Bayesowskie testowanie modeli GARCH i IGARCH

• Autorzy: Jacek Osiewalski , Mateusz Pipień

Warianty tytułu

Bayesian Testing of GARCH and IGARCH Models

• Języki publikacji: PL

Abstrakty

Artykuł prezentuje bayesowskie podejście do wyboru typu (GARCH lub IGARCH) i rzędu procesu wykorzystanego w modelowaniu zmian cen jednomiesięcznych lokat międzybankowych w okresie od połowy 1995 r. do końca 1997 r. Stosowana metodologia umożliwia czysto probablistyczną i wolną od odwołań do własności asymptotycznych ocenę stopnia adekwatności poszczególnych modeli poprzez ich prawdopodobieństwa a posteriori.

EN

In this paper we review the posterior odds approach to model comparison. We use this Bayesian methodology to test stationary GARCH specifications against IGARCH models as well as to choose the order of the conditional variance equation. We examine daily financial data from the Polish inter-bank market (WIBOR - Warsaw Inter-Bank Offer Rate, one month deposits), from the period: July 1995-December 1997. We consider an AR(1) model with conditionally Normal errors, where the conditional variance follows one of the five competing specifications: GARCH(2,2), IGARCH(2,2), GARCH(1,1), IGARCH(1,1), GARCH(0,0). Under each of four different discrete prior distributions over the five-element model space, the IGARCH specifications receive more than 90% of the posterior probability mass. The banchmark conditionally homosecedastic model, GARCH(0,)), fails to explain the volatility of the series, receiving virtually zero posterior probability. Moreover, we estimate the same conditional variance specifications under the assumption of Student-t errors with unknown degrees of freedom. In all our models, the posterior distributions of the degrees of the freedom parameter are located near the lower bound of the parameter space [3, + ∞), clearly indicating both the conditional and marginal sampling distribution and the complete inadequacy of the usual assumption of normality. The changes of the conditional sampling distribution of shocks has increased the model fit (as measured by the value of the marginal data density) by as much as 1060. (original abstract)

Słowa kluczowe

PL

Wnioskowanie bayesowskie; Model GARCH; Metody ekonometryczne

EN

Bayesian inference; GARCH model; Econometric methodology

• Czasopismo: Przegląd Statystyczny
• Rocznik: 1999
• Tom: 46
• Numer: z. 1
• Strony: 5--23

Twórcy

autor

Jacek Osiewalski

• Akademia Ekonomiczna w Krakowie

autor

Mateusz Pipień

• Akademia Ekonomiczna w Krakowie

Bibliografia

• [1] Bauwens L., Lubrano M., Bayesian inference on GARCH models using the Gibbs sampler, [referat na konferencji:] Simulation Methods in Econometrics, Florencja, grudzień 1996 (maszynopis).
• [2] Berger J.O., Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York 1985.
• [3] Bollerslev T., Generalised Autoregressive Conditional Heteroscedasticity, Journal of Econometrics 31, 1986, 307-327.
• [4] Bollerslev T., Chou R.Y., Kroner K.F., ARCH modelling in finance, Journal of Econometrics 52,1992, 5-59.
• [5] Boüttslev T.,Engle R.F.., Common persistence in conditional variances,Econometńca. 61,1993,167 - 186.
• [6] Engle R.F., Bollerslev T., Modelling the persistence of conditional variances, Econometric Reviews 5, 1986, 1-50.
• [7] Fama E.F., The behaviour of stock marked prices, Journal of Business 38, 1965, 34 - 105.
• [8] Geweke J., Exact predictive densities for linear models with ARCH disturbances, Journal of Econometrics 40, 1989, 63-86.
• [9] Geweke J., Positive economics and the Bayesian comparison of econometric models, maszynopis, University of Minnesota, 1996.
• [10] Greene W.H., Econometric Analysis, Macmillan, New York, 1993.
• [11] Grzesiak S., Konieczny P., Prognozowanie zmieności cen lokat międzybankowych z użyciem modeli GARCH, [w:] Dynamiczne Modele Ekonometryczne, Materiały na V Ogólnopolskie Seminarium Naukowe, Katedra Ekonometrii i Statystyki UMK, Toruń 1997.
• [12] Harvey A., Time Series ModeL·, Harvester Wheatsheaf, New York, 1993.
• [13] Jeffreys H., Theory of Probability, Oxford University Press, London 1961.
• [14] KJeibergen F., Van Dijk H.K., Non-stationarity in GARCH models: A Bayesian analysis, Journal of Applied Econometrics, 8, 1993, S41-S61.
• [15] Mandelbrot B.B., New methods in statistical economics, Journal of Political Economy 71, 1963, 412-440.
• [16] Nelson D.B., Stationarity and persistence in GARCH(1,1) model, Econometric Theory 6, 1990 318-334.
• [17] Nelson D.B., Conditional heteroskedasticity in asset returns: a new approach, Econometrica 59, 1991, 347-370.
• [18] Nelson D.B., Cao C.Q., Inequality constraints in the univariate GARCH model, Journal of Business and Economic Statistics 10, 1992, 221-235.
• [19] O'Hagan A., Bayesian Inference, Edward Arnold, London 1994.
• [20] Osiewalski J., Steel M.F.J., A Bayesian perspective on model selection, maszynopis; opublikowano wj. hiszpańskim: Una perspectiva bayesiana en selecciön de modelos, Cuadernos Economicos 55/3, 1993, 327-351.
• [21] Pipień M., Estymacja modeli GARCH: MNW i podejście bayesowskie. maszynopis opracowania w ramach grantu KBN nr 1-H02B-015-11, Akademia Ekonomiczna, Kraków 1997; Przegląd Statystyczny 45 (1998), w druku.
• [22] Poirier D.J., Bayesian hypothesis testing with consistent priors across modeL·, [w:] Bayesian Statistics 2 (podred. J.?. Bernardo, M.H. DeGroot, D.V. Lindley, A.F.M. Smith),North-Holland, Amsterdam 1985.
• [23] Shepard N., Statistical aspects of ARCH and stochastic volatility, [w:] Likelihood, Time Series and Other Applications, (pod red. D.R. Cox, D.V. Hinkley, O. Barndorf-Nielsen), Chapman & Hall, London 1995.
• [24] Zellner A., An Introduction to Bayesian Inference in Econometrics, J. Wiley, New York 1971.