Sequential testing with uniformly distributed size

0493022 - NHU-C 2019 RIV DE eng J - Journal Article
Anatolyev, Stanislav - Kosenok, G.
Sequential testing with uniformly distributed size.
Journal of Time Series Econometrics. Roč. 10, č. 2 (2018), s. 1-22. ISSN 2194-6507
Institutional support: Progres-Q24
Keywords : structural stability * sequential tests * CUSUM
OECD category: Applied Economics, Econometrics

Sequential procedures for the testing for structural stability do not provide enough guidance on the shape of boundaries that are used to decide on acceptance or rejection, requiring only that the overall size of the test is asymptotically controlled. We introduce and motivate a reasonable criterion for the shape of boundaries which requires that the test size be uniformly distributed over the testing period. Under this criterion, we numerically construct boundaries for the most popular sequential tests that are characterized by a test statistic behaving asymptotically either as a Wiener process or Brownian bridge. We handle this problem both in the context of retrospecting a historical sample and in the context of monitoring newly arriving data. We tabulate the boundaries by fitting them to certain flexible yet parsimonious functional forms. Interesting patterns emerge in an illustrative application of sequential tests to the Phillips curve model.
Permanent Link: http://hdl.handle.net/11104/0286491