The asymptotic covariance matrix of the empirical cepstrum is analyzed. We show that for Gaussian processes, cepstral coefficients derived from smoothed periodograms are asymptotically uncorrelated and their variances multiplied by the sample size T tend to unity. For an autoregressive process and its autoregressive cepstrum estimate, somewhat weaker results hold.

For a zero-mean Gaussian process, the covariances of zero crossings can be expressed as the sum of quadrivariate normal orthant probabilities. In this paper, we demonstrate the evaluation of zero crossing covariances using one-dimensional integrals. Furthermore, we provide asymptotics of zero crossing covariances for large time lags and derive bounds and approximations. Based on these results, ...

The Gaussian product inequality is an important conjecture concerning the moments of random vectors. While all attempts to prove in full generality have been unsuccessful date, numerous partial results derived recent decades and we provide here further on problem. Most importantly, establish a strong version for multivariate gamma distributions case nonnegative correlations, thereby extending r...

The multi-variate Gaussian distribution is used to model random processes with distinct pair-wise correlations, such as stock prices that tend to rise and fall together. Multi-variate Gaussian vectors with length n are usually produced by first generating a vector of n independent Gaussian samples, then multiplying with a correlation inducing matrix requiring O(n) multiplications. This paper pr...

A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information–theoretical principles, lies at the center of this framework. The PP is invariant under linear coordinate transformations and applies to multivariate predictions irrespective of assumptions about the probab...

We investigate a privacy-signaling game problem in which sender with privacy concerns observes pair of correlated random vectors are modeled as jointly Gaussian. The aims to hide one these and convey the other whereas objective receiver is accurately estimate both vectors. analyze conflicting objectives theoretic framework quadratic costs where depending on commitment conditions (of sender), we...

In this paper, we propose a new correlation, called stable to measure the dependence between two random vectors. The correlation is well defined without moment condition and zero if only vectors are independent. We also study its other theoretical properties. Based on further robust model-free feature screening procedure for ultrahigh dimensional data establish sure property rank consistency im...

It is proposed to jointly estimate the parameters of nonGaussian autoregressive (AR) processes in a Bayesian context using the Gibbs sampler. Using the Markov chains produced by the sampler an approximation to the vector MAP estimator is implemented. The results reported here used AR(4) models driven by noise sequences where each sample is iid as a two component Gaussian sum mixture. The result...

This work is concerned with nonlinear time series models and, in particular, with nonparametric models for the dynamics of the mean of the time series. We build on the functional-coefficient autoregressive (FAR) model of Chen and Tsay (1993) which is a generalization of the autoregressive (AR) model where the coefficients are varying and are given by functions of the lagged values of the series...

Let X be an n-dimensional random centered Gaussian vector with independent but not identically distributed coordinates and let T be an orthogonal transformation of Rn. We show that the random vector Y = T (X) satisfies E k ∑ j=1 jmin i≤n Xi 2 ≤ CE k ∑ j=1 jmin i≤n Yi 2 for all k ≤ n, where “jmin” denotes the j-th smallest component of the corresponding vector and C > 0 is a universal constant. ...