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)Run the code above in your browser using DataCamp Workspace