부산대학교 도서관

Summary: ``This paper develops a test for the onset of a time trend,using a wavelet-type estimator. The series level is a nonlinearfunction of time, with a slope that is zero initially, butnon-negative and non-decreasing, or non-positive and non-increasing,beyond the onset point, permitting divergence. The series level isotherwise unspecified, and to estimate it we regress the data serieson wavelet scaling functions of time, with a coefficient restrictionthat makes the fitted level constant until some point in thesample. Since the true onset point is unknown, we examine several suchrestrictions, yielding candidate onset points at equally spacedpositions in the sample. We base our test on some $F$-type statistics,which compare the performance of successive fitted levels. To exploitthe asymmetry of the true level under the alternative, we use aweighted sum of $F$ statistics, with linearly increasing weight atpoints further in the sample. This test statistic has a nonstandarddistribution, which we tabulate. Asymptotically, we show that linearweighting gives better local power than equal weighting. A simulationstudy confirms the power advantage of our test.''