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.

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

nsdiffs(x, m = frequency(x), test = c("ocsb", "ch"), max.D = 1)

## Arguments

x A univariate time series Level of the test, possible values range from 0.01 to 0.1. Type of unit root test to use Specification of the deterministic component in the regression Maximum number of non-seasonal differences allowed Length of seasonal period Maximum number of seasonal differences allowed

An integer.

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