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To perform a KPSS test in R, you need to first install the tseries package. Then, you can use the kpss.test() function to run the KPSS test. This function takes in a time series as its argument and returns the test statistic, p-value, and critical values. As an example, you can use the kpss.test() function to test the stationarity of a simulated random walk with drift, which can be generated with the arima.sim() function.
A KPSS test can be used to determine if a time series is trend stationary.
This test uses the following null and alternative hypothesis:
- H0: The time series is trend stationary.
- HA: The time series is not trend stationary.
If the of the test is less than some significance level (e.g. α = .05) then we reject the null hypothesis and conclude that the time series is not trend stationary.
Otherwise, we fail to reject the null hypothesis.
The following examples show how to perform a KPSS test in R.
Example 1: KPSS Test in R (With Stationary Data)
First, let’s create some fake data in R to work with:
#make this example reproducible
set.seed(100)
#create time series data
data<-rnorm(100)
#plot time series data as line plot
plot(data, type='l')
We can use the kpss.test() function from the tseries package to perform a KPSS test on this time series data:
library(tseries) #perform KPSS test kpss.test(data, null="Trend") KPSS Test for Trend Stationarity data: data KPSS Trend = 0.034563, Truncation lag parameter = 4, p-value = 0.1 Warning message: In kpss.test(data, null = "Trend") : p-value greater than printed p-value
The p-value is 0.1. Since this value is not less than .05, we fail to reject the null hypothesis of the KPSS test.
This means we can assume that the time series is trend stationary.
Note: The p-value is actually even greater than 0.1, but the lowest value that the kpss.test() function will output is 0.1.
Example 2: KPSS Test in R (With Non-Stationary Data)
First, let’s create some fake data in R to work with:
#make this example reproducible
#create time series data
data <-c(0, 3, 4, 3, 6, 7, 5, 8, 15, 13, 19, 12, 29, 15, 45, 23, 67, 45)
#plot time series data as line plot
plot(data, type='l')
Once again, we can use the kpss.test() function from the tseries package to perform a KPSS test on this time series data:
library(tseries) #perform KPSS test kpss.test(data, null="Trend") KPSS Test for Trend Stationarity data: data KPSS Trend = 0.149, Truncation lag parameter = 2, p-value = 0.04751
The p-value is 0.04751. Since this value is less than .05, we reject the null hypothesis of the KPSS test.
This means the time series is not trend stationary.
The following tutorials provide additional information on how to work with time series data in R: