3,317 research outputs found
The Mean Variance Mixing GARCH (1,1) model
Here we present a general framework for a GARCH (1,1) type of process with innovations with a probability law of the mean- variance mixing type, therefore we call the process in question the mean variance mixing GARCH \ (1,1) or MVM GARCH\(1,1). One implication is a GARCH\ model with skewed innovations and constant mean dynamics. This is achieved without using a location parameter to compensate for time dependence that affects the mean dynamics. From a probabilistic viewpoint the idea is straightforward. We just construct our stochastic process from the desired behavior of the cumulants. Further we provide explicit expressions for the unconditional second to fourth cumulants for the process in question. In the paper we present a specification of the MVM-GARCH process where the mixing variable is of the inverse Gaussian type. On the basis on this assumption we can formulate a maximum likelihood based approach for estimating the process closely related to the approach used to estimate an ordinary GARCH (1,1). Under the distributional assumption that the mixing random process is an inverse Gaussian i.i.d process the MVM-GARCH process is then estimated on log return data from the Standard and Poor 500 index. An analysis for the conditional skewness and kurtosis implied by the process is also presented in the paperGARCH Skewness Conditional Skewness
War of attrition with implicit time cost
In the game-theoretic model war of attrition, players are subject to an
explicit cost proportional to the duration of contests. We construct a model
where the time cost is not explicitly given, but instead depends implicitly on
the strategies of the whole population. We identify and analyse the underlying
mechanisms responsible for the implicit time cost. Each player participates in
a series of games, where those prepared to wait longer win with higher
certainty but play less frequently. The model is characterised by the ratio of
the winner's score to the loser's score, in a single game. The fitness of a
player is determined by the accumulated score from the games played during a
generation. We derive the stationary distribution of strategies under the
replicator dynamics. When the score ratio is high, we find that the stationary
distribution is unstable, with respect to both evolutionary and dynamical
stability, and the dynamics converge to a limit cycle. When the ratio is low,
the dynamics converge to the stationary distribution. For an intermediate
interval of the ratio, the distribution is dynamically but not evolutionarily
stable. Finally, the implications of our results for previous models based on
the war of attrition are discussed.Comment: Accepted for publication in Journal of Theoretical Biolog
Reconstruction of annular bi-layered media in cylindrical waveguide section
A radial transverse resonance model for two cylindrical concentric layers
with different complex dielectric constants is presented. An inverse problem
with four unknowns - 3 physical material parameters and one dimensional
dielectric layer thickness parameter- is solved by employing TE110 and TE210
modes with different radial field distribution. First a Newton-Raphson
algorithm is used to solve a least square problem with a Lorentzian function
(as resonance model and "measured" data generator). Then found resonance
frequencies and quality factors are used in a second inverse Newton-Raphson
algorithm that solves four transverse resonance equations in order to get four
unknown parameters. The use of TE110 and TE210 models offers one dimensional
radial tomographic capability. An open ended coax quarter-wave resonator is
added to the sensor topology, and the effect on the convergence is
investigated
Approximating the probability distribution of functions of random variables: A new approach
We introduce a new approximation method for the distribution of functions of random variables that are real-valued. The approximation involves moment matching and exploits properties of the class of normal inverse Gaussian distributions. In the paper we we examine the how well the different approximation methods can capture the tail behavior of a function of random variables relative each other. This is obtain done by simulate a number functions of random variables and then investigate the tail behavior for each method. Further we also focus on the regions of unimodality and positive definiteness of the different approximation methods. We show that the new method provides equal or better approximations than Gram-Charlier and Edgeworth expansioApproximation of random variables
Forecasting Realized Volatility Using A Nonnegative Semiparametric Model
This paper introduces a parsimonious and yet flexible nonnegative semiparametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndorff-Nielsen & Shephard (2001) and Nielsen & Shephard (2003) by way of a power transformation. It is semiparametric in the sense that the dependency structure and distributional form of its error component are left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Simulation studies validate the new estimation method and suggest that it works reasonably well in finite samples. The out-of-sample performance of the proposed model is evaluated against a number of standard methods, using data on S&P 500 monthly realized volatilities. The competing models include the exponential smoothing method, a linear AR(1) model, a log-linear AR(1) model, and two long-memory ARFIMA models. Various loss functions are utilized to evaluate the predictive accuracy of the alternative methods. It is found that the new model generally produces highly competitive forecasts.Autoregression, nonlinear/non-Gaussian time series, realized volatility, semiparametric model, volatility forecast
A Lévy process for the GNIG probability law with 2nd order stochastic volatility and applications to option pricing
Here we derive the Lévy characteristic triplet for the GNIG
probability law. This characterizes the corresponding Lévy
process. In addition we derive equivalent martingale measures with
which to price simple put and call options. This is done under two
different equivalent martingale measures. We also present a
multivariate Lévy process where the marginal probability
distribution follows a GNIG Lévy process. The main contribution
is, however, a stochastic process which is characterized by
autocorrelation in moments equal and higher than two, here a
multivariate specification is provided as well. The main tool for
achieving this is to add an integrated Feller square root process to
the dynamics of the second moment in a time-deformed Browninan
motion. Applications to option pricing are also considered, and a
brief discussion is held on the topic of estimation of the suggested
process
Approximating the Probability Distribution of Functions of Random Variables: A New Approach
We introduce a new approximation method for the distribution of functions of random variables that are real-valued. The approximation involves moment matching and exploits properties of the class of normal inverse Gaussian distributions. In the paper we examine the how well the different approximation methods can capture the tail behavior of a function of random variables relative each other. This is done by simulate a number functions of random variables and then investigate the tail behavior for each method. Further we also focus on the regions of unimodality and positive definiteness of the different approximation methods. We show that the new method provides equal or better approximations than Gram-Charlier and Edgeworth expansions. Nous introduisons une nouvelle méthode pour approximer la distribution de variables aléatoires. L'approximation est basée sur la classe de distribution normale inverse gaussienne. On démontre que la nouvelle approximation est meilleure que les expansions Gram-Charlier et Edgeworth.normal inverse Gaussian, Edgeworth expansions, Gram-Charlier, distribution normale inverse gaussienne, expansions d'Edgeworth, Gram-Charlier
Forecasting Realized Volatility Using A Nonnegative Semiparametric Model
This paper introduces a parsimonious and yet flexible nonnegative semiparametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndorff-Nielsen & Shephard (2001) and Nielsen & Shephard (2003) by way of a power transformation. It is semiparametric in the sense that the dependency structure and distributional form of its error component are left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Simulation studies validate the new estimation method and suggest that it works reasonably well in finite samples. The out-of-sample performance of the proposed model is evaluated against a number of standard methods, using data on S&P 500 monthly realized volatilities. The competing models include the exponential smoothing method, a linear AR(1) model, a log-linear AR(1) model, and two long-memory ARFIMA models. Various loss functions are utilized to evaluate the predictive accuracy of the alternative methods. It is found that the new model generally produces highly competitive forecasts.Autoregression, nonlinear/non-Gaussian time series, realized volatility, semiparametric model, volatility forecast.
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