A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model

Abadir, Karim M.; Lucas, André

doi:10.1016/s0304-4076(03)00155-6

Cited by 6 publications

(3 citation statements)

References 20 publications

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“…Abadir derived in a number of papers in the 1990s (see, e.g. Abadir, 1993b;Abadir and Lucas, 2004). In spite of work by Van Garderen (1999, 2000, the underlying geometry of non-stationary autoregressive models is still not fully characterized.…”

Section: Discussionmentioning

confidence: 99%

Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series

McCrorie

2020

Sankhya B

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This paper considers the representation of odd moments of the distribution of a four-step uniform random walk in even dimensions, which are based on both linear combinations of two constants representable as contiguous very well-poised generalized hypergeometric series and as even moments of the square of the complete elliptic integral of the first kind. Neither constants are currently available in closed form. New symmetries are found in the critical values of the L-series of two underlying cusp forms, providing a sense in which one of the constants has a formal counterpart. The significant roles this constant and its counterpart play in multidisciplinary contexts is described. The results unblock the problem of representing them in terms of lower-order generalized hypergeometric series, offering progress towards identifying their closed forms. The same approach facilitates a canonical characterization of the hypergeometry of the parbelos, adding to the characterizations outlined by Campbell, D'Aurozio and Sondow (2020, The American Mathematical Monthly127(1), 23-32). The paper also connects the econometric problem of characterizing the bias in the canonical autoregressive model under the unit root hypothesis to very well-poised generalized hypergeometric series. The confluence of ideas presented reflects a multidisciplinarity that accords with the approach and philosophy of Prasanta Chandra Mahalanobis.

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Section: Discussionmentioning

confidence: 99%

Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series

McCrorie

2020

Sankhya B

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“…[16] used it in pricing of callable bonds. Also, [17] showed that this function is necessary to represent densities associated with the minimal sufficient functionals of Ornstein-Uhlenbeck processes, and all the related processes satisfying an invariance principle. The reason for the success of confluent hypergeometric function in these applications is that it includes as special cases the incomplete-gamma and the normal distribution functions, in addition to mixtures of the function, which makes certain classes of these functions closed under such operations.…”

Section: Introductionmentioning

confidence: 99%

Calculation of a Class of Confluent Hypergeometric Equation and Analysis of its Roles in Option Pricing Models

Adindu-Dick¹

2023

African Journal of Mathematics and Statistics Studies

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The confluent hypergeometric equation is one of the most important differential equations in physics, chemistry, finance and many more. This work deals with the power series solution of a class of confluent hypergeometric equation with α, a real constant and z, an independent variable. The confluent hypergeometric function of the first kind M(α,α+2,z) is derived together with the second power series solution, M ̃(α,α+2,z). The analysis of the roles of the derived function in option pricing models are given.

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“…First, in the presence of non-Gaussian data -mainly, excess kurtosis -the asymptotic power envelope generally differs from the Gaussian envelope; see e.g. Rothenberg and Stock (1997), Abadir and Lucas (2004) and Jansson (2007). Second, UR tests based on M-estimation, including non-Gaussian quasi maximum likelihood [QML], may benefit from substantial power gains over Gaussian QML inference methods; see Lucas (1995a,b).…”

Section: Introductionmentioning

confidence: 99%

Robust Inference in Autoregressions With Multiple Outliers

Cavaliere

Georgiev

2009

Econom. Theory

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We consider robust methods for estimation and unit root [UR] testing in autoregressions with infrequent outliers whose number, size and location can be random and unknown. We show that in this setting standard inference based on OLS estimation of an augumented Dickey-Fuller [ADF] regression may not be reliable, since (i) clusters of outliers may lead to inconsistent estimation of the autoregressive parameters, and (ii) large outliers induce a jump component in the asymptotic null distribution of UR test statistics. In the benchmark case of known outlier location, we discuss why the augmentation of the ADF regression with appropriate dummy variables not only ensures consistent parameter estimation, but also gives rise to UR tests with significant power gains, growing with the number and the size of the outliers. In the case of unknown outlier location, the dummy based approach is compared with a robust, mixed Gaussian, Quasi Maximum Likelihood [QML] approach, novel in this context. It is proved that, when the ordinary innovations are Gaussian, the QML and the dummy-based approach are asymptotically equivalent, yielding UR tests with the same asymptotic size and power. Moreover, as a by-product of QML the outlier dates can be consistently estimated. When the innovations display tails fatter than Gaussian, the QML approach ensures further power gains over the dummybased method. Simulations show that the QML ADF-type t-test, in conjunction with standard Dickey-Fuller critical values, yields the best combination of finite-sample size and power.

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A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model

Cited by 6 publications

References 20 publications

Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series

Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series

Calculation of a Class of Confluent Hypergeometric Equation and Analysis of its Roles in Option Pricing Models

Robust Inference in Autoregressions With Multiple Outliers

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