simulation of Real‐Valued Discrete‐Time Periodically Correlated Gaussian Processes with Prescribed Spectral Density Matrices

In this article, we provide a spectral characterization for a real-valued discrete-time periodically correlated process, and then proceed on to establish a simulation procedure to simulate such a Gaussian process for a given spectral density. We also prove that the simulated process, at each time index, converges to the actual process in the mean square. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

Moving Average Representations for Multivariate Stationary Processes

Backward and forward moving average (MA) representations are established for multivariate stationary processes. It is observed that in the multivariate case, in contrast to the univariate case, the backward and forward MA coefficients correspondingly, in general, are different. A method is presented to adopt the known techniques in deriving the backward MA to obtain the forward ones. Copyright 2006 The Authors Journal compilation 2006 Blackwell Publishing Ltd.

A CHARACTERIZATION THEOREM FOR STABLE RANDOM MEASURES

Let (S, ∥ ∥) be a Banach space of jointly symmetric α-stable random variables and let ρ be the ∞-ring of Bore1 sets of finite ν measure, where ν is a regular measure in the real line. In this paper we identify every stable random measure by a vector measure . This leads to a method for identifying spectral domain of a certain class of stable processes including harmonizable processes

Asymptotic distribution for periodograms of infinite dimensional discrete time periodically correlated processes

In this article we shall consider a class of strongly T-periodically correlated processes with values in a separable complex Hilbert space H. The periodograms of these processes and their statistical properties were previously studied by the authors. In this paper we derive the asymptotic distribution of the periodogram, that appears to be a certain Wishart distribution on H^T.

Forward Moving Average Representation in Multivariate MA(1) Processes

Forward-moving average coefficients are in general different from their corresponding backward-moving average coefficients in multivariate stationary time series. There is lack of practical methods to derive forward-moving average coefficients from the backward ones. In this article, we establish a new practical approach for obtaining the forward-moving average coefficients for multivariate moving average processes of order one.

An Alternative Cluster Detection Test in Spatial Scan Statistics

We establish a hypotheses testing procedure equivalent to the Kulldorff (1997) spatial scan hypotheses test for cluster detection, then provide transparent test statistics for cluster detection in a spatial setting. We also specify the limiting distribution of the test statistics. We apply our method to North Carolina sudden infant death syndrome cases; it detects the same primary and secondary clusters as Kulldorff (1997). Simulated data is used to compare the performance of our method with that of Kulldorff and the findings show that our test is more sensitive and accurate in detecting clusters.

Forward Moving Average Representations for MA Processes of Finite Order: Multivariate Stationary and Periodically Correlated

Soltani and Mohammadpour (2006) observed that in general the backward and forward moving average coefficients, correspondingly, for the multivariate stationary processes, unlike the univariate processes, are different. This has stimulated researches concerning derivations of forward moving average coefficients in terms of the backward moving average coefficients. In this article we develop a practical procedure whenever the underlying process is a multivariate moving average (or univariate periodically correlated) process of finite order. Our procedure is based on two key observations: order reduction (Li, 2005) and first-order analysis (Mohammadpour and Soltani, 2010).

Time Domain Interpolation Algorithm for Innovations of Discrete Time Multivariate Stationary Processes

Abstract Time domain calculus of Wiener and Masani together with the von Neumanns alternating projection formula are employed to obtain a time domain algorithm for the best linear interpolator of unrecorded innovations in discrete time multivariate second order stationary processes. From the interpolated innovations of a multivariate discrete-time ARMA process we indicate how to compute interpolated values of the process itself.