Portmanteau test
Encyclopedia
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. Thus, in applied statistics, 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.
in the residuals of a model: it tests whether any of a group of autocorrelation
s of the residual time series
are different from zero. This test is the Ljung–Box test,
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
models.
In the context of regression analysis
, including regession analysis with time series
structures, a portmanteau test has been devised which allows a general test to 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.
Null hypothesis
The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position...
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
Statistical power
The power of a statistical test is the probability that the test will reject the null hypothesis when the null hypothesis is actually false . The power is in general a function of the possible distributions, often determined by a parameter, under the alternative hypothesis...
against a wide range of departures from the null hypothesis. Thus, in applied statistics, a portmanteau test provides a reasonable way of proceeding as a general check of a model's
Statistical model
A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but...
match to a dataset where there are many different ways in which the model may depart from the underlying data generating process
Data generating process
The term data generating process is used in statistical and scientific literature to convey a number of different ideas:*the data collection process, being routes and procedures by which data reach a database ;...
. Use of such tests avoids having to be very specific about the particular type of departure being tested.
Examples
In time series analysis, two well-known versions of a portmanteau test are available for testing for autocorrelationAutocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
in the residuals of a model: it tests whether any of a group of autocorrelation
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
s of the residual time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
are different from zero. This test is the Ljung–Box test,
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
The Royal Borough of Arima is the fourth largest town in Trinidad and Tobago. Located east of the capital, Port of Spain, Arima supports the only organised indigenous community in the country, the Santa Rosa Carib Community and is the seat of the Carib Queen...
models.
In the context of regression analysis
Regression analysis
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...
, including regession analysis with time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
structures, a portmanteau test has been devised which allows a general test to 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.