Overview

1.1 The DevelopmentofARCH Models Time series models have been initially introduced either for descriptive purposes like prediction and seasonal correction or for dynamic control. In the 1970s, the researchfocusedonaspecificclassoftimeseriesmodels,theso-calledautoregres- sive moving average processes (ARMA), which were very easy to implement. In thesemodels,thecurrentvalueoftheseriesofinterestiswrittenasalinearfunction ofits own laggedvalues andcurrentandpastvaluesofsomenoiseprocess, which can be interpreted as innovations to the system. However, this approach has two major drawbacks: 1) it is essentially a linear setup, which automatically restricts the type of dynamics to be approximated; 2) it is generally applied without im- posing a priori constraintson the autoregressive and moving average parameters, which is inadequatefor structural interpretations. Among the field ofapplications where standard ARMA fit is poorare financial and monetary problems. The financial time series features various forms ofnon- lineardynamics,the crucialone being the strongdependenceofthe instantaneous variabilityoftheseriesonitsownpast. Moreover,financial theoriesbasedoncon- ceptslikeequilibriumorrationalbehavioroftheinvestorswouldnaturallysuggest including and testing some structural constraints on the parameters. In this con- text, ARCH (Autoregressive Conditionally Heteroscedastic) models, introduced by Engle (1982), arise as an appropriate framework for studying these problems. Currently, there existmorethan onehundredpapers and some dozenPh.D. theses on this topic, which reflects the importance ofthis approach for statistical theory, finance and empirical work. 2 1. Introduction From the viewpoint ofstatistical theory, the ARCH models may be considered as some specific nonlinear time series models, which allow for aquite exhaustive studyoftheunderlyingdynamics.Itisthereforepossibletoreexamineanumberof classicalquestions like the random walkhypothesis, prediction intervals building, presenceoflatentvariables [factors] etc., and to test the validity ofthe previously established results.

Full Product Details

Author:   Christian Gourieroux
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1997
Dimensions:   Width: 15.50cm , Height: 1.30cm , Length: 23.50cm
Weight:   0.379kg
ISBN:  

9781461273141

ISBN 10:   1461273145
Pages:   229
Publication Date:   06 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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.- 2.5 Exercises.- 3 Univariate ARCH Models.- 3.1 A Heteroscedastic Model of Order One.- 3.2 General Properties of ARCH Processes.- 3.3 Exercises.- 4 Estimation and Tests.- 4.1 Pseudo Maximum Likelihood Estimation.- 4.2 Two Step Estimation Procedures.- 4.3 Forecast Intervals.- 4.4 Homoscedasticity Test.- 4.5 The Test Statistic Interpretation.- 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.- 5.2 ARCH Processes as an Approximation of Continuous Time Processes.- 5.3 The Random Walk Hypothesis.- 5.4 Threshold Models.- 5.5 Integrated Models.- 5.6 Exercises.- 6 Multivariate ARCH Models.- 6.1 Unconstrained Models.- 6.2 Constrained Models.- 6.3 Estimation of Heteroscedastic Dynamic Models.- 7 Efficient Portfolios and Hedging Portfolios.- 7.1 Determination of an Efficient Portfolio.- 7.2 Properties of the Set of Efficient Portfolios.- 7.3 Asymmetric Information and Aggregation.- 7.4 Hedging Portfolios.- 7.5 Empirical Study of Performance Measures.- Appendix 1: Presentation in Terms of Utility.- Appendix 2: Moments of the Truncated Log-Normal Distribution.- Appendix 3: Asymptotic Properties of the Estimators.- 7.6 Exercises.- 8 Factor Models, Diversification and Efficiency.- 8.1 Factor Models.- 8.2 Arbitrage Theory.- 8.3 Efficiency Tests and Diversification.- 8.5 Exercises.- 9 Equilibrium Models.- 9.1 Capital Asset Pricing Model.- 9.2 Test of theCAPM.- 9.3 Examples of Structural Models.

Reviews

From the reviews: RISKBOOK.COM Gourieroux offers a nice balance of theory and application in this book on ARCH modeling in finance...The book is well written and has extensive references. Its focus on finance will appeal to financial engineers and financial risk managers.

From the reviews: RISKBOOK.COM Gourieroux offers a nice balance of theory and application in this book on ARCH modeling in finance...The book is well written and has extensive references. Its focus on finance will appeal to financial engineers and financial risk managers.

From the reviews: RISKBOOK.COM Gourieroux offers a nice balance of theory and application in this book on ARCH modeling in finance...The book is well written and has extensive references. Its focus on finance will appeal to financial engineers and financial risk managers.

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