Skew Generalized Normal Innovations for the AR(p) Process Endorsing Asymmetry

Merwe, Ané van der; Ferreira, Johan; Bekker, Andriëtte; Naderi, Mehrdad

doi:10.3390/sym12081253

Cited by 3 publications

(2 citation statements)

References 17 publications

(28 reference statements)

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“…Overall, the skew two-piece, skew-normal distribution provides a more flexible and accurate model for capturing the specific characteristics of economic time series data [36].…”

Section: Extensions Of the Normal Distribution For Greater Flexibilit...mentioning

confidence: 99%

Expectation and Optimal Allocations in Existential Contests of Finite, Heavy-Tail-Distributed Outcomes

Vince

2023

Mathematics

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Financial time series and other human-driven, non-natural processes are known to exhibit fat-tailed outcome distributions. That is, such processes demonstrate a greater tendency for extreme outcomes than the normal distribution or other natural distributional processes would predict. We examine the mathematical expectation, or simply “expectation”, traditionally the probability-weighted outcome, regarded since the seventeenth century as the mathematical definition of “expectation”. However, when considering the “expectation” of an individual confronted with a finite sequence of outcomes, particularly existential outcomes (e.g., a trader with a limited time to perform or lose his position in a trading operation), we find this individual “expects” the median terminal outcome over those finite trials, with the classical seventeenth-century definition being the asymptotic limit as trials increase. Since such finite-sequence “expectations” often differ in values from the classic one, so do the optimal allocations (e.g., growth-optimal). We examine these for fat-tailed distributions. The focus is on implementation, and the techniques described can be applied to all distributional forms. We make no assertion that the empirical data for any financial time series comports to the generalized hyperbolic distribution (GHD), which we will use as a proxy of any heavy-tailed distribution herein. Rather, we have selected the GHD to highlight the process for determining expectation and other important time-dependent metrics in existential contests, using the GHD as a generic proxy for the specific distributional form an implementor of the presented technique might ascribe to the empirical data.

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“…Overall, the skew two-piece, skew-normal distribution provides a more flexible and accurate model for capturing the specific characteristics of economic time series data [36].…”

Section: Extensions Of the Normal Distribution For Greater Flexibilit...mentioning

confidence: 99%

Expectation and Optimal Allocations in Existential Contests of Finite, Heavy-Tail-Distributed Outcomes

Vince

2023

Mathematics

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“…In the future, it might be worthwhile to consider alternative weight constructions for ω, as well as to further consider the ncLII (6) developed in this paper as a candidate for error structures in the usual autoregressive cases, for example, juxtaposed against results similar to those of [38].…”

Section: Number Of Strikesmentioning

confidence: 99%

An Adapted Discrete Lindley Model Emanating from Negative Binomial Mixtures for Autoregressive Counts

Merwe

Ferreira

2022

Mathematics

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Analysing autoregressive counts over time remains a relevant and evolving matter of interest, where oftentimes the assumption of normality is made for the error terms. In the case when data are discrete, the Poisson model may be assumed for the structure of the error terms. In order to address the equidispersion restriction of the Poisson distribution, various alternative considerations have been investigated in such an integer environment. This paper, inspired by the integer autoregressive process of order 1, incorporates negative binomial shape mixtures via a compound Poisson Lindley model for the error terms. The systematic construction of this model is offered and motivated, and is analysed comparatively against common alternate candidates with a number of simulation and data analyses. This work provides insight into noncentral-type behaviour in both the continuous Lindley model and in the discrete case for meaningful application and consideration in integer autoregressive environments.

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