ECM Algorithm for Auto-Regressive Multivariate Skewed Variance Gamma Model with Unbounded Density

Nitithumbundit, Thanakorn; Chan, Jennifer

doi:10.1007/s11009-019-09762-0

Cited by 12 publications

(11 citation statements)

References 24 publications

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“…The statistical density is observed to be symmetric with some kurtosis [7]. Several studies were performed in the past using the VG process [8][9][10][11][12][13][14][15], but the practicability of VG in modelling system degradation has never been explored in the past.…”

Section: Introductionmentioning

confidence: 99%

Prognostic and Classification of Dynamic Degradation in a Mechanical System Using Variance Gamma Process

2021

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Recently, maintaining a complex mechanical system at the appropriate times is considered a significant task for reliability engineers and researchers. Moreover, the development of advanced mechanical systems and the dynamics of the operating environments raises the complexity of a system’s degradation behaviour. In this aspect, an efficient maintenance policy is of great importance, and a better modelling of the operating system’s degradation is essential. In this study, the non-monotonic degradation of a centrifugal pump system operating in the dynamic environment is considered and modelled using variance gamma stochastic process. The covariates are introduced to present the dynamic environmental effects and are modelled using a finite state Markov chain. The degradation of the system in the presence of covariates is modelled and prognostic results are analysed. Two machine learning algorithms k-nearest-neighbour (KNN) and neural network (NN) are applied to identify the various characteristics of degradation and the environmental conditions. A predefined degradation threshold is assigned and used to propose a prognostic result for each classification state. It was observed that this methodology shows promising prognostic results.

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Section: Introductionmentioning

confidence: 99%

Prognostic and Classification of Dynamic Degradation in a Mechanical System Using Variance Gamma Process

2021

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“…Luciano et al [24] and Wallmeier and Diethelm [44] confirm the use of the variance-gamma distribution for the modeling of the US and the Swiss stock markets, respectively. Groups of various financial indices are modeled by the multivariate variance-gamma distribution in Nitithumbundit and Chan [34].…”

Section: Introductionmentioning

confidence: 99%

The Downside and Upside Beta Valuation in the Variance-Gamma Model

Иванов

2021

ijaa

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The paper is aimed to assess the risks and gains of investment portfolio which relate to the impact of a particular asset. We consider the investment portfolios which consist of assets with variancegamma, gamma distributed and deterministic returns. The returns are assumed to be dependent. We derive analytical formulas for the downside and upside betas in the discussed framework. The established formulas depend on the values of a number of special mathematical functions including the values of the generalized hypergeometric ones.

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“…Others attempt to derive algorithms for estimating the parameters of MSVG distribution with unbounded density. Nitithumbundit & Chan (2020) established an ECM algorithm framework to estimate parameters for the MSVG distribution and demonstrated the efficiency of the proposed ECM algorithm over some other algorithms and the R package ghyp for both cases of bounded and unbounded densities. If the density is unbounded, they proposed capping the density within a small interval of the location parameter.…”

Section: Introductionmentioning

confidence: 99%

“…However, they did not provide any applicable procedures for the implementation of the EM algorithm. Although Nitithumbundit & Chan (2020) provided the procedures and techniques that deal with many technical issues, these techniques do not solve the problems encountered in maximising the LOO likelihood.…”

Section: Introductionmentioning

confidence: 99%

ECM algorithm for estimating vector ARMA model with variance gamma distribution and possible unbounded density

Nitithumbundit

Chan

2021

Aus NZ J of Statistics

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The simultaneous analysis of several financial time series is salient in portfolio setting and risk management. This paper proposes a novel alternating expectation conditional maximisation (AECM) algorithm to estimate the vector autoregressive moving average (VARMA) model with variance gamma (VG) error distribution in the multivariate skewed setting. We explain why the VARMA-VG model is suitable for high-frequency returns (HFRs) because VG distribution provides thick tails to capture the high kurtosis in the data and unbounded central density further captures the majority of near-zero HFRs. The distribution can also be expressed in normal-mean-variance mixtures to facilitate model implementation using the Bayesian or expectation maximisation (EM) approach. We adopt the EM approach to avoid the time-consuming Markov chain Monto Carlo sampling and solve the unbounded density problem in the classical maximum likelihood estimation. We conduct extensive simulation studies to evaluate the accuracy of the proposed AECM estimator and apply the models to analyse the dependency between two HFR series from the time zones that only differ by one hour.

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ECM Algorithm for Auto-Regressive Multivariate Skewed Variance Gamma Model with Unbounded Density

Cited by 12 publications

References 24 publications

Prognostic and Classification of Dynamic Degradation in a Mechanical System Using Variance Gamma Process

Prognostic and Classification of Dynamic Degradation in a Mechanical System Using Variance Gamma Process

The Downside and Upside Beta Valuation in the Variance-Gamma Model

ECM algorithm for estimating vector ARMA model with variance gamma distribution and possible unbounded density

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