ADF.rectest: Augmented Dickey-Fuller Recursive Test
In uroot: Unit Root Tests and Graphics for Seasonal Time Series

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

    ADF.rectest (wts, type="moving", nsub=48, itsd, selectlags=list(mode="signf", Pmax=NULL),
                 trace=list(remain=1, plot=0, elaps=1))

`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: `c(0,0,c(0))`, if the first and/or second elements are set equal to 1, it indicates that an intercept, and/or linear trend, respectively, are included. The third element is a vector indicating which seasonal dummies should be included. If no seasonal dummies are desired it must be set equal to zero. For example, `regular=c(1,0,c(1,2,3))` would include an intercept, no trend, and the first three seasonal dummies.
`selectlags`	lag selection method. A list object indicating the method to select lags, `mode`, and the maximum lag considered. Available methods are `"aic"`, `"bic"`, and `"signf"`. See details. `Pmax` is a numeric object indicating the maximum lag order. By default, the maximum number of lags considered is round(10log10(n))*, where n is the number of observations.
`trace`	a list object indicating if a trace of the iteration progress should be printed. Three levels of information can be printed: `remain`, the percentage of the whole procedure that has been completed; `plot`, a plot of the computed statistics; and `elaps`, how much time the whole procedure has consumed.

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 javlacalle@yahoo.es and Ignacio Diaz-Emparanza Ignacio.Diaz-Emparanza@ehu.es

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.

ADF.test.

    ## 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)