# Meaning of a “portmanteau test”?

From Wikipedia

A portmanteau test is a type of statistical hypothesis test in which the null hypothesis is well specified, but the alternative hypothesis is more loosely specified. Tests constructed in this context can have the property of being at least moderately powerful against a wide range of departures from the null hypothesis. ... Use of such tests avoids having to be very specific about the particular type of departure being tested.

Then there are two examples

1. In time series analysis, two well-known versions of a portmanteau test are available for testing for autocorrelation in the residuals of a model: the Box–Pierce test, and the Ljung–Box test.

Are other tests such as the turning point test, the difference sign test, and the rank test, also considered as portmanteau tests?

In Brockwell and Davis' Introduction to Time Series and Forecasting, why are they not written as portmanteau tests, but only the Box–Pierce test, and the Ljung–Box test are?

2. In the context of regression analysis, a portmanteau test has been devised ....

In regression, what are some examples of tests considered as portmanteau tests and not considered as such?

• With regard to 2. Wouldn't an F-test of joint significance be considered a Portmanteau test (according to that definition), since its testing $H_0:$ coefficients are all zero vs $H_A$ all/some coefficients are not zero? – fredrikhs Jul 23 '13 at 7:39
• @fredrikhs: Thanks! With regard to 2, what is an example of non-portmanteau test then? – Tim Jul 23 '13 at 17:50
• It was meant more as an addition to your question, not an answer. Just to see if I got the meaning right. I guess an example of a non-portmanteau test would be the trace test in co-integration analysis, testing $H_0:$ there are $h$ co-integrating vectors vs $H_A:$ there are $n$ co-integrating vectors. There $n$ is specified, hence making it a non-portmanteau, contrary to $H_A:$ there are $\neq n$ co-integrating vectors. See what I mean? – fredrikhs Jul 24 '13 at 13:45

## 1 Answer

As far as I know "portmanteau test" is synonymous with "omnibus test". Either term gets used in two cases:

(1) When the null hypothesis specifies values for a vector of parameters that are thought of as being on an equal footing, & the alternative is that at least one parameter value is different from that specified by the null. So the null for the ANOVA F-test is that all treatment means are zero; for the Ljung-Box test, that all autocorrelations up to a given lag are zero; &c.

(2) When a test has decent power against a wide range of alternative hypotheses: contrasted with a "directional test" with high power against a narrow range of alternatives, but low power against others. This is typically in the context of goodness of fit.

Don't get your hopes up for more exact definitions—after all, it doesn't really matter what you call a test.