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\name{DickeyFullerPValues}
\alias{DickeyFullerPValues}
\alias{padf}
\alias{qadf}
\alias{adfTable}
\concept{unit root tests}
\concept{distribution of Dickey-Fuller test statistic}
\concept{distribution of augmented Dickey-Fuller test statistic}
\title{Dickey-Fuller p Values}
\description{
A collection and description of functions to compute the distribution
and quantile function for the ADF unit root test statistics.
}
\usage{
padf(q, N = Inf, trend = c("nc", "c", "ct"), statistic = c("t", "n"))
qadf(p, N = Inf, trend = c("nc", "c", "ct"), statistic = c("t", "n"))
adfTable(trend = c("nc", "c", "ct"), statistic = c("t", "n"),
includeInf = TRUE)
}
\arguments{
\item{q}{
vector of quantiles or test statistics. Missing values are allowed.
}
\item{p}{
vector of probabilities. Missing values are allowed.
}
\item{N}{
the number of observations in the sample from which the quantiles
are to be computed.
}
\item{trend}{
a character string describing the regression from which the
quantiles are to be computed. Valid choices are: \code{"nc"} for a
regression with no intercept (constant) nor time trend, \code{"c"}
for a regression with an intercept (constant) but no time trend, and
\code{"ct"} for a regression with an intercept (constant) and a time
trend. The default is \code{"c"}.
}
\item{statistic}{
a character string describing the type of test statistic. Valid
choices are \code{"t"} for t-statistic and \code{"n"} for normalized
statistic, sometimes referred to as the rho-statistic. The default
is \code{"t"}.
}
\item{includeInf}{
a logical flag. Should the asymptotic value be included into the
table?
}
}
\details{
\code{padf} computes cumulative probabilities for the ADF test.
\code{qadf} computes quantiles for the ADF test.
With sufficiently fine grid for the first argument, \code{padf} and
\code{qadf} compute, respectively, cumulative distribution functions
and quantile functions of ADF test statistics.
\code{adfTable} produces tables of p-values for ADF tests.
}
\value{
for \code{padf} and \code{qadf}, a named numeric vector with attribute
\code{"control"} holding \code{N},
for \code{adfTable}, an object from class \code{"gridData"}, which is
a list with the following components:
\item{x}{the values of \code{N} (length of the time series) for which
the statistics are provided,}
\item{y}{quantiles for which the statistics are provided,}
\item{Table}{ a matrix with one row for each \code{N} in \code{x} and
one column for each quantile in \code{y}.}
The \code{"gridData"} object contains also attribute \code{"control"}
with information about the requested test.
}
\note{
\code{padf} and \code{qadf} is based on the tables from A. Banerjee et
al. (1993). Interpolation is used For value of \code{N} not in the
tables. For small \code{N} (\code{N < 25}) the result is \code{NA}.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\references{
Banerjee A., Dolado J.J., Galbraith J.W., Hendry D.F. (1993);
\emph{Cointegration, Error Correction, and the Econometric
Analysis of Non-Stationary Data},
Oxford University Press, Oxford.
Dickey, D.A., Fuller, W.A. (1979);
\emph{Distribution of the estimators for autoregressive time
series with a unit root},
Journal of the American Statistical Association 74, 427--431.
}
\examples{
padf(q = -2:2, N = 25)
qadf(p = (1:9)/10, N = 25)
adfTable()
}
\keyword{distribution}
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