A new autoregressive time series model in exponential variables (NEAR(1))

Lawrance, A. J.; Lewis, Peter

doi:10.1017/s0001867800036533

Cited by 56 publications

(73 citation statements)

References 6 publications

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“…This problem, in different guises, appears in numerous fields: physics [16], engineering [11], ecology [4], and finance [12], to name just a few. Due to its applicability in the generation of synthetic optimization problems, it has also received special attention by the simulation community [9], [8].…”

Section: Introductionmentioning

confidence: 99%

Multivariate Distributions with Fixed Marginals and Correlations

Huber

Maric

2015

J. Appl. Probab.

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Consider the problem of drawing random variates (X 1 , . . . , X n ) from a distribution where the marginal of each X i is specified, as well as the correlation between every pair X i and X j . For given marginals, the Fréchet-Hoeffding bounds put a lower and upper bound on the correlation between X i and X j . Any achievable correlation between X i and X j is a convex combinations of these bounds. The value λ(X i , X j ) ∈ [0, 1] of this convex combination is called here the convexity parameter of (X i , X j ), with λ(X i , X j ) = 1 corresponding to the upper bound and maximal correlation. For given marginal distributions functions F 1 , . . . , F n of (X 1 , . . . , X n ) we show that λ(X i , X j ) = λ ij if and only if there exist symmetric Bernoulli random variables (B 1 , . . . , B n ) (that is {0, 1} random variables with mean 1/2) such that λ(B i , B j ) = λ ij . In addition, we characterize completely the set of convexity parameters for symmetric Bernoulli marginals in two, three and four dimensions.

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Section: Introductionmentioning

confidence: 99%

Multivariate Distributions with Fixed Marginals and Correlations

Huber

Maric

2015

J. Appl. Probab.

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“…Two approaches will be discussed rather briefly. One allows 3 in the randomly linear combination of E-, and E 2 to be replaced by 3-i for X-, and 3 2 for Xp , while in Section 6 a two parameter randomlylinear operation is used: this stems from the NEAR(l) model of Lawrance [1980], Lawrance and Lewis [1981].…”

Section: Nps55-82-011mentioning

confidence: 99%

“…The NEAR(l) exponential time series models of Lawrance and Lewis [1981] suggests a class of four-parameter models; these are likely to be over- For a model of maximum positive dependency the appropriate joint distributions of (V-,,V ? ) and (I-,,I 2 ) could be obtained using constructions as at (4.4).…”

Section: More General Four Parameter Models: Ep+ Ep-modelsmentioning

confidence: 99%

Simple Dependent Pairs of Exponential and Uniform Random Variables

Lawrance

Lewis

1983

Operations Research

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The accurate characterization of input processes for simulation models can require the representation of dependencies among input values. Results are presented on the generation of dependent exponential and uniform pairs of random variates. A random-coefficient linear function of two independent exponential variables yielding a third exponential variable is used in the construction of simple, dependent pairs of exponential variables. To model negative dependency, the constructions employ antithetic exponential variables. By employing negative exponentiation, the constructions yield simple multiplicative-based models for dependent uniform pairs. The ranges of dependency allowable in the models are assessed by correlation calculations, both of the product moment and Spearman types. Broad ranges within the theoretically allowable ranges are found. Because of their simplicity, all models are particularly suitable for simulation and are free of point and line concentrations of probabilities.

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“…Such algorithms are encountered in a variety of fields, for example: statistics and applied probability [8][9][10][11], finance [12], environmental science [13], physics [14], engineering [15], and ecology where "demographic" or "weather" stochasticity is an increasingly more relevant component of species dynamics [16]. Much of the development of these algorithms has so far relied on coupling ideasor antithetic coupling for negatively-correlated variables [17] -and copula-based methods [18,19].…”

Section: Introductionmentioning

confidence: 99%

Minimum correlation in construction of multivariate distributions

Dukić

Maric

2013

Phys. Rev. E

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In this paper we present an algorithm for exact generation of multivariate samples with prespecified marginal distributions and a given correlation matrix, based on a mixture of Fréchet-Hoeffding bounds and marginal products. The algorithm can accommodate any among the theoretically possible correlation coefficients, and explicitly provides a connection between simulation and the minimum correlation attainable for different distribution families. We calculate the minimum correlations in several common distributional examples, including in some that have not been looked at before. As an illustration, we provide the details and results of implementing the algorithm for generating three-dimensional negatively and positively correlated Beta random variables, making it the only non-copula algorithm for correlated Beta simulation in dimensions greater than two. This work has potential for impact in a variety of fields where simulation of multivariate stochastic components is desired.

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A new autoregressive time series model in exponential variables (NEAR(1))

Cited by 56 publications

References 6 publications

Multivariate Distributions with Fixed Marginals and Correlations

Multivariate Distributions with Fixed Marginals and Correlations

Simple Dependent Pairs of Exponential and Uniform Random Variables

Minimum correlation in construction of multivariate distributions

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