Bilateral Bootstrap Tests for Long Memory: An Application to the Silver Market

Many time series in diverse fields of application may exhibit long-memory.The class of fractionally integrated (FI) processes can be used to try to model this strong data dependence. Asymptotic tests for FI include the re-scaled range statistic test and its modified form, the frequency-domain regression-based procedure, the modified Higuchi's test and Jensen's test. De Peretti and Marimoutou (2002) finds that proper finite-sample inferences are not possible using these techniques without correcting for size distortions. Some attempt this correction through `bootstrapping', but this method is not perfect and needs more study and improvements. In this paper, I examine and compare the finite-sample properties of parametric andnonparametric bootstrap tests by using graphical techniques of Davidson and MacKinnon (1998a) for showing whether they properly correct the distortions while retaining their power relative to the corresponding asymptotic tests.One of the tests uses a double bootstrap that provide better true power and size properties. I use a bilateral P value that permits the true power of the tests to grow when the size distortions are asymmetric. We then apply these procedures to a realtime series to investigate its long memory properties.