Autocorrelation Functions

Finlay, Richard; Fung, Thomas; Seneta, E.

doi:10.1111/j.1751-5823.2011.00148.x

Cited by 14 publications

(22 citation statements)

References 21 publications

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“…A nice review of several versions of Pólya‐type functions can be found in Finlay et al . (). As Chung () and Finlay et al .…”

Section: Construction Of Stationary Process With Pólya‐type Covariancmentioning

confidence: 97%

“…As Chung () and Finlay et al . () pointed out, the condition

\lim_{x \to \infty} g (x) = 0

in a Pólya‐type function may be substituted by

\lim_{x \to \infty} g (x) = a_{0} ⩾ 0

. Theorem can be modified appropriately to cover this case as well.…”

Section: Construction Of Stationary Process With Pólya‐type Covariancmentioning

confidence: 99%

“…Its marginal distributions may be taken as any infinitely divisible distribution with finite variance, just like those in Finlay et al . (). But, in terms of a second‐order Lévy process and a positive random variable that generates the Pólya‐type function, our construction method is much simpler than that of Finlay et al .…”

Section: Introductionmentioning

confidence: 97%

“…Recently, Finlay et al . () explained the connection between (auto)correlation functions of stationary stochastic processes on the real line and real characteristic functions and gave probabilistic constructions for time series reformulations of Pólya's theorem on characteristic functions, whose constructions allow the marginal distributions of the process to be any infinitely divisible distribution with finite variance. Du and Ma () constructed a class of stationary Gaussian or elliptically contoured vector stochastic processes on

double-struckR

, with Pólya‐type direct and cross‐covariance functions.…”

Section: Introductionmentioning

confidence: 99%

“…But, in terms of a second‐order Lévy process and a positive random variable that generates the Pólya‐type function, our construction method is much simpler than that of Finlay et al . () based on sums of independent and identically distributed random variables.…”

Section: Introductionmentioning

confidence: 99%

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Vector Stochastic Processes with Pólya‐Type Correlation Structure

2016

Int Statistical Rev

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Summary This paper introduces a simple method to construct a stationary process on the real line with a Pólya‐type covariance function and with any infinitely divisible marginal distribution, by randomising the timescale of the increment of a second‐order Lévy process with an appropriate positive random variable. With the construction method extended to the multivariate case, we construct vector stochastic processes with Pólya‐type direct covariance functions and with any specified infinitely divisible marginal distributions. This makes available a new class of non‐Gaussian vector stochastic processes with flexible correlation structure for use in modelling and simulation.

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“…A nice review of several versions of Pólya‐type functions can be found in Finlay et al . (). As Chung () and Finlay et al .…”

Section: Construction Of Stationary Process With Pólya‐type Covariancmentioning

confidence: 97%

“…As Chung () and Finlay et al . () pointed out, the condition