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