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Bayesian Analysis of Stochastic Volatility Model and Portfolio Allocation

100%
Pajor A., Cracow University of Economics D. o. E.
Acta Universitatis Lodziensis. Folia Oeconomica
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2005
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vol. 192
EN
In this paper we present the multivariate stochastic volatility model based on the Cholesky decomposition. This model and the Bayesian approach is used to model bivariate daily financial time series and construct an optimal portfolio. We consider the hypothetical portfolios consisted of two currencies that were most important for the Polish economy: the US dollar and the German mark. In the optimization process we used the predictive distributions of future returns and the predictive covariance matrix obtained from the MSV model.
PL
W artykule przedstawiono model zmienności stochastycznej, oparty na dekompozycji Choleskiego. Następnie model SV oraz podejście Bayesowskie zostało wykorzystane do modelowania zmienności dwuwymiarowych finansowych szeregów czasowych oraz budowy optymalnego portfela walutowego. Rozważono hipotetyczny portfel, w skład którego wchodzą złotówkowe kursy dwóch walut: dolara amerykańskiego i marki niemieckiej. W procesie optymalizacji portfela wykorzystano predyktywny rozkład stóp zwrotu oraz predyktywny rozkład macierzy warunkowych kowariancji, uzyskany w rozważanym modelu MSV za pomocą metod Monte Carlo (MCMC).
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On Bayesian inference of reliability parameter in Burr-type XII model based on imprecise data: a survey on fuzzy modelling

75%
Makhdoom I., Pak A.
Statistics in Transition new series
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2024
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vol. 25
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issue 1
125-143
EN
There are always two major sources of uncertainty in measurements related to lifetime surveys: variation among the observations and imprecision of individual observation called fuzziness. The typical statistical analysis is based on variation among the observations and does not consider the imprecision due to individual observation. However, ignoring the imprecision of individual observations may cause losing information and getting misleading results. It is mandatory to analyse such data, to extend the real numbers classically and Bayesian estimation methods to fuzzy numbers. Inference on the Burr-type (BT) XII model, based on precise measurements, is carried out by researchers, yet the problem of estimating parameters, in the presence of fuzzy data, remains unresolved. We are estimating the BT XII distribution parameters and their corresponding reliability when the available data are in the fuzzy numbers. The maximum likelihood estimation (MLE), the Bayesian method and the method of moments are used for estimating parameters. Finally, these estimators are compared via a Monte-Carlo simulation study.
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