unirootTest function

Unit root test

Unit root test is performed on a set of quantitative variables. A single group factor may be taken into account.

unirootTest(x = NULL, group = NULL, time = NULL, data, test = NULL, log = FALSE)

Arguments

• x: A vector including the name of the quantitative variables to be tested. If NULL (the default), all the quantitative variables contained in data will be tested.
• group: The name of the group factor (optional). If NULL, no groups are considered.
• time: The name of the time factor (optional). This variable must be either a numeric identificative or a date in format '%Y/%m/%d','%d/%m/%Y', or '%Y-%m-%d'. If time is NULL and group is not NULL, data are assumed to be temporally ordered within each group. If both time and group are NULL, data are assumed to be temporally ordered.
• data: An object of class data.frame containing the variables to be tested, the group factor if group is not NULL, and the time factor if time is not NULL.
• test: The test to apply, that may be either "kpss" (Kwiatkowski, 1992) or "adf" (Dickey & Fuller, 1981). If NULL (the default), the choice is for the KPSS test if the number of periods is less than 100, otherwise the ADF test is used.
• log: Logical. If TRUE, logarithmic transformation is applied to all strictly positive quantitative variables. Default is FALSE.

Returns

An object of class unirootTest, consisting of a list with one component for each variable tested. Each list contains the following components: - statistic: The value of the test statistic.

• lag.order: The lag order at which the test statistic is computed. It is automatically selected according to the precedure by Ng & Perron (2001).

• n: The total number of observations if group is NULL, otherwise the number of observations per group.

• z.value: The z-value of the test.

• p.value: The p-value of the test.

Note

The null hypothesis of the ADF test is the presence of a unit root. The lag order to calculate the statistic of the ADF test is automatically selected according to the precedure by Ng & Perron (2001).

The null hypothesis of the KPSS test is stationarity. The statistic of the KPSS test is calculated at the lag order 4*(n/100)^0.25.

If the group factor is specified, p-values of each group are combined using the method proposed by Demetrescu (2006).

References

M. Demetrescu, U. Hassler, and A. Tarcolea (2006). Combining Significance of Correlated Statistics with Application to Panel Data. Oxford Bulletin of Economics and Statistics, 68(5), 647-663. DOI: 10.1111/j.1468-0084.2006.00181.x

D. A. Dickey, and W. A. Fuller (1981). Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica, 49: 1057-1072. DOI: 10.2307/1912517

D. Kwiatkowski, P. C. B. Phillips, P. Schmidt and Y. Shin (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1-3): 159-178.

S. Ng, and W. P. Perron (2001). Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power. Econometrica, 60: 1519-1554. DOI: 10.1111/1468-0262.00256.

Examples

data(industry)
indus.urt <- unirootTest(c("Job","Consum","Population","GDP"),
  group="Region",time="Year",data=industry,log=TRUE)
indus.urt      ## p-values
indus.urt$Job  ## details for variable 'Job'