Sequential Testing with Uniformly Distributed Size

Stanislav Anatolyev and Grigory Kosenok

Journal of Time Series Econometrics, 2018, vol. 10, issue 2, 22

Abstract: 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.

Keywords: structural stability; sequential tests; CUSUM; retrospection; monitoring; boundaries; asymptotic size (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Related works:
Working Paper: Sequential Testing with Uniformly Distributed Size (2011)
Working Paper: Sequential Testing with Uniformly Distributed Size (2011)
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DOI: 10.1515/jtse-2017-0002

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