Stock market indices from several countries are modelled as discretely sampled diffusions whose parameters change at certain times. To estimate these times of parameter changes we employ both a sequential likelihood-ratio test and a non-parametric, spectral algorithm designed specifically for time series with multiple changepoints. Finally, we use point-process techniques to model relationships between changepoints of different financial time series.Suppose for simplicity we have observations of X t at times t ¼ 1; . . . ; n: Our goal will be to detect times at which the parameters y 1 and y 2 change. Intuitively, to decide if there is a change at time k we can maximize the log likelihood on t ¼ 1; . . . ; k À 1 and on t ¼ k; . . . ; n and M. J. LENARDON AND A. AMIRDJANOVA 576 Both the likelihood-based and the spectral-based sliding window methods of changepoint detection provide an entire time series of test statistics. To decide to what extent changes in one STOCK INDICES 577