forecast (version 7.3)

# ndiffs: 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 and `nsdiffs` estimates the number of seasonal differences.

## Usage

```ndiffs(x, alpha=0.05, test=c("kpss","adf", "pp"), max.d=2)
nsdiffs(x, m=frequency(x), test=c("ocsb","ch"), max.D=1)```

## Arguments

x
A univariate time series
alpha
Level of the test
m
Length of seasonal period
test
Type of unit root test to use
max.d
Maximum number of non-seasonal differences allowed
max.D
Maximum number of 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`.

`nsdiffs` uses seasonal unit root tests to determine the number of seasonal differences required for time series `x` to be made stationary (possibly with some lag-one differencing as well). If `test="ch"`, the Canova-Hansen (1995) test is used (with null hypothesis of deterministic seasonality) and if `test="ocsb"`, the Osborn-Chui-Smith-Birchenhall (1988) test is used (with null hypothesis that a seasonal unit root exists).

## References

Canova F and Hansen BE (1995) "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability", Journal of Business and Economic Statistics 13(3):237-252.

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 DR, Chui APL, Smith J, and Birchenhall CR (1988) "Seasonality and the order of integration for consumption", Oxford Bulletin of Economics and Statistics 50(4):361-377.

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

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

`auto.arima`
``````nsdiffs(log(AirPassengers))