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Sequential Testing with Uniformly Distributed Size

Author

Listed:
  • Stanislav Anatolyev

    (New Economic School)

  • Grigory Kosenok

    (New Economic School)

Abstract

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 tting them to certain exible but parsimonious functional forms. Interesting patterns emerge in an illustrative application of sequential tests to the Phillips curve model.

Suggested Citation

  • Stanislav Anatolyev & Grigory Kosenok, 2011. "Sequential Testing with Uniformly Distributed Size," Working Papers w0123_April2011, Center for Economic and Financial Research (CEFIR).
    • Handle: RePEc:cfr:cefirw:w0123_april2011
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    Keywords

    Structural stability; sequential tests; CUSUM; retrospection; monitoring; boundaries; asymptotic size;
    All these keywords.

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