A bootstrap method to test for the existence of finite moments

We provide evidence suggesting that the cross-sectional distributions of U.S. consumption and consumption growth obey the power law in both the upper and lower tails, with exponents approximately equal to 4. Consequently, high order moments are unlikely to exist, and the GMM estimation of Euler equations that employ cross-sectional moments may be inconsistent. Through bootstrap studies, we find that the power law appears to generate spurious non-rejection of heterogeneous-agent asset pricing models in explaining the equity premium. Dividing households into age groups, we propose an estimation approach which appears less susceptible to fat tail issues.

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“…Fortunately, there is a simple bootstrap test for testing the existence of moments directly (Fedotenkov, 2013), which we explain briefly.…”

Section: Testing the Existence Of Moments Directlymentioning

confidence: 99%

The Double Power Law in Consumption and Implications for Testing Euler Equations

Toda

Walsh

2015

Journal of Political Economy

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“…Nevertheless, in the literature only few statistical methods exist to verify or disprove the existence of moments, given a specific sample of random variables (see e.g. [20,15,22,10,12,11]) . One of the earlier methods to verify the existence of moments of a distribution was proposed in 1963 by Mandelbrot (see [20] and [8]).…”

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

“…On the other side, if the theoretical moment does not exist, the estimated moment will diverge or behave unstable when the sample size increases. However, this quite intuitive method is rather heuristic and depends highly on the experience of the researcher (see also [10]). Another popular direct way to investigate the existence of moments of a certain distribution is the sample-based estimation of a decay rate α for the corresponding density function proposed by Hill in [15].…”

Section: Statistical Methods To Test the Existence Of Moments Of A Ra...mentioning

confidence: 99%

Subordinated Gaussian Random Fields

Barth,

Merkle

2020

Preprint

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Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal distribution of the constructed random fields, derive a Lévy-Khinchin-type formula and semiexplicit formulas for the covariance function. Further, we study the pointwise stochastic regularity and validate our theoretical findings in various numerical examples.

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“…Following the method of Fedotenkov (2013), the test proposed in this paper is based on the strong law of large numbers, when the first moment does not exist as developed by Derman and Robbins (1955). The advantage of our proposal is that it is incomparably faster -the time gained being proportional to the number of bootstrap subsamples.…”

Section: Introductionmentioning

confidence: 99%

“…A direct bootstrap-based method for testing if the first finite moment exists was developed by Fedotenkov (2013), using the fact that under some general conditions, if the first moment does not exist, the arithmetic mean of the sample diverges to infinity faster than the arithmetic means of the subsamples of a smaller size. Following the method of Fedotenkov (2013), the test proposed in this paper is based on the strong law of large numbers, when the first moment does not exist as developed by Derman and Robbins (1955).…”

Section: Introductionmentioning

confidence: 99%

A Simple Nonparametric Test for the Existence of Finite Moments

Fedotenkov

2012

SSRN Journal

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This paper proposes a simple, fast and direct nonparametric test to verify if a sample is drawn from a distribution with a finite first moment. The method can also be applied to test for the existence of finite moments of another order by taking the sample to the corresponding power. The test is based on the difference in the asymptotic behaviour of the arithmetic mean between cases when the underlying probability function either has or does not have a finite first moment. Test consistency is proved; then, test performance is illustrated with Monte-Carlo simulations and a practical application for the S&P500 index.JEL classification: C12, C14 MSC2010 classification: 62G10, 62G20, 62G32, 65C05

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A bootstrap method to test for the existence of finite moments

Cited by 15 publications

References 10 publications

The Double Power Law in Consumption and Implications for Testing Euler Equations

The Double Power Law in Consumption and Implications for Testing Euler Equations

Subordinated Gaussian Random Fields

A Simple Nonparametric Test for the Existence of Finite Moments

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