Sequential Testing with Uniformly Distributed Size

35 Pages Posted: 18 Sep 2008

See all articles by Stanislav Anatolyev

Stanislav Anatolyev

New Economic School; CERGE-EI

Grigory Kosenok

New Economic School

Date Written: September 2008


Sequential procedures of 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 a shape of boundaries which requires that the test size be uniformly distributed over the testing period. Under this criterion, we numerically construct boundaries for 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 a context of retrospecting a historical sample and in a context of monitoring newly arriving data. We tabulate the boundaries by fitting them to certain flexible but parsimonious functional forms. Interesting patterns emerge in an illustrative application of sequential tests to the Phillips curve model.

Keywords: Structural stability, sequential tests, CUSUM, retrospection, monitoring, boundaries, asymptotic size

JEL Classification: C12, C22, C44

Suggested Citation

Anatolyev, Stanislav and Kosenok, Grigory, Sequential Testing with Uniformly Distributed Size (September 2008). Available at SSRN: or

Stanislav Anatolyev (Contact Author)

New Economic School ( email )

Skolkovskoe shosse, 45
Moscow, 121353

CERGE-EI ( email )

P.O. Box 882
7 Politickych veznu
Prague 1, 111 21
Czech Republic

Grigory Kosenok

New Economic School ( email )

47 Nakhimovsky Prospekt
Suite 1721
117418 Moscow

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