skpss_test: Simulate a KPSS Test to Assess Unit Root in a Time Series

In sTSD: Simulate Time Series Diagnostics

Simulate a KPSS Test to Assess Unit Root in a Time Series

Description

skpss_test() provides a simulation approach to assessing unit root in a time series by way of KPSS test, first proposed by Kwiatkowski et al. (1992). It takes a vector and extracts the residuals from two models to assess stationarity around a level or trend, producing a KPSS test statistic (eta). Rather than interpolate or approximate a p-value, it simulates some user-specified number of KPSS of either a known, stationary time series (default) or a known, non-stationary time series matching the length of the time series the user provides. This allows the user to make assessments of non-stationarity or stationarity by way of simulation rather than approximation from received critical values by way of various books/tables.

Usage

skpss_test(x, lag_short = TRUE, n_sims = 1000, sim_hyp = "stationary")

Arguments

x	a vector
lag_short	logical, defaults to TRUE. If TRUE, the "short-term" lag is used for the KPSS test. If FALSE, the "long-term" lag is used. These lags are those suggested by Schwert (1989).
n_sims	the number of simulations for calculating an interval or distribution of test statistics for assessing stationarity or non-stationarity. Defaults to 1,000.
sim_hyp	can be either "stationary" or "nonstationary". If "stationary" (default), the function runs KPSS tests on simulated stationary (pure white noise) data. This allows the user to assess compatibility/plausibility of the test statistic against a distribution of test statistics that are known to be pure white noise (in expectation). If "nonstationary", the simulations are conducted on two different random walks. The "trend" test includes a level drawn from a Rademacher distribution with a time trend of that level, divided by 10.

Details

Recall that this procedure defaults from almost every other unit root test by making stationarity a null hypothesis. Non-stationarity is the alternative hypothesis.

As of writing, the default lags are those suggested by Schwert (1989) to apply to the Bartlett kernel generating the KPSS test statistic (eta).

aTSA has a particularly interesting approach to this test that draws on on insights seemingly proposed by Hobijn et al. (2004). Future updates may include those, but this function, as is, performs calculations of eta identical to what tseries or urca would produce. Right now, I don't have the time or energy to get into the weeds of what Hobijn et al. (2004) are doing or what aTSA is implementing, but it seems pretty cool.

This function removes missing values from the vector before calculating test statistics.

Value

skpss_test() returns a list of length 3. The first element in the list is a matrix of eta statistics calculated by the test. The first of those is the level statistic and the second of those is the trend statistic. The second element is a data frame of the simulated eta statistics, where the type of simulation (level, trend) is communicated in the cat column. The third element contains some attributes about the procedure for post-processing.

Author(s)

Steven V. Miller

References

Hobijn, Bart, Philip Hans Franses, and Marius Ooms. 2004. "Generalizations of the KPSS-test for Stationarity". Statistica Neerlandica 58(4): 483–502.

Kwiatkowski, Denis, Peter C.B. Phillips, Peter Schmidt, and Yongcheol Shin. 1992. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We that Economic Time Series Have a Unit Root?" Journal of Econometrics 54(1-3): 159–78.

Examples

x <- USDSEK$close[1:500] # note: one missing obs here; becomes series of 499

skpss_test(x, n_sims = 25) # make it quick...

sTSD documentation built on April 3, 2025, 7:37 p.m.