ARCH models and financial applications.

*(English)*Zbl 0880.62107
Springer Series in Statistics. New York, NY: Springer. ix, 228 p. (1997).

ARCH (autoregressive conditionally heteroscedastic) models have become increasingly popular in econometrics and in particular in the modelling of financial time series over recent years. This book gives a survey of ARCH modelling with emphasis on theory and financial models. It is aimed at statisticians and econometricians with a strong background in theoretical and empirical finance.

The contents of the book can roughly be split in two halves. The first one is more statistically oriented and includes a detailed theoretical analysis (chapter 3) and applications (chapter 5) of univariate ARCH models, estimation and test procedures (chapter 4) and extensions to multivariate ARCH models (chapter 6). The shorter second half is more finance-oriented and discusses among other things efficient and hedging portfolios (chapter 7) and equilibrium models (chapter 9) with a view to estimating and testing model-derived properties or restrictions.

The book contains an extensive bibliography which is ordered by chapters. An apparent sparseness of more recent references (only \(15\%\) dated after 1990) is slightly surprising; this is even more pronounced in the second (financial) half of the book.

The contents of the book can roughly be split in two halves. The first one is more statistically oriented and includes a detailed theoretical analysis (chapter 3) and applications (chapter 5) of univariate ARCH models, estimation and test procedures (chapter 4) and extensions to multivariate ARCH models (chapter 6). The shorter second half is more finance-oriented and discusses among other things efficient and hedging portfolios (chapter 7) and equilibrium models (chapter 9) with a view to estimating and testing model-derived properties or restrictions.

The book contains an extensive bibliography which is ordered by chapters. An apparent sparseness of more recent references (only \(15\%\) dated after 1990) is slightly surprising; this is even more pronounced in the second (financial) half of the book.

Reviewer: M.Schweizer (Berlin)

##### MSC:

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62P20 | Applications of statistics to economics |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

91G70 | Statistical methods; risk measures |

91B84 | Economic time series analysis |