Abstract
Structural break tests are often applied as a pre-step to ensure the validity of subsequent statistical analyses. Without any a priori knowledge of the type of breaks to expect, eye-balling the data can indicate changes in some parameter, e.g., the mean. This, however, can distort the result of a structural break test for that parameter, because the data themselves suggested the hypothesis. In this paper, we formalize the eye-balling procedure and theoretically derive the implied size distortion of the structural break test. We also show that eye-balling a stretch of historical data for possible changes in a parameter does not invalidate the subsequent procedure that monitors for structural change in new incoming observations. An empirical application to Bitcoin returns shows that taking into account the data-dredging bias, which is incurred by looking at the data, can lead to different test decisions.
Highlights
An empirical application to Bitcoin returns shows that taking into account the data-dredging bias, which is incurred by looking at the data, can lead to different test decisions
Remark 5 The result illustrated in Remark 4 for the different conditional rejection probabilities in structural break testing and monitoring has some analogy with the following example
In general, fresh data is desirable to validly verify a hypothesis, in some applications hypotheses need to be tested on the same data that generated it
Summary
The importance of plotting the data as a first step of a statistical analysis is stressed in numerous textbooks (e.g., Ruppert and Matteson 2015; Brockwell and Davis 2016). The first main aim of this paper is to quantify these size distortions for structural break tests that are applied conditional on large deviations being observed in the data. We show that these size distortions can become so large that a true null is rejected with certainty. This changes when one moves from a structural break context, where all data are available in advance, to a monitoring context, where—after having observed some training data—the data become available ‘as you go’ for sequential tests of parameter stability.
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