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"), max.d = 2)`nsdiffs(x, m = frequency(x), test = c("ocsb", "ch"), max.D = 1)

x

A univariate time series

alpha

Level of the test

test

Type of unit root test to use

max.d

Maximum number of non-seasonal differences allowed

m

Length of seasonal period

max.D

Maximum number of seasonal differences allowed

An integer.

`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).

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.

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

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