ARCH Models and Financial Applications [Paperback]

1 Introduction.- 1.1 The Development of ARCH Models.- 1.2 Book Content.- 2 Linear and Nonlinear Processes.- 2.1 Stochastic Processes.- 2.2 Weak and Strict Stationarity.- 2.3 A Few Examples.- 2.4 Nonlinearities.- 2.4.1 Portmanteau Statistic.- 2.4.2 Some Implications of the White Noise Hypothesis..- 2.5 Exercises.- 3 Univariate ARCH Models.- 3.1 A Heteroscedastic Model of Order One.- 3.1.1 Description of the Model.- 3.1.2 Properties of the Innovation Process ?.- 3.1.3 Properties of the Y Process.- 3.1.4 Distribution of the Error Process.- 3.2 General Properties of ARCH Processes.- 3.2.1 Various Extensions.- 3.2.2 Stationarity of a GARCH(p, q) Process.- 3.2.3 Kurtosis.- 3.2.4 YuleWalker Equations for the Square of a GARCH Process.- 3.3 Exercises.- 4 Estimation and Tests.- 4.1 Pseudo Maximum Likelihood Estimation.- 4.1.1 Generalities.- 4.1.2 The i.i.d. case.- 4.1.3 Regression Model with Heteroscedastic Errors.- 4.1.4 Regression Model with ARCH Errors.- 4.1.5 Application to a GARCH Model.- 4.1.6 Stochastic Variance Model.- 4.2 Two Step Estimation Procedures.- 4.2.1 Description of the Procedures.- 4.2.2 Comparison of the Estimation Methods under Conditional Normality.- 4.2.3 Efficiency Loss Analysis.- 4.3 Forecast Intervals.- 4.4 Homoscedasticity Test.- 4.4.1 Regression Models with Heteroscedastic Errors.- 4.5 The Test Statistic Interpretation.- 4.5.1 Application to Regression Models with ARCH or GARCH Errors.- Appendix 4.1: Matrices I and J.- Appendix 4.2: Derivatives of the Log-Likelihood Function and Information Matrix for a Regression Model with ARCH Errors.- 4.6 Exercises.- 5 Some Applications of Univariate ARCH Models.- 5.1 Leptokurtic Aspects of Financial Series and Aggregation.- 5.1.1 The Normality Assumption.- 5.1.2 The Choice of a Time Unit.- 5.2 ARCH Processes as an Approximation of Continuous Time Processes.- 5.2.1 Stochastic Integrals.- 5.2.2 Stochastic Differential Equations.- 5.2.3 Some Equations and Their Solutions.- 5.2.4 Continuous and Discrete Time.- 5l#…