KPSS test for stationarity

Computes the KPSS statistic (Kwiatkowski, Phillips, Schmidt & Shin, 1992) for level stationarity of a one-dimensional signal. The residuals from regressing the signal on a constant are cumulatively summed, and the statistic is \(\eta = N^{-2}\sum_t S_t^2 / \hat\lambda^2\), where \(S_t\) are the partial sums and \(\hat\lambda^2\) is a Bartlett (Newey-West) long-run variance estimate with truncation lag. Unlike the Augmented Dickey-Fuller test, the KPSS null is stationarity: a small statistic (below the critical value) means the series is consistent with stationarity. The statistic is the same deterministic quantity as statsmodels.tsa.stattools.kpss(regression = "c", nlags = lag).

Usage

kpssTest(x, lag = 10L)

Arguments

x: A numeric vector (the time series).
lag: Bartlett truncation lag \(L\) for the long-run variance (default 10).

Value

A list with statistic (the KPSS \(\eta\)), n (the signal length), and lag.

Details

Note: only the statistic is computed here (an exact quantity). The KPSS critical values and p-value come from the reference tables (an approximation) and are not returned.

References

Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1-3), 159-178.

Examples

set.seed(1)
kpssTest(rnorm(500), lag = 10)$statistic   # stationary -> small statistic
#> [1] 0.07720669