Gamma stochastic volatility models

Abraham, Bovas; Balakrishna, N.; Sivakumar, Ranjini

doi:10.1002/for.982

Cited by 15 publications

(12 citation statements)

References 34 publications

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“…The absolute moments are often useful to detect non‐linearity and are given by

E (| Y_{t} {false|}^{r}) = \frac{{(2 λ)}^{\frac{r}{2}} Γ (\frac{r + 1}{2}) Γ (\frac{r}{2 τ} + θ)}{\sqrt{π} Γ (θ)} .

An important characteristic useful for analysing the tail behaviour of the marginal distribution is the kurtosis of Y t and is given by

κ_{Y} = 3 \frac{Γ (θ) Γ (\frac{2}{τ} + θ)}{Γ {(\frac{1}{τ} + θ)}^{2}} .

Note that the kurtosis is a function of both θ and τ and is independent of λ . Observe that if τ = θ = 1, then κ Y = 6, the kurtosis of Laplace distribution; and if τ = 1, then

κ_{Y} = 3 \frac{θ + 1}{θ} > 3,

a result given in Abraham et al (). It is also noted that when θ = 1,

κ_{Y} = 6 τ \frac{normalΓ ((), \frac{2}{τ})}{normalΓ {((), \frac{1}{τ})}^{2}}

is a monotone decreasing function in τ .…”

Section: Stochastic Volatility Sequence Generated By Gg Par(1) Modelmentioning

confidence: 66%

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Stochastic volatility generated by product autoregressive models

Anvar

Balakrishna

Abraham

2019

Stat

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This paper analyses the stochastic volatility models induced by non‐negative Markov sequences generated by product autoregressive models. In particular, a stationary sequence of generalized gamma random variables is proposed to generate volatilities. The method of combined estimating functions is employed for parameter estimation. Simulation studies and real data analysis are provided to demonstrate the utility of the model.

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“…The absolute moments are often useful to detect non‐linearity and are given by

E (| Y_{t} {false|}^{r}) = \frac{{(2 λ)}^{\frac{r}{2}} Γ (\frac{r + 1}{2}) Γ (\frac{r}{2 τ} + θ)}{\sqrt{π} Γ (θ)} .

An important characteristic useful for analysing the tail behaviour of the marginal distribution is the kurtosis of Y t and is given by

κ_{Y} = 3 \frac{Γ (θ) Γ (\frac{2}{τ} + θ)}{Γ {(\frac{1}{τ} + θ)}^{2}} .

Note that the kurtosis is a function of both θ and τ and is independent of λ . Observe that if τ = θ = 1, then κ Y = 6, the kurtosis of Laplace distribution; and if τ = 1, then

κ_{Y} = 3 \frac{θ + 1}{θ} > 3,

a result given in Abraham et al (). It is also noted that when θ = 1,

κ_{Y} = 6 τ \frac{normalΓ ((), \frac{2}{τ})}{normalΓ {((), \frac{1}{τ})}^{2}}

is a monotone decreasing function in τ .…”

Section: Stochastic Volatility Sequence Generated By Gg Par(1) Modelmentioning

confidence: 66%

“…Note that the kurtosis is a function of both and and is independent of . Observe that if = = 1, then Y = 6, the kurtosis of Laplace distribution; and if = 1, then Y = 3 +1 > 3, a result given in Abraham et al (2006). It is also noted that when…”

Section: Propertiesmentioning

confidence: 99%

Stochastic volatility generated by product autoregressive models

Anvar

Balakrishna

Abraham

2019

Stat

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“…with parameter l; ExðlÞ; and P½I t ¼ 0 ¼ 1 À P½I t ¼ 1 ¼ r: Then fy t g defines a stationary Markov sequence with exponential marginals. It has been used to model stochastic volatility in finance E. DE ALBA [30]. The starting value to generate the series was y 0 ¼ 5 and 100 values were generated.…”

Section: Applicationmentioning

confidence: 99%

The Bayesian method of moments (BMOM) in some aggregation problems in econometrics

Alba

2006

Appl Stoch Models Bus & Ind

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The BMOM is particularly useful for obtaining post-data moments and densities for parameters and future observations when the form of the likelihood function is unknown and thus a traditional Bayesian approach cannot be used. Also, even when the form of the likelihood is assumed known, in time series problems it is sometimes difficult to formulate an appropriate prior density. Here, we show how the BMOM approach can be used in two, nontraditional problems. The first one is conditional forecasting in regression and time series autoregressive models. Specifically, it is shown that when forecasting disaggregated data (say quarterly data) and given aggregate constraints (say in terms of annual data) it is possible to apply a Bayesian approach to derive conditional forecasts in the multiple regression model. The types of constraints (conditioning) usually considered are that the sum, or the average, of the forecasts equals a given value. This kind of condition can be applied to forecasting quarterly values whose sum must be equal to a given annual value. Analogous results are obtained for AR(p) models. The second problem we analyse is the issue of aggregation and disaggregation of data in relation to predictive precision and modelling. Predictive densities are derived for future aggregate values by means of the BMOM based on a model for disaggregated data. They are then compared with those derived based on aggregated data.

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“…In addition, the SV models are extended by assuming a mixture of two normal distributions (Asai [8]) and scale mixtures of normal distributions (Andrews and Mallows [6]; Lange and Sinsheimer [24]; Meyer and Yu [28]; Fernández and Steel [20]; Chow and Chan [16]; Asai [7]; Abanto-Valle et al [1]). Watanabe [40] and Cappuccio [14] employed the GED distribution in the SV model, meanwhile Abraham [2] considered Gamma SV model to explain the heavy tails behavior.…”

Section: Introductionmentioning

confidence: 99%