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

estimates the number of first
differences necessary.

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

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

An integer indicating the number of differences required for stationarity.

`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`

.

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.

`auto.arima`

and `ndiffs`

# NOT RUN { ndiffs(WWWusage) ndiffs(diff(log(AirPassengers), 12)) # }