R: Number of differences required for a stationary series

ndiffs {forecast} | R Documentation

## Number of differences required for a stationary series

### Description

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

### 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`.

### Value

An integer indicating the number of differences required for stationarity.

### Author(s)

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

### 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.

### See Also

`auto.arima` and `ndiffs`

### Examples

    ndiffs(WWWusage)
    ndiffs(diff(log(AirPassengers),12))

[Package forecast version 8.4 Index]