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**Empirical modeling of exchange rate dynamics.**
*(English)*
Zbl 0648.90002

Lecture Notes in Economics and Mathematical Systems, 303. Berlin etc.: Springer-Verlag. 143 p. DM 32.00 (1988).

Structural exchange rate modeling has proven extremely difficult during the recent post 1973 float. One purpose of this monograph is to explore the temporal behaviour of seven major dollar exchange rates using nonstructural time series methods. Optimal model specification techniques are used, including formal unit root tests which allow for trend, and it is found that all of the exchange rates studied evolve as random walks or random walks with drifts. It is shown that all exchange rates display substantial conditional heteroskedasticity.

Chapter 2 develops a reasonable parametrization of this heteroskedasticity. Estimation and hypothesis testing of this ARCH (autoregressive conditional heteroskedasticity) model is treated: successive first-differentiated observations, while uncorrelated, are not independent. The nature of this serial dependence is studied. Conditional and unconditional ARCH moment structures, central limit theorems for temporal aggregation of ARCH processes are studied.

Chapter 3 treats the univariate stochastic structures of seven major weekly dollar spot exchange rates; maximum likelihood estimates of the ARCH model parameters are obtained and used to construct measures of exchange rate volatility.

In chapter 4 the data are aggregated to monthly frequency, and the results of chapter 2 are verified.

Real exchange rates are examined in chapter 5 leading to tests of absolute and relative purchasing power parity (PPP). While absolute PPP is rejected, relative PPP is accepted apart from low-order ARCH effects in the residuals. Finally, the nature and implications of long run versus short run deviations from PPP are considered.

Chapter 2 develops a reasonable parametrization of this heteroskedasticity. Estimation and hypothesis testing of this ARCH (autoregressive conditional heteroskedasticity) model is treated: successive first-differentiated observations, while uncorrelated, are not independent. The nature of this serial dependence is studied. Conditional and unconditional ARCH moment structures, central limit theorems for temporal aggregation of ARCH processes are studied.

Chapter 3 treats the univariate stochastic structures of seven major weekly dollar spot exchange rates; maximum likelihood estimates of the ARCH model parameters are obtained and used to construct measures of exchange rate volatility.

In chapter 4 the data are aggregated to monthly frequency, and the results of chapter 2 are verified.

Real exchange rates are examined in chapter 5 leading to tests of absolute and relative purchasing power parity (PPP). While absolute PPP is rejected, relative PPP is accepted apart from low-order ARCH effects in the residuals. Finally, the nature and implications of long run versus short run deviations from PPP are considered.

Reviewer: W.Bertrand

### MSC:

91B84 | Economic time series analysis |

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |

62P20 | Applications of statistics to economics |

60F05 | Central limit and other weak theorems |

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

62M07 | Non-Markovian processes: hypothesis testing |

60G50 | Sums of independent random variables; random walks |

62M09 | Non-Markovian processes: estimation |