Description Usage Arguments Details Value Author(s) References See Also Examples

This function computes the augmented Dickey-Fuller statistic recursively along subsamples of the original data.

1 2 3 |

`wts` |
a univariate time series object. |

`type` |
a character string indicating how subsamples are selected. See details. |

`nsub` |
the number of observations in each subsample. |

`itsd` |
deterministic components to include in the model. Three types of regressors can be included: regular deterministic components, seasonal deterministic components, and any regressor variable previously defined by the user. This argument must be a vector object with the following elements: |

`selectlags` |
lag selection method. A list object indicating the method to select lags, |

`trace` |
a list object indicating if a trace of the iteration progress should be printed. Three
levels of information can be printed: |

The auxiliar regression is defined as,

*δ y_t = ρ y_{t-1} + ε_t,*

where *δ* is the first order operator. Hence, under the null hypothesis *ρ=0* and the
long run unit root 1 exists.

Three types of subsamples are considered: "backw", the statistic is computed for the last `nsub`

observations and then one year backwards is added until the beginning of the sample; "forw", the
statistic is computed for the first `nsub`

observations and then one year forwards is added until
the end of the sample; "moving", the statistic is computed over moving subsamples of length `nsub`

.

Available methods are the following. `"aic"`

and `"bic"`

follows a top-down strategy based on
the Akaike's and Schwarz's information criteria, and `"signf"`

removes the non-significant lags at
the 10% level of significance until all the selected lags are significant. By default, the maximum
number of lags considered is *round(10*log10(n))*, where *n* is the number of observations.

It is also possible to set the argument `selectlags`

equals to a vector, `mode=c(1,3,4)`

, then
those lags are directly included in the auxiliar regression and `Pmax`

is ignored.

Regressor variables are not considered in this procedure.

An object of class `adfrecst-class`

.

Javier Lopez-de-Lacalle [email protected] and Ignacio Diaz-Emparanza [email protected]

D.A. Dickey and W.A. Fuller (1981), Likelihood ratio statistics for autoregressive time series with a
unit root. *Econometrica*, **49**, 1057-1071.

W.A. Fuller (1976), Introduction to Statistical Time Series. Jonh Wiley, New York.

1 2 3 4 5 6 7 8 9 | ```
## ADF recursive test with constant, trend and seasonal dummies.
data(AirPassengers)
lairp <- log(AirPassengers)
adf.out1 <- ADF.rectest(wts=lairp, type="backw", nsub=84, itsd=c(1,1,c(1:11)),
selectlags=list(mode="bic", Pmax=NULL),
trace=list(remain=1, plot=1, elaps=1))
show(adf.out1)
plot(adf.out1)
``` |

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