Detecting multiple breaks in time series covariance structure: a non-parametric approach based on the evolutionary spectral density

Abstract

This article estimates the number of breaks and their locations in the covariance structure of a series based on the evolutionary spectral density and uses some standard information criteria. The adopted approach is non-parametric and does not privilege a priori any modelling of the series. One carries out a Monte Carlo analysis and an empirical illustration using the daily return series of exchange rate euro/US dollar to support the relevance of the theory and to produce additional insights. The simulation results are globally adequate and show that the criteria having heavy penalty are more accurate in the selection of the number of breaks. The empirical results indicate that the covariance structure of the return series considerably varies between 30 March 2000 and 6 April 2001. The unconditional volatility appears non-constant over this interval.

Acknowledgements

The authors would like to thank Claude Deniau for some helpful comments and remarks.

Notes

 This condition implies that E(X _t ) = 0.

 For more details on the relations (i) and (ii) and the choice of h and T ′ , the readers are referred to Priestley and Rao (1969).

 This is because the spectral density is independent of time in each interval where the process is stationary.

 Note that θ is the minimal number of observations in each segment (θ ≥ 1, not depending on I). From Bai and Perron (2003), if tests are required, then θ must be set of [εI ] for some arbitrary small positive number ε.

 The same selection as Artis et al. (1992) was adopted.

 The corresponding results are not reported here and are available upon request from the authors.

 These confidence intervals are computed using the asymptotic distribution of the estimated break dates derived in Bai and Perron (1998).

 For more details, the readers are referred to Bai and Perron (2003).