Choosing Type I and Type II Error Rates for Backtesting Tests

Summary

This question asks whether acceptable Type I and Type II error rates can be chosen in advance for backtesting, using an unconditional coverage test as an example. It notes that Type I error is linked to the test’s significance level and raises the possibility of selecting a higher significance level when missing a problem has more serious consequences than raising a false alarm. The underlying topic is statistical test design and the tradeoff between false rejection and failure to detect a violation.

The document asks whether both error probabilities can be quantified to guide a choice of significance level, but it provides no answer or calculation. In practice, the probability of a Type II error depends on the alternative being tested and the test’s power, so it cannot be determined from the significance level alone. The question identifies a relevant decision problem, while leaving unspecified the alternative scenarios, sample size, and consequence weights needed to evaluate a particular test design.

Key ideas

• The significance level sets the Type I error probability under the test’s null assumptions.
• Type II error concerns failing to detect a specified alternative and depends on the test’s power.
• A choice of error rates may reflect the relative consequences of false alarms and missed violations.
• Quantifying the tradeoff requires a defined alternative and relevant test design details.

Tags

# A priori selection of acceptable backtesting errors (type I and II)


# A priori selection of acceptable backtesting errors (type I and II)












Is it possible to a priori select an acceptable values of type I and II errors in backtesting (f.e. in case of the unconditional coverage test)? Type I error is directly connected to the significance level, so manipulating it can lead to the desired outcome. What is more, when type II error has more serious consequences than type I error, a higher significance level should be selected.

Is there a way to quantify this problem? So as to choose a given significance level and at the same time know the probability of commiting those two types of errors?

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