Number of differences required for a stationary series

Functions to estimate the number of differences required to make a given time series stationary. ndiffs estimates the number of first differences necessary.

Usage

ndiffs(
  x,
  alpha = 0.05,
  test = c("kpss", "adf", "pp"),
  type = c("level", "trend"),
  max.d = 2,
  ...
)

Arguments

x: A univariate time series
alpha: Level of the test, possible values range from 0.01 to 0.1.
test: Type of unit root test to use
type: Specification of the deterministic component in the regression
max.d: Maximum number of non-seasonal differences allowed
...: Additional arguments to be passed on to the unit root test

Value

An integer indicating the number of differences required for stationarity.

Details

ndiffs uses a unit root test to determine the number of differences required for time series x to be made stationary. If test="kpss", the KPSS test is used with the null hypothesis that x has a stationary root against a unit-root alternative. Then the test returns the least number of differences required to pass the test at the level alpha. If test="adf", the Augmented Dickey-Fuller test is used and if test="pp" the Phillips-Perron test is used. In both of these cases, the null hypothesis is that x has a unit root against a stationary root alternative. Then the test returns the least number of differences required to fail the test at the level alpha.

References

Dickey DA and Fuller WA (1979), "Distribution of the Estimators for Autoregressive Time Series with a Unit Root", Journal of the American Statistical Association 74:427-431.

Kwiatkowski D, Phillips PCB, Schmidt P and Shin Y (1992) "Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root", Journal of Econometrics 54:159-178.

Osborn, D.R. (1990) "A survey of seasonality in UK macroeconomic variables", International Journal of Forecasting, 6:327-336.

Phillips, P.C.B. and Perron, P. (1988) "Testing for a unit root in time series regression", Biometrika, 72(2), 335-346.

Said E and Dickey DA (1984), "Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order", Biometrika 71:599-607.

Author

Rob J Hyndman, Slava Razbash & Mitchell O'Hara-Wild

Examples

ndiffs(WWWusage)
#> [1] 1
ndiffs(diff(log(AirPassengers), 12))
#> [1] 1