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Autor
Osiewalski Krzysztof, Osiewalski Jacek (Cracow University of Economics, Poland / Wydział Zarządzania)
Tytuł
Missing observations in daily returns - Bayesian inference within the MSF-SBEKK model
Źródło
Central European Journal of Economic Modelling and Econometrics (CEJEME), 2012, vol. 4, nr 3, s. 169-197, rys., tab., bibliogr. 16 poz.
Słowa kluczowe
Ekonometria bayesowska, Prognozowanie, Rynki finansowe, Rynki towarowe
Bayesian econometric, Forecasting, Financial markets, Commodity markets
Uwagi
summ.; Klasyfikacja JEL: C11, C32, C51, C58
Abstrakt
Often daily prices on different markets are not all observable. The question is whether we should exclude from modelling the days with prices not available on all markets (thus loosing some information and implicitly modifying the time axis) or somehow complete the missing (non-existing) prices. In order to compare the effects of each of two ways of dealing with partly available data, one should consider formal procedures of replacing the unavailable prices by their appropriate predictions. We propose a fully Bayesian approach, which amounts to obtaining the marginal posterior (or predictive) distribution for any particular day in question. This procedure takes into account uncertainty on missing prices and can be used to check validity of informal ways of "completing" the data (e.g. linear interpolation). We use the MSF-SBEKK structure, the simplest among hybrid MSV-MGARCH models, which can parsimoniously describe volatility of a large number of prices or indices. In order to conduct Bayesian inference, the conditional posterior distributions for all unknown quantities are derived and the Gibbs sampler (with Metropolis-Hastings steps) is designed. Our approach is applied to daily prices from six different financial and commodity markets; the data cover the period from December 21, 2005 till September 30, 2011, so the time of the global financial crisis is included. We compare inferences (on individual parameters, conditional correlation coefficients and volatilities), obtained in the cases where unavailable observations are either deleted or forecasted. (original abstract)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka Szkoły Głównej Handlowej w Warszawie
Biblioteka Główna Uniwersytetu Ekonomicznego w Poznaniu
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Bibliografia
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  1. Doman M. and Doman R. (2010), Modelowanie zależności pomiędzy notowaniami giełdowymi o różnych wzorcach (Modelling dependencies between stock quotes of different patterns [in:], Ekonometria i statystyka w procesie modelowania (Econometrics and Statistics in the Process of Modelling), edited by T.Walczak, Główny Urząd Statystyczny (Central Statistical Office), Warszawa.
  2. Jacquier E., Polson N. and Rossi P. (1994), Bayesian analysis of stochastic volatility models [with discussion], Journal of Business & Economic Statistics, vol. 12, s. 371-417.
  3. Kim J. (2005), Parameter Estimation in Stochastic Volatility Models with Missing Data Using Particle Methods and The EM Algorithm. PhD dissertation, University of Pittsburgh.
  4. Kim J. and Stroffer D. (2008), Fitting Stochastic Volatility Models in the Presence of Irregular Sampling Via Particle Methods And The EM Algorithm. Journal of Time Series Analysis Vol. 29, No. 5, p. 811-833.
  5. Osiewalski J. (2009), New Hybrid Models of Multivariate Volatility (a Bayesian Perspective). Przegląd Statystyczny (Statistical Review), vol. 56(1).
  6. Osiewalski J. and Osiewalski K. (2011a), Modele hybrydowe MSV-MGARCH z dwoma procesami ukrytymi (Hybrid MSV-MGARCH models with two latent processes), Zeszyty Naukowe Uniwersytetu Ekonomicznego w Krakowie, seria Finanse, nr 895 (forthcoming)
  7. Osiewalski J. and Osiewalski K. (2011b), Modele hybrydowe MSV-MGARCH z trzema procesami ukrytymi w badaniu zmienności cen na różnych rynkach (Hybrid MSV-MGARCH models with three latent processes in examining price volatility on different markets), Folia Oeconomica Cracoviensia, vol. LII (2011), 71-85.
  8. Osiewalski J. and Pajor A. (2007), Flexibility and Parsimony in Multivariate Financial Modelling: A Hybrid Bivariate DCC-SV Model [in:] Financial Markets: Principles of Modelling, Forecasting and Decision-Making, FindEcon Monograph Series No 3 [eds.] Milo W. and Wdowiński P., Łódź University Press.
  9. Osiewalski J. and Pajor A. (2009), Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility. Central European Journal ofEconomic Modelling and Econometrics vol 1 issue 2, 179-202.
  10. Osiewalski J. and Pajor A. (2010), Bayesian Value-at-Risk for a portfolio: multi-and univariate approaches using MSF-SBEKK models. Central European Journal of Economic Modelling and Econometrics vol 2 issue 4, 253-277.
  11. Pajor A. (2003), Procesy zmienności stochastycznej w bayesowskiej analizie finansowych szeregów czasowych (Stochastic Variance Processes in Bayesian analysis of Financial Time Series), Monografie: Prace Doktorskie Nr 2, Wydawnictwo Akademii Ekonomicznej w Krakowie, Kraków.
  12. Pajor A. (2010), Wielowymiarowe procesy 'wariancji stochastycznej w ekonometrii finansowej. Ujęcie bayesowskie (Multivariate Stochastic Variance Processes in Financial Econometrics. Bayesian approach), Wydawnictwo Uniwersytetu Ekonomicznego w Krakowie, Kraków.
  13. Pajor A. and Osiewalski J. (2012), Bayesian Value-at-Risk and Expected Shortfall for a Large Portfolio (Multi- and Univariate Approaches). Acta Physica Polonica A vol 121 issue 2B, 101-109.
  14. Roesser R. (2009), Natural Gas Price Volatility, California Energy Commission. CEC-200-2009-009-SD.
  15. Tsay R. (2005), Analysis of Financial Time Series, 2nd ed., Wiley.
  16. Yu B. and Mykland P. (1998), Looking at Markov samplers through cusum path plots: a simple diagnostic idea, Statistics and Computing 8, 275-286.
Cytowane przez
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ISSN
2080-0886
Język
eng
URI / DOI
http://dx.doi.org/DOI: 10.24425/cejeme.2012.119282
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