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,
...
)
```

An integer indicating the number of differences required for stationarity.

- 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

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

`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`

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

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