A portmanteau test is a type of

statistical hypothesis test A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...

in which the

null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...

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. Thus, in

applied statistics Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industri ...

, a portmanteau test provides a reasonable way of proceeding as a general check of a model's match to a dataset where there are many different ways in which the model may depart from the underlying data generating process. Use of such tests avoids having to be very specific about the particular type of departure being tested.

Examples

time series analysis In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in m ...

, two well-known versions of a portmanteau test are available for testing for

autocorrelation Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable ...

in the residuals of a model: it tests whether any of a group of

s of the residual

time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...

are different from zero. This test is the

Ljung–Box test The Ljung–Box test (named for Greta M. Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tes ...

, which is an improved version of the Box–Pierce test, having been devised at essentially the same time; a seemingly trivial simplification (omitted in the improved test) was found to have a deleterious effect. This portmanteau test is useful in working with

ARIMA Arima, officially The Royal Chartered Borough of Arima is the easternmost and second largest in area of the three boroughs of Trinidad and Tobago. It is geographically adjacent to Sangre Grande and Arouca at the south central foothills of th ...

models. In the context of

regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...

, including regression analysis with

structures, a portmanteau test has been devised, which allows a general test to be made for the possibility that a range of types nonlinear transformations of combinations of the explanatory variables should have been included in addition to a selected model structure.

References

* Time series statistical tests Regression diagnostics Autocorrelation {{statistics-stub