Variance-Gamma and Normal-Inverse Gaussian models: Goodness-of-fit to Chinese high-frequency index returns

2016 ◽  
Vol 36 ◽  
pp. 279-292 ◽  
Author(s):  
Ahmet Göncü ◽  
Hao Yang
Keyword(s):  
High Frequency ◽  
Goodness Of Fit ◽  
Inverse Gaussian ◽  
Gaussian Models ◽  
Variance Gamma ◽  
Frequency Index ◽  
Normal Inverse Gaussian

scholarly journals Discriminating between the normal inverse Gaussian and generalized hyperbolic skew-t distributions with a follow-up the stock exchange data

2018 ◽  
Vol 28 (2) ◽  
pp. 185-199
Author(s):  
Hanieh Panahi
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Stock Exchange ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Information Criteria ◽  
Inverse Gaussian ◽  
Unknown Parameters ◽  
Normal Inverse Gaussian ◽  
Exchange Data

The statistical methods for the financial returns play a key role in measuring the goodness-of-fit of a given distribution to real data. As is well known, the normal inverse Gaussian (NIG) and generalized hyperbolic skew-t (GHST) distributions have been found to successfully describe the data of the returns from financial market. In this paper, we mainly consider the discrimination between these distributions. It is observed that the maximum likelihood estimators (MLEs) cannot be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators. The approximate confidence intervals of the unknown parameters have been constructed. We then perform a number of goodness-of-fit tests to compare the NIG and GHST distributions for the stock exchange data. Moreover, the Vuong type test, based on the Kullback-Leibler information criteria, has been considered to select the most appropriate candidate model. An important implication of the present study is that the GHST distribution function, in contrast to NIG distribution, may describe more appropriate for the proposed data.

scholarly journals Modeling Baltic market benchmark index: a comparison of models

2019 ◽  
Vol 60 ◽  
pp. 6-10
Author(s):  
Igoris Belovas
Keyword(s):  
Maximum Likelihood Method ◽  
Gaussian Model ◽  
Likelihood Method ◽  
Ratio Test ◽  
Inverse Gaussian ◽  
Gaussian Models ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Student’S T ◽  
Normal Inverse Gaussian

In this paper we perform a statistical analysis of the returns of OMX Baltic Benchmark index. We construct symmetric α-stable, non-standardized Student’s t and normal-inverse Gaussian models of daily logarithmic returns of the index, using maximum likelihood method for the estimation of the parameters of the models. The adequacy of the modeling is evaluated with the Kolmogorov-Smirnov tests for composite hypothesis. The results of the study indicate that the normal-inverse Gaussian model outperforms alternative heavy-tailed models for long periods of time, while the non-standardized Student’s t model provides the best overall fit for the data for shorter intervals. According to the likelihood-ratio test, the four-parameter models of the log-returns of OMX Baltic Benchmark index could be reduced to the three-parameter (symmetric) models without much loss.  

scholarly journals MULTIVARIATE FACTOR-BASED PROCESSES WITH SATO MARGINS

2018 ◽  
Vol 21 (01) ◽  
pp. 1850005
Author(s):  
MARINA MARENA ◽  
ANDREA ROMEO ◽  
PATRIZIA SEMERARO
Keyword(s):  
Derivative Pricing ◽  
Nonlinear Dependence ◽  
Dependence Structure ◽  
Inverse Gaussian ◽  
Marginal Distributions ◽  
Variance Gamma ◽  
Term Structures ◽  
The Impact ◽  
Normal Inverse Gaussian ◽  
Over Time

We introduce a class of multivariate factor-based processes with the dependence structure of Lévy [Formula: see text]-models and Sato marginal distributions. We focus on variance gamma and normal inverse Gaussian marginal specifications for their analytical tractability and fit properties. We explore if Sato models, whose margins incorporate more realistic moments term structures, preserve the correlation flexibility in fitting option data. Since [Formula: see text]-models incorporate nonlinear dependence, we also investigate the impact of Sato margins on nonlinear dependence and its evolution over time. Further, the relevance of nonlinear dependence in multivariate derivative pricing is examined.

A normal inverse Gaussian model for a risky asset with dependence

2012 ◽  
Vol 82 (1) ◽  
pp. 109-115 ◽  
Author(s):  
N.N. Leonenko ◽  
S. Petherick ◽  
A. Sikorskii
Keyword(s):  
Gaussian Model ◽  
Risky Asset ◽  
Inverse Gaussian ◽  
Normal Inverse Gaussian

A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability

2005 ◽  
Vol 288 (1) ◽  
pp. H424-H435 ◽  
Author(s):  
Riccardo Barbieri ◽  
Eric C. Matten ◽  
AbdulRasheed A. Alabi ◽  
Emery N. Brown
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Gaussian Model ◽  
Quantitative Measure ◽  
Local Maximum ◽  
Inverse Gaussian ◽  
Design Of Algorithms

Heart rate is a vital sign, whereas heart rate variability is an important quantitative measure of cardiovascular regulation by the autonomic nervous system. Although the design of algorithms to compute heart rate and assess heart rate variability is an active area of research, none of the approaches considers the natural point-process structure of human heartbeats, and none gives instantaneous estimates of heart rate variability. We model the stochastic structure of heartbeat intervals as a history-dependent inverse Gaussian process and derive from it an explicit probability density that gives new definitions of heart rate and heart rate variability: instantaneous R-R interval and heart rate standard deviations. We estimate the time-varying parameters of the inverse Gaussian model by local maximum likelihood and assess model goodness-of-fit by Kolmogorov-Smirnov tests based on the time-rescaling theorem. We illustrate our new definitions in an analysis of human heartbeat intervals from 10 healthy subjects undergoing a tilt-table experiment. Although several studies have identified deterministic, nonlinear dynamical features in human heartbeat intervals, our analysis shows that a highly accurate description of these series at rest and in extreme physiological conditions may be given by an elementary, physiologically based, stochastic model.

scholarly journals Pricing of basket options using univariate normal inverse Gaussian approximations

2010 ◽  
Vol 30 (3) ◽  
pp. 355-376 ◽  
Author(s):  
Fred Espen Benth ◽  
Pål Nicolai Henriksen
Keyword(s):  
Inverse Gaussian ◽  
Basket Options ◽  
Normal Inverse Gaussian
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