the number of observations in the sample from which the
quantiles are to be computed.
na.rm
a logical value. If set to TRUE, missing values will
be removed otherwise not, the default is FALSE.
p
a numeric vector of probabilities. Missing values are
allowed.
q
vector of quantiles or test statistics. Missing values
are allowed.
statistic
a character string describing the type of test statistic.
Valid choices are "t" for t-statistic, and "n"
for normalized statistic, sometimes referred to as the
rho-statistic. The default is "t".
trend
a character string describing the regression from which the
quantiles are to be computed. Valid choices are: "nc"
for a regression with no intercept (constant) nor time trend,
and "c" for a regression with an intercept (constant)
but no time trend, "ct" for a regression with an intercept
(constant) and a time trend. The default is "c".
Value
The function punitroot returns the cumulative probability
of the asymptotic or finite sample distribution of the unit root
test statistics.
The function qunitroot returns the quantiles of the
asymptotic or finite sample distribution of the unit root test
statistics, given the probabilities.
Note
The function punitroot and qunitroot use Fortran
routines and the response surface approach from J.G. MacKinnon (1988).
Many thanks to J.G. MacKinnon putting his code and tables under the
GPL license, which made this implementation possible.
Author(s)
J.G. MacKinnon for the underlying Fortran routine and the tables,
Diethelm Wuertz for the Rmetrics R-port.
References
Dickey, D.A., Fuller, W.A. (1979);
Distribution of the estimators for autoregressive time
series with a unit root,
Journal of the American Statistical Association 74, 427–431.
MacKinnon, J.G. (1996);
Numerical distribution functions for unit root and
cointegration tests,
Journal of Applied Econometrics 11, 601–618.
Phillips, P.C.B., Perron, P. (1988);
Testing for a unit root in time series regression,
Biometrika 75, 335–346.
Examples
## qunitroot -
# Asymptotic quantile of t-statistic
qunitroot(0.95, trend = "nc", statistic = "t")
## qunitroot -
# Finite sample quantile of n-statistic
qunitroot(0.95, N = 100, trend = "nc", statistic = "n")
## punitroot -
# Asymptotic cumulative probability of t-statistic
punitroot(1.2836, trend = "nc", statistic = "t")
## punitroot -
# Finite sample cumulative probability of n-statistic
punitroot(1.2836, N = 100, trend = "nc", statistic = "n")
## Mac Kinnon's unitrootTable -
unitrootTable(trend = "nc")