xis a non-stationary time series).
pp.test(x, type = c("Z_rho", "Z_tau"), lag.short = TRUE, output = TRUE)
p.value) and three rows (
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_rhoand 10.A.2 for
Z_tauin Fuller (1996)) with a given sample size $n$ = length(
Fuller, W. A. (1996). Introduction to statistical time series, second ed., Wiley, New York.
# 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)