Kwiatkowski-Phillips-Schmidt-Shin (KPSS) Test

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A Kwiatkowski-Phillips-Schmidt-Shin (KPSS) Test is a statistical test for the null hypothesis of stationarity against the alternative hypothesis of unit root.

  • Context:
  • It may be defined as:
  1. [math]\displaystyle{ H_0 }[/math]: An observable time series is stationarity around a deterministic trend.
  2. [math]\displaystyle{ H_a }[/math]: An unit root is present in the time series.


References

2016

Contrary to most unit root tests, the presence of a unit root is not the null hypothesis but the alternative. Additionally, in the KPSS test, the absence of a unit root is not a proof of stationarity but, by design, of trend-stationarity. This is an important distinction since it is possible for a time serie to be non-stationary, have no unit root yet be trend-stationary. In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time serie will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent impact on the mean (i.e. no convergence over time).
Such models were proposed in 1982 by Alok Bhargava in his Ph.D. thesis where several John von Neumann- or Durbin–Watson-type finite sample tests for unit roots were developed (see Bhargava, 1986). Later, Denis Kwiatkowski, Peter C. B. Phillips, Peter Schmidt and Yongcheol Shin (1992) proposed a test of the null hypothesis that an observable series is trend stationary (stationary around a deterministic trend). The series is expressed as the sum of deterministic trend, random walk, and stationary error, and the test is the Lagrange multiplier test of the hypothesis that the random walk has zero variance. KPSS-type tests are intended to complement unit root tests, such as the Dickey–Fuller tests. By testing both the unit root hypothesis and the stationarity hypothesis, one can distinguish series that appear to be stationary, series that appear to have a unit root, and series for which the data (or the tests) are not sufficiently informative to be sure whether they are stationary or integrated.

2004

An important argument against the use of tests for the null hypothesis of stationarity is the difficulty to control their size when the process is stationary, but highly autoregressive. Probably the best known test for stationarity in econometrics, the so-called KPSS test introduced by Kwiatkowski, Phillips, Schmidt and Shin (1992) is oversized in that case: it rejects the true hypothesis of stationarity too often, again leading to undue preference for the hypothesis if unit root nonstationarity.

1992