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% File src/library/stats/man/box.test.Rd
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2018 R Core Team
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% Distributed under GPL 2 or later
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\name{Box.test}
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\alias{Box.test}
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\concept{portmanteau}
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\title{Box-Pierce and Ljung-Box Tests}
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\description{
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  Compute the Box--Pierce or Ljung--Box test statistic for examining the
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  null hypothesis of independence in a given time series.  These are
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  sometimes known as \sQuote{portmanteau} tests.
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}
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\usage{
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Box.test(x, lag = 1, type = c("Box-Pierce", "Ljung-Box"), fitdf = 0)
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}
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\arguments{
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  \item{x}{a numeric vector or univariate time series.}
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  \item{lag}{the statistic will be based on \code{lag} autocorrelation
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    coefficients.}
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  \item{type}{test to be performed: partial matching is used.}
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  \item{fitdf}{number of degrees of freedom to be subtracted if \code{x}
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    is a series of residuals.}
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}
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\details{
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  These tests are sometimes applied to the residuals from an
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  \code{ARMA(p, q)} fit, in which case the references suggest a better
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  approximation to the null-hypothesis distribution is obtained by
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  setting \code{fitdf = p+q}, provided of course that \code{lag > fitdf}.
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}
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\note{
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  Missing values are not handled.
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}
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\value{
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  A list with class \code{"htest"} containing the following components:
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  \item{statistic}{the value of the test statistic.}
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  \item{parameter}{the degrees of freedom of the approximate chi-squared
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    distribution of the test statistic (taking \code{fitdf} into account).}
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  \item{p.value}{the p-value of the test.}
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  \item{method}{a character string indicating which type of test was
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    performed.}
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  \item{data.name}{a character string giving the name of the data.}
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}
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\references{
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  Box, G. E. P. and Pierce, D. A. (1970),
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  Distribution of residual correlations in autoregressive-integrated
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  moving average time series models.
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  \emph{Journal of the American Statistical Association}, \bold{65},
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  1509--1526.
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  \doi{10.2307/2284333}.
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  Ljung, G. M. and Box, G. E. P. (1978),
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  On a measure of lack of fit in time series models.
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  \emph{Biometrika}, \bold{65}, 297--303.
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  \doi{10.2307/2335207}.
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  Harvey, A. C. (1993)
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  \emph{Time Series Models}.
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  2nd Edition, Harvester Wheatsheaf, NY, pp.\sspace{}44, 45.
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}
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\author{A. Trapletti}
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\examples{
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x <- rnorm (100)
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Box.test (x, lag = 1)
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Box.test (x, lag = 1, type = "Ljung")
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}
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\keyword{ts}