Positively Correlated Normal Variables are Associated

Pitt, Loren D.

doi:10.1214/aop/1176993872

Cited by 189 publications

(108 citation statements)

References 3 publications

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“…The concept of associated random variables (Esary, Proschan, and Walkup 1967) extends the concept of nonnegative correlation in a manner that can be extended to the multivariate setting. In particular, jointly normal random variables are associated if and only if they are nonnegatively correlated (Pitt 1982), and increasing functions of associated random variables are associated; thus Example 3a is a special case of Example 3b.…”

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confidence: 99%

What Is the Expected Return on the Market?

Martin

2016

SSRN Journal

194

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I derive a lower bound on the equity premium in terms of a volatility index, SVIX, that can be calculated from index option prices. The bound implies that the equity premium is extremely volatile and that it rose above 20% at the height of the crisis in 2008. The time-series average of the lower bound is about 5%, suggesting that the bound may be approximately tight. I run predictive regressions and find that this hypothesis is not rejected by the data, so I use the SVIX index as a proxy for the equity premium and argue that the high equity premia available at times of stress largely reflect high expected returns over the very short run. I also provide a measure of the probability of a market crash, and introduce simple variance swaps, tradable contracts based on SVIX that are robust alternatives to variance swaps. JEL Codes: E44, G1.

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confidence: 99%

What Is the Expected Return on the Market?

Martin

2016

SSRN Journal

194

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“…As immediate other examples of associated sequences, we may cite Gaussian random vectors with nonnegatively correlated components (see Pitt, 1982) and homogenuous Markov chains (Daley, 1968).…”

Section: A Brief Reminder Of Associationmentioning

confidence: 99%

A Review on asymptotic normality of sums of associated random variables

Lo¹,

Sangaré²,

Ndiaye³

2016

jas

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Abstract. Association between random variables is a generalization of independence of these random variables. This concept is more and more commonly used in current trends in any research fields in Statistics. In this paper, we proceed to a simple, clear and rigorous introduction to it. We will present the fundamental asymptotic normality theorem on stationary and associated sequences of random variables. A coherent and modern frame is used. This review will be profitable to new resarchers in the topic.Résumé. Le concept de variables aléatoires associées est une généralisation de l'indépendance entre variables aléatoires. Il devient de plus en plus important dans les probabilités et les applications statistiques de tous les jours. Dans ce papier, nous introduisonsà ce concept et présentons le théorème fondamental de la normalité asymptotique de sommes partielles d'une suite stationnaire de variables aléatoires associées. Nous utilisons un cadre moderne et cohérent qui sera profitable aux chercheurs débutants dans ce domaine.

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“…Furthermore, positive association seems to be a natural assumption to model certain clinical trials as those described in Ying and Wei (1994). It is also known, see Pitt (1982), that Gaussian processes are positively associated, if and only if, their covariance function is positive. We note that an important property of associated random variables is that non correlation implies independence; the only alternative frame for this to hold is the Gaussian one.…”

Section: Definitionmentioning

confidence: 99%