ARCH MODELS
by T. Bollerslev, R. F. Engle, and D. B. Nelson
Northwestern University and N.B.E.R., University of California, San Diego and N.B.E.R., and University of Chicago
and N.B.E.R.
Contents
1. Introduction
1.1. Definitions
1.2. Empirical Regularities of Asset Returns
(i) Thick tails
(ii) Volatility Clustering
(iii) Leverage Effects
(iv) Non-Trading Periods
(v) Forecastable Events
(vi) Volatility and Serial Correlation
(vii) Co-Movements in Volatilities
(viii) Macroeconomic Variables and Volatility
1.3. Examples of Univariate Parametric Models
(i) Generalized ARCH
(ii) Exponential GARCH
(iii) Other Univariate Parameterizations
1.4. ARCH in Mean Models
1.5. Nonparametric and Semiparametric Methods
2. Inference Procedures
2.1. Testing for ARCH
(i) Serial Correlation and Lagrange Multiplier Tests
(ii) BDS tests
2.2. Maximum Likelihood Methods
(i) Estimation
(ii) Testing
2.3. Quasi Maximum Likelihood Methods
2.4. Specification Checks
(i) Lagrange Multiplier Diagnostic Tests
(ii) BDS Specification Tests
3. Stationary and Ergodic Properties
3.1. Strict Stationarity
3.2. Persistence
4. Continuous Time Methods
4.1. ARCH Models as Approximations to Diffusions
4.2. Diffusions as Approximations to ARCH Models
4.3. ARCH Models as Filters and Forecasters
5. Aggregation and Forecasting
5.1. Temporal Aggregation
5.2. Forecast Error Distributions
6. Multivariate Specifications
6.1. Vector ARCH and Diagonal ARCH
6.2. Factor ARCH
6.3. Constant Conditional Correlations
6.4. Bivariate EGARCH
6.5. Stationarity and Co-Persistence
7. Model Selection
8. Alternative Sources of Information About Volatility
9. Empirical Examples
9.1. U.S. Dollar/Deutschemark Exchange Rates
9.2. U.S. Stock Prices
(i) Model Specification
(ii) Persistence of Shocks to Volatility
(iii) Conditional Mean of Returns
(iv) Conditional Distribution of Returns
(v) News Impact Function
10. Conclusion
References
Prepared for The Handbook of Econometrics, Volume 4
114837.pdf
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