Robust Estimation in VaR Modelling - Univariate Approaches using Bounded Innovation Propagation and Regression Quantiles Methodology

• Autorzy: Ewa Ratuszny
• Języki publikacji: EN

Abstrakty

EN

In the paper we present robust estimation methods based on bounded innovation propagation filters and quantile regression, applied to measure Value at Risk. To illustrate advantage connected with the robust methods, we compare VaR forecasts of several group of instruments in the period of high uncertainty on the financial markets with the ones modelled using traditional quasi-likelihood estimation. For comparative purpose we use three groups of tests i.e. based on Bernoulli trial models, on decision making aspect, and on the expected shortfall. (original abstract)

Słowa kluczowe

EN

GARCH model; VaR method; Estimation methods; Quantile regression

PL

Model GARCH; Miernik ryzyka (VaR); Metody estymacji; Regresja kwantylowa

• Czasopismo: Central European Journal of Economic Modelling and Econometrics (CEJEME)
• Rocznik: 2013
• Tom: 5
• Numer: nr 1
• Strony: 35--63

Twórcy

autor

Ewa Ratuszny

• Warsaw School of Economics, Poland

Bibliografia

• Andersen T.G., Bollerslev T. (1988) Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts, International Economic Review 39, 885-905.
• Bianco A. M., Garcia Ben M., Yohai V. J. (2005) Robust Estimation for Linear Regression with Asymmetric Errors, Canadian Journal of Statistics 33, 511-528.
• Bollerslev T. (1986) Generalized Autoregressive Conditional Heteroskedasticy, Journal of Econometrics 31, 307-327.
• Bollerslev T., Engle R. (1986) Modeling the Persistence of Conditional Variances, Econometric Reviews 5, 1-50.
• Bollerslev T., Wooldridge J. (1992) Quasi-Maximum Likelihood Estimation Inference in Dynamic Models with Time-Varying Covariances, Econometric Theory 11, 143- 172.
• Boudt K., Danielsson J., Laurent S. (2013) Robust Forecasting of Dynamic Conditional Correlation GARCH Models, International Journal of Forecasting 29, 244-257.
• Christoffersen P. (1998) Evaluating Interval Forecasts, International Economics Review 39, 841-862.
• Doman M., Doman R. (2004) Ekonometryczne modelowanie dynamiki polskiego rynku finansowego, Wydawnictwo Akademii Ekonomicznej w Poznaniu, Poznań.
• Doman M. (2005) Modeling Value at Risk with CAViaR Models. The Case of Polish Financial Markets, Acta Universitatis Lodziensis, Folia Oeconomica 190, 129-143.
• Engle R.F., Manganelli S. (2004) CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles, Journal of Business and Economic Statistics 22, 367-381.
• Fox A.J. (1972) Outliers in Time Series, Journal of the Royal Statistical Society B 34, 350-363.
• Frances P., Ghijsels H. (1999) Additive Outliers, GARCH and Forecasting Volatilities, International Journal of Forecasting 15, 1-9
• Glosten L. R., Jagannathan R., Runkle D. (1993) Relationship between Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance 48, 1779-1801.
• Hamilton J.D. (1994) Time Series Analysis, Princeton University Press.
• Huber P.J. (1973) Robust Regression, Asymptotics, Conjectures and Monte Carlo, Annals of Statistics 1, 815-821.
• Jorion P. (1995) Predicting Volatility in Foreign Exchange Market, Journal of Forecasting 50, 507-528.
• Kaszuba B. (2008) Odporne metody estymacji współczynnika beta na przykładzie polskiego rynku akcji, [in:] Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu 18, Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu, Wrocław, 38-48.
• Koenker R., Bassett G.S. (1978) Regression Quantiles, Econometrica 46, 33-50.
• Kupiec P. (1995) Techniques for Verifying the Accuracy of Risk Measurement Models, Journal of Derivatives 3, 73-84.
• Laurent S., Lecourt C., Palm F. (2011) Testing for Jumps in GARCH Models, a Robust Approach, Working paper, School of Business and Economics, Maastricht University, The Netherlands.
• Ledorter J. (1989) The Effect of Aditive Outliers on the Forecasts from ARIMA Models, International Journal of Forecasting 5, 231-240.
• Lopez J.A. (1998) Testing your Risk test, The Financial Survey May-June, 18-20.
• Lopez J.A. (1999) Methods for Evaluating Value at Risk Estimates, Federal Reserve Bank of San Francisco Economic Review 2, 3-15.
• Lumsdaine R.L., Ng S. (1999) Testing for ARCH in the Presence of a Possibly Mis- specified Conditional Mean, Journal of Econometrics 93, 257-279.
• Majewska J. (2008) Odporna optymalizacja portfela inwestycyjnego na przykładzie polskiego rynku kapitałowego, [in:] Modelowanie preferencji a ryzyko'07, [ed.:] T. Trzaskalik, Wydawnictwo Akademii Ekonomicznej w Katowicach, Katowice.
• Martin R. D., Yohai V. (1996) Highly Robust Estimation of Autoregressive Integrated Time Series Models, Publicaciones Previas No. 89, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires.
• Martin R.D., Samarov A., Vandaele W. (1983) Robust Methods for ARIMA Models, [in:] Applied Time Series Analysis of Economic Data, [ed.:] E. Zellner, Washington Bureau of the Census, Washington, 153-177
• Mazur B., Pipień M. (2012) On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process, Central European Journal of Economic Modelling and Econometrics 4, 95-116.
• Muler N., Yohai V.J. (2008) Robust Estimates for GARCH Models, Journal of Statistical Planning and Inference 138, 2918-2940.
• Muler N., Pena D., Yohai V.J. (2009) Robust Estimation for ARMA Models, The Annals of Statistics 37, 816-840.
• Nelson D. (1991) Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica 59, 347-70.
• Orwat A. (2007) Wielowymiarowe metody odporne w estymacji ryzyka portfela aktywów długoterminowych na polskim rynku kapitałowym, [in:] Modelowanie preferencji a ryzyko'06, [ed.:] T. Trzaskalik, Wydawnictwo Akademii Ekonomicznej w Katowicach, Katowice.
• Osiewalski J., 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 2, 253-277.
• Park B.J. (2002) An Outlier Robust GARCH Model and Forecasting Volatility of Exchange Rate Returns, Journal of Forecasting 21, 381-393.
• Pipień M. (2006) Wnioskowanie Bayesowskie w Ekonometrii finansowej, (eng. Bayesian Inference in Financial Econometrics ), Wydawnictwo Akademii Ekonomicznej w Krakowie, Kraków.
• Sarma M., Thomas S., Shah A. (2003) Selecting of VaR Models, Journal of Forectasing 22, 337-358.
• Trzpiot G. (2008) Implementacja metodologii regresji kwantylowej w estymacji VaR, [in:] Rynek kapitałowy - skuteczne inwestowanie, [ed.:] W. Tarczyński, Wydawnictwo Uniwersytetu Szczecińskiego, Szczecin.
• Trzpiot G., Majewska J. (2008) Investment Decisions and Portfolios Classifications based on Robust Methods of Estimation, Operations Research and Decissions 1/2008, 83-96.
• Zieliński R., (1983), Robust statistical procedures: a general approach, [in:] Stability problems for stochastic models, [ed.:] Kalashnikov V. V. and Zolotarev V. M., Springer-Verlag, 283-295.

Identyfikatory

DOI

DOI: 10.24425/cejeme.2013.119252