x
(equivalently, x
is a non-stationary time series).pp.test(x, type = c("Z_rho", "Z_tau"), lag.short = TRUE, output = TRUE)
Z_rho
.TRUE
.lag
,Z_rho
or Z_tau
, p.value
) and three rows (type1
, type2
, type3
).
Each row is the test results (including lag parameter, test statistic and p.value) for
each type of linear equation.ADF
. The calculations of each type
of the Phillips-Perron test can be see in the reference below. If the
lag.short = TRUE
, we use the default number of Newey-West lags
$floor(4*(length(x)/100)^0.25)$,
otherwise $floor(12*(length(x)/100)^0.25)$ to calculate the test statistics.
In order to calculate the test statistic, we consider
three types of linear regression models. The first type (type1
) is the one
with no drift and linear trend with respect to time:
$$x[t] = \rho*x[t-1] + e[t],$$
where $e[t]$ is an error term.
The second type (type2
) is the one with drift but no linear trend:
$$x[t] = \mu + \rho*x[t-1] + e[t].$$
The third type (type3) is the one with both drift and linear trend:
$$x[t] = \mu + \alpha*t + \rho*x[t-1] + e[t].$$
The p.value is calculated by the interpolation of test statistics from the critical values
tables (Table 10.A.1 for Z_rho
and 10.A.2 for Z_tau
in Fuller (1996))
with a given sample size $n$ = length(x
).Fuller, W. A. (1996). Introduction to statistical time series, second ed., Wiley, New York.
adf.test
, kpss.test
, stationary.test
# PP test for ar(1) process
x <- arima.sim(list(order = c(1,0,0),ar = 0.2),n = 100)
pp.test(x)
# PP test for co2 data
pp.test(co2)
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