Anticipating instability: a similar examination between GARCH ...

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Foreseeing instability: a similar investigation between GARCH Models and Neural Network Models MCs Student: Miruna State Supervisor: Professor Moisa Altar - Bucharest, June 2002 -

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Contents Introduction Models for return arrangement GARCH models Mixture Density Networks Aplication and results Conclusion and further research Selective list of sources Doctoral School of Finance and Banking

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1. Presentation Concepts of hazard and unpredictability Objective: compare the GARCH instability models with neural system based models for modeling restrictive thickness Doctoral School of Finance and Banking

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2. Models for time arrangement returns 2.1 ARCH(p) models Doctoral School of Finance and Banking

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2.2 GARCH (p,q) GARCH(1,1) Doctoral School of Finance and Banking

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GARCH (1,1) it can be composed as an endless ARCH model : The unlimited fluctuation from the GARCH (1,1) Doctoral School of Finance and Banking

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2.3 Mixture Density Networks Venkatamaran (1997), Zangari (1996) - utilized genuine blend densities for computing VaR Lockarek-Junge and Prinzler (1998) - utilized one neural system to display the thickness restrictively Schittenkopf and Dorffner(1998, 1999) - focused on the execution of the of neural system based models to gauge instability Doctoral School of Finance and Banking

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Mixture Densities the irregular variable is drawn from one out of numerous conceivable ordinary disseminations takes into account substantial tails safeguards some helpful qualities of a typical dispersion Doctoral School of Finance and Banking

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Neural Networks have been utilized for medicinal diagnostics, framework control, design acknowledgment, nonlinear relapse, and thickness estimation relates an arrangement of information factors x t t=1,… ,k, to an arrangement of at least one yield factors, y t , t=1,… ,k it is made out of hubs Doctoral School of Finance and Banking

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three basic sorts of non-linearities utilized as a part of ANNs Doctoral School of Finance and Banking

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Multi-Layer Perceptron (MLP) has one shrouded layer The mapping performed by the MLP is given by Doctoral School of Finance and Banking

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Mixture Density Network consolidates a MLP and a blend model the contingent circulation of the information - communicated as a whole of ordinary appropriations Estimation of MDN - by minimizing the negative logarithm of the probability work - by utilizing backpropagation angle descendent calculation Doctoral School of Finance and Banking

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RPROP calculation fractional subsidiary of a weight changes its sign - the upgrade esteem is diminished by an element η - If the subordinate doesn't change its sign - marginally increment the overhaul esteem by the element η + 0< η - <1< η + η + =1.2 η - =0.5 Doctoral School of Finance and Banking

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3. Application and results Data utilized every day shutting estimations of the BET-C from 17.04.1998 to 10.05.2002 Returns computed as takes after: r t = ln(P t/P t-1 ) Two information sets: - a preparation one - a testing one Softwere utilized: Eviews, Matlab Netlab Doctoral School of Finance and Banking

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GARCH Estimation The day by day BET-C returns Histogram of the profits arrangement Doctoral School of Finance and Banking

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Mean condition Doctoral School of Finance and Banking

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ARCH LM test for serial relationship in the residuals from the mean condition Doctoral School of Finance and Banking

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Estimation of GARCH (1,1) Doctoral School of Finance and Banking

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MDN Estimation encourage forward single-concealed layer neural system 4 shrouded units 3 Gaussians m-dimensional info x t-1 ,… ,x t-m 3n dimensional yield : weights, contingent mean, and restrictive change Doctoral School of Finance and Banking

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Evaluation of the models Normalized mean total mistake Normalized mean squared blunder Doctoral School of Finance and Banking

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Hit rate Weighted hit rate Doctoral School of Finance and Banking

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Results Doctoral School of Finance and Banking

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4. Conclusion and further research Recurrent neural systems The structure of the system utilized Trading or supporting methodologies Methodoligies for measuring market chance Doctoral School of Finance and Banking

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5. Specific book index Bartlmae, K. what's more, R.A. Rauscher (2000) – Measuring DAX Market Risk: A Neural Network Volatility Mixture Approach, www.gloriamundi.org/var/bar/bartlmae_rauscher.pdf . Religious administrator, W. (1994) - Mixture Density Network , Technical Report NCRG/94/004,Neural Computing Research Group, Aston University, Birmingham, February . Jordan, M. furthermore, C. Cleric (1996)– Neural Networks , in CDR Handbook of Computer Science, Tucker, A. (ed.), CRC Press, Boca Raton. Locarek-Junge, H. what's more, R. Prinzler (1998) - Estimating Value-at-Risk Using Neural Networks , Application of Machine Learning and Data Mining in Finance, ECML'98 Workshop Notes, Chemnitz. Schittenkopf, C. furthermore, G. Dockner (1999) – Forecasting Time-subordinate Conditional Densities: A Neural Network Approach , Vienna University of Economic Studies and Business Administration, Report Series no.36. (1998) – Volatility Prediction with Mixture Density Networks , Vienna University of Economic Studies and Business Administration, Report Series no.15. Venkatamaran, S. (1997) – Value at hazard for a blend of ordinary conveyances: The utilization of semi Bayesian estimation procedures , Economic Perspectives (Federal Bank of Chicago), pp. 3-13. Zangari, P. (1996)- An enhanced strategy for measuring VaR , in RiskMetrics Monitor 2. Doctoral School of Finance and Banking

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