purtest
implements several testing procedures that have been proposed
to test unit root hypotheses with panel data.
purtest(object, data = NULL, index = NULL, test = c("levinlin",
"ips", "madwu", "Pm", "invnormal", "logit", "hadri"), exo = c("none",
"intercept", "trend"), lags = c("SIC", "AIC", "Hall"), pmax = 10,
Hcons = TRUE, q = NULL, dfcor = FALSE, fixedT = TRUE, ...)# S3 method for purtest
print(x, ...)
# S3 method for purtest
summary(object, ...)
# S3 method for summary.purtest
print(x, ...)
Either a "data.frame"
or a matrix containing the
time series, a "pseries"
object, a formula, or the name of a
column of a "data.frame"
, or a "pdata.frame"
on which the
test has to be computed; a "purtest"
object for the print and
summary methods,
a "data.frame"
or a "pdata.frame"
object,
the indexes,
the test to be computed: one of "levinlin"
for
LEVIN:LIN:CHU:02;textualplm, "ips"
for
IM:PESAR:SHIN:03;textualplm, "madwu"
for
MADDA:WU:99;textualplm, "Pm"
, "invnormal"
,
or "logit"
for various tests as in
CHOI:01;textualplm, or "hadri"
for
HADR:00;textualplm, see Details,
the exogenous variables to introduce in the augmented
Dickey--Fuller (ADF) regressions, one of: no exogenous
variables ("none"
), individual intercepts ("intercept"
), or
individual intercepts and trends ("trend"
), but see Details,
the number of lags to be used for the augmented
Dickey-Fuller regressions: either an integer (the number of
lags for all time series), a vector of integers (one for each
time series), or a character string for an automatic
computation of the number of lags, based on either the AIC
("AIC"
), the SIC ("SIC"
), or on the method by
HALL:94;textualplm ("Hall"
),
maximum number of lags,
logical, only relevant for test = "hadri"
,
indicating whether the heteroskedasticity-consistent test of
HADR:00;textualplm should be computed,
the bandwidth for the estimation of the long-run variance,
logical, indicating whether the standard deviation of the regressions is to be computed using a degrees-of-freedom correction,
logical, indicating whether the different ADF regressions are to be computed using the same number of observations,
further arguments.
An object of class "purtest"
: a list with the elements
"statistic"
(a "htest"
object), "call"
, "args"
,
"idres"
(containing results from the individual regressions),
and "adjval"
(containing the simulated means and variances
needed to compute the statistic).
All these tests except "hadri"
are based on the estimation of
augmented Dickey-Fuller (ADF) regressions for each time series. A
statistic is then computed using the t-statistics associated with
the lagged variable. The Hadri residual-based LM statistic is the
cross-sectional average of the individual KPSS statistics
KWIA:PHIL:SCHM:SHIN:92plm, standardized by their
asymptotic mean and standard deviation.
Several Fisher-type tests that combine p-values from tests based on ADF regressions per individual are available:
"madwu"
is the inverse chi-squared test
MADDA:WU:99plm, also called P test by
CHOI:01;textualplm.
"Pm"
is the modified P test proposed by
CHOI:01;textualplm for large N,
"invnormal"
is the inverse normal test by CHOI:01plm, and
"logit"
is the logit test by CHOI:01plm.
The individual p-values for the Fisher-type tests are approximated as described in MACK:94;textualplm.
The kind of test to be computed can be specified in several ways, depending on how the data is handed over to the function:
For the formula
/data
interface (if data
is a data.frame
,
an additional index
argument should be specified); the formula
should be of the form: y ~ 0
, y ~ 1
, or y ~ trend
for a test
with no exogenous variables, with an intercept, or with individual
intercepts and time trend, respectively. The exo
argument is
ignored in this case.
For the data.frame
, matrix
, and pseries
interfaces: in
these cases, the exogenous variables are specified using the exo
argument.
With the associated summary
and print
methods, additional
information can be extracted/displayed (see also Value).
# NOT RUN {
data("Grunfeld", package = "plm")
y <- data.frame(split(Grunfeld$inv, Grunfeld$firm))
purtest(y, pmax = 4, exo = "intercept", test = "madwu")
## same via formula interface
purtest(inv ~ 1, data = Grunfeld, index = c("firm", "year"), pmax = 4, test = "madwu")
# }
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