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Abstract
In this paper, we investigate detecting single change point under time series regression model with GARCH errors using the cumulative sum of squares of the least squares residuals test and the log-likelihood ratio test. Furthermore we think it is important to calculate confidence interval for an estimated change point, for which we need to know the sampling distribution of the estimated change point. We obtain the sampling distribution to calculate confidence interval using Monte Carlo simulation based on a circular block bootstrap method and verify the performance of the above break point tests by Monte Carlo experiment. Then we detect a change point in the exchange rate of Indonesian Rupiah (IDR) using the above test to detect. The Government of Indonesia officially announced (de jure) to adopt a floating exchange rate regime in August 1997. However, from time to time, Bank Indonesia nevertheless maintains the stability of rupiah value in the market. Since there is no official information regarding on central bank's intervention in the foreign exchange market, therefore detecting a structural change in the time series of the exchange market can be used as an indicator of exchange rate management. Our real data analysis shows that the IDR had been moving with the USD since 2000, but that the direction of the relationship changed in March 2002. This indicates that there was some control over the Rupiah's movement.