1,720,976 research outputs found
Maximum Likelihood Estimation of the APARCH model with Skew Distribution for the Innovation Process
No full textA method normally used in empirical financial studies to estimate the parameters of a general autoregressive conditional heteroskedasticity model is the quasi-maximum likelihood, which maximizes the likelihood function assuming conditional normality, also if it can be a false assumption. When it is possible to assume a nonnormal distribution of errors for this kind of models, it has been shown that there is a loss of efficiency of quasi-maximum likelihood estimators in finite samples with respect to maximum likelihood estimators. In this paper we study, with an empirical application to the daily returns of NASDAQ stock market index, the maximum likelihood estimates of the parameters of the asymmetric power ARCH model, a generalization of the general autoregressive conditional heteroskedasticity model, with skew distributions for the innovation process. The distributions considered are the Student-t, the exponential power and the generalized secant hyperbolic distributions, with reparametrization of the densities which adds inverse scale factors in positive and negative orthants in order to take the
skewness into account. For comparison, we have analyzed the daily returns also with the quasi-maximum and the semiparametric maximum likelihood estimation procedures. We have used a quasi-Newton algorithm to optimize the average log-likelihood functions, in which analytical derivatives of the parameters have been obtained by MathStatica, a package of the computer algebra system Mathematica
Estimating distribution functions in Johnson translation system by the starship procedure with simulated annealing
No full textThe computer intensive starship procedure by Owen allows to obtain the best transformation to normality using the global optimization of some measure of non-normality. In this paper, we propose to apply the procedure to estimate a cumulative distribution function in the Johnson translation system by means of the optimization of sampling statistics derived by the minimum distance and non-linear least squares methods. As global optimization method we consider a stochastic optimization method, specifically the simulated annealing, as an alternative to the method proposed by Owen and Li which is based on the Slifker and Shapiro criterion. The application of the starship procedure to a simulated
sample shows that the simulated annealing algorithm inserted in the procedure supplies results better than the results obtained with the Slifker and Shapiro criterion. Moreover the problems of convergence that occur with traditional optimization methods are not present
Estimating distribution functions in Johnson translation system by the Starship Procedure with simulated annealing
No full textThe computer intensive starship procedure byOwenallows to obtain the best transformation to normality using the global optimization of some measure of non-normality. In this paper, we propose to apply the procedure to estimate a cumulative distribution function in the Johnson translation system by means of the optimization of sampling statistics derived by the minimum distance and non-linear least squares methods. As global
optimization method we consider a stochastic optimization method, specifically the simulated annealing, as an alternative to the method proposed by Owen and Li which is based on
the Slifker and Shapiro criterion. The application of the starship procedure to a simulated sample shows that the simulated annealing algorithm inserted in the procedure supplies
results better than the results obtained with the Slifker and Shapiro criterion. Moreover the problems of convergence that occur with traditional optimization methods are not present
Modelling multivariate volatility processes using temporal independent component analysis
No full textForecasting temporal dependence in second order moments of returns is a relevant problem in many contexts of financial econometrics. It is commonly accepted that financial volatilities move together over time across assets and markets. For this reason in the paper we propose an approach based on the analysis of independent temporal components to model the multivariate volatility. We have assumed that the underlying factors or sources of the model are AR-APARCH processes with errors interpreted by the Meixner distribution. An application with two sets of real data shows the use of the model in the analysis of parallel financial series
GSH Dependence Modeling with an Application to Risk Management
No full textThe generalized secant hyperbolic distribution (GSH) can be used to represent financial data with heavy tails as an alternative to the Student-t, because it guarantees the existence of all moments, also with a high kurtosis value. In order to obtain a multivariate extension of the GSH distribution, in this article we present two approaches to model the dependence, the copula approach and independent component analysis. Since the methodologies considered allow to simulate the GSH dependence, we show also the empirical results obtained in the estimation of risk of a financial portfolio by the Monte Carlo method
Aggregation of Dependent Risk Using the Koelher-Symanowski Copula Function
No full textThis study examines the Koehler and Symanovski copula function with specific marginals, such as the skew Student-t, the skew generalized secant hyperbolic, and the skew generalized exponential power distributions, in modelling financial returns and measuring dependent risks. The copula function can be specified by adding interaction terms to the cumulative distribution function for the case of independence. It can also be derived using a particular transformation of independent gamma functions. The advantage of using this distribution relative to others lies in its ability to model complex dependence structures among subsets of marginals, as we show for aggregate dependent risks of some
market indices
GARCH-type Models with Generalized Secant Hyperbolic Innovations
Full text linkGARCH-type models have been analyzed assuming various nongaussian distributions of errors. In general, the asymmetric generalized Student-t random variable seems to be the distribution which better captures the nonnormality features of financial data. However, a drawback of this distribution is represented by the technical dificulties due to the evaluation of moments, especially in the case of fractional degrees of freedom. In the paper we propose to model high frequency
time series returns using GARCH-type models with a generalized secant hyperbolic (GSH) distribution. The main advantage of the GSH distribution over the Student-t distribution is that all
the moments are finite for each value of the shape parameter. The distribution is symmetric with respect to the mean, but we show that it is still possible to obtain the density in a closed form
introducing a skewness parameter according to the method proposed by Fernandez and Steel. We use a Monte Carlo experiment to validate this distribution in the context of GARCH models with maximum likelihood estimates of parameters. Finally, we show an application to log returns of a stock index
Asymptotic and Bootstrap Inference for the Generalized Gini Indices
No full textThe Gini index represents a special case of the generalized Gini indices, which allow to choose a level of inequality aversion and to stress the different proportions of the income distribution. In order to apply these indices to income sampledata, it is necessary to use reliable inferential procedures. In fact, even if often in income studies we have large samples for which the precision of estimates is not of primary interest, it has been noticed that standard errors are very high. Motivated by these reasons, in this paper inferential procedures for generalized Gini indices are studied, specifically for S- and E-Gini indices, defined by means of the asymptotic distribution of their estimators and using bootstrap technique. To do this, the level of coverage of confidence intervals of the indices has been validated using Monte Carlo simulations, assuming as a model for the size distribution of incomes the generalized beta of the second kind, which is very flexible, with the ability to take a wide variety of shapes depending on particular values of its parameters
Asymptotic and bootstrap inference for the generalized Gini indices
No full textThe Gini index represents a special case of the generalized Gini indices, which allow to choose a level of inequality aversion and to stress the different proportions of the income distribution. In order to apply these indices to income sampledata, it is necessary to use reliable inferential procedures. In fact, even if often in income studies we have large samples for which the precision of estimates is not of primary interest, it has been noticed that standard errors are very high. Motivated by these reasons, in this paper inferential procedures for generalized Gini indices are studied, specifically for S- and E-Gini indices, defined by means of the asymptotic distribution of their estimators and using bootstrap technique. To do this, the level of coverage of confidence intervals of the indices has been validated using Monte Carlo simulations, assuming as a model for the size distribution of incomes the generalized beta of the second kind, which is very flexible, with the ability to take a wide variety of shapes depending on particular values of its parameters
Confidence Interval Estimation for Inequality Indices of the Gini Family
No full textIn this paper we present some nonparametric bootstrap methods to construct distribution-free confidence intervals for inequality indices belonging to the Gini family. These methods have a coverage accuracy better than that obtained with the asymptotic distribution of their natural estimators, typically the standard normal. The coverage performances of these methods are evaluated for the index R by Gini with a Monte Carlo experiment on samples simulated from the Dagum income model (Type I), which is usually used to describe the income distribution
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