Multifractal Models, Intertrade Durations And Return Volatility

Transcription

1 Multifractal Models, Intertrade Durations And Return Volatility Inaugural-Dissertation zur Erlangung des akademischen Grades eines Doktors der Wirtschafts- und Sozialwissenschaften der Wirtschafts- und Sozialwissenschaftlichen Fakultät der Christian-Albrechts-Universität zu Kiel vorgelegt von Dipl. -Kim Mawufi Kouami Segnon aus Kponou, Togo Kiel, June 17, 2015 Christian-Albrechts-Universität zu Kiel, Leibnizstraße 3, Kiel

2 Contents Notation and Abbreviations Acknowledgements Abstract Preface xiv xvii xix xxi 1. Introduction Motivation ] 1.2. Structure of the Thesis 2 1. Review Of Multifractal And Autoregressive Conditional Duration Models 4 2. Multifractal Models In Finance: Their Origin, Properties, and Applications Introduction Stylized Facts of Financial Data Fat Tails Volatility Clustering Benchmark Models: GARCH and Stockastic Volatility A New Stylized Fact: Multifractality Multifractal Measures and Processes Multifractal Measures Multifractal Models Multifractal Models in Discrete Time Shortcomings of MF Models Estimation and Forecasting Maximum Likelihood Estimation Simulated Maximum Likelihood GMM Estimation Forecasting Empirical Applications Conclusion 37 ii

3 3. Financial Duration Models: A Survey Introduction Theoretical Microstructure Models ACD Models 4^ The Standard ACD Model The Logarithmic ACD (Log-ACD) Model 4S The Augmented ACD (AACD) Model Long Memory ACD Models.SO Regime-Switching ACD Models Stochastic Conditional Duration Model Stochastic Volatility Duration Models Markov Switching Multifractal Duration Models Chen/Diebold/Schorfheide Model Baruruk/Shenai/Zikes Model Diagnostic Tests Some Empirical Results 5V 3.7. Conclusion hl II. Forecasting Return Volatility: An Application To Crude Oil Prices Modeling and Forecasting Crude Oil Price Volatility: Evidence from Historical and Recent Data Introduction Data 4.3. Model Framework GARCH-type Models The Markov-Switching Multifractal Model Forecast Evaluation Methodologies Forecasting Evaluation Criteria * Superior Predictive Ability Test ^ 4.5. Empirical Results ^ Estimation Results ls< Forecasting Results w 4.6. Conclusion 86 III. Application Of Multifractal Processes To Modeling Financial Markets Mi-

4 crostructure 108 Assessing Forecast Performance of Financial Duration Models via Density Forecasts and Likelihood Ratio Test Introduction Model Review The ACD Model The Log-ACD Model The Fractionally Integrated ACD Model The Binomial MSMD Model Estimation Methods ML Estimation for ACD Models ML Estimation for the Binomial MSMD Model Density Forecasts Testing Density Forecasts Empirical Application Data Results of Performance Comparison Conclusion 123 Modeling Financial Duration Data Using Alternative Markov Switching Multifractal Duration Models Introduction Alternative Markov Switching Multifractal Duration Models Mixture of Generalized Gamma Distribution The Mixture of Burr Distribution Statistical Properties Moments Long Memoiy Feature Numerical Simulations ML Estimation Small-Sample Properties Model Selection Criteria Empirical Application Raw Data Seasonal Adjustment Comparison of the MSMD Models Conclusion 165

5 7. A Bivariate Markov-Switching Multifractal Duration Model Introduction A Bivariate MSMD Model Statistical Properties of the Model Estimation Approach Empirical Application Data Data Adjustment Results Conclusion Forecasting Intraday Value-at-Risk Using Markov-Switching Multifractal Duration Model Introduction Intraday Volatility Instantaneous Price Changes Volatility Conditional Hazard Functions Irregularly Spaced Intraday VaR GMM Duration-Based Test Approach Orthonormal Polynomials and Moment Conditions Empirical Test Method Empirical Study Data Data Adjustment Results of Backtesting Conclusion 215 IV. General Conclusions And Outlooks General Conclusions and Outlooks General Conclusion Outlooks 228 Appendices 230 A. Supplement to the Thesis 231 A.l. Transformation of Random Variables 231 A.2. Transformation of Random Variables in 2-D case 232 A.3. Uni- and Bivariate Lognormal Distribution Function 232 A.4. The Joint Probability Density Function of the Bivariate MSMD Model 233

6 A.5. The Delta Method 211 A.6. Classical Discrete Orthogonal Polynomials 234 A.7. A Special Case of Meixner Orthonormal Polynomials 236 Affirmation 261