Ratio test for variance change point in linear process with long memory

In this paper we consider the detection problem of variance change point in linear process with long memory. We propose the ratio test to detect the variance change point. The limiting distribution for test statistics under H ₀ is derived and the consistency of the test is also established. In comparison with the existing CUSUM of squares (SCUSUM) test, the ratio test does not need to estimate the long memory parameter in practical situation and therefore it can be used more conveniently.