UnitrootDistribution {fSeries} | R Documentation

## Unit Root Distributions

### Description

A collection and description of functions to compute the distribution and and quantile function for the unit root test statistics.

The functions are:

`punitroot` | the cumulative probability,
`qunitroot` | the quantiles of the unit root test statistics,
`adfTable` | the table of cumulative probabilities,
`pdftest` | the cumulative probability for the ADF test,
`qdftest` | the quantiles for the ADF test.

### Usage

    punitroot(q, n.sample = 0, trend = c("c", "nc", "ct", "ctt"),
        statistic = c("t", "n"), na.rm = FALSE)
    qunitroot(p, n.sample = 0, trend = c("c", "nc", "ct", "ctt"),
        statistic = c("t", "n"), na.rm = FALSE)

    pdftest(q, n.sample, trend = c("nc", "c", "ct"), statistic = c("t", "n"))
    qdftest(p, n.sample, trend = c("nc", "c", "ct"), statistic = c("t", "n"))
    dfTable(trend = c("nc", "c", "ct"), statistic = c("t", "n"))

### Arguments

`n.sample` | the number of observations in the sample from which the quantiles are to be computed. [*unitroot] - Specify `n.sample=0` for asymptotic quantiles. The default is 0.
`na.rm` | a logical value. If set to `TRUE`, missing values will be removed otherwise not, the default is `FALSE`.
`p` | a numeric vector of probabilities. Missing values are allowed.
`q` | vector of quantiles or test statistics. Missing values are allowed.
`statistic` | a character string describing the type of test statistic. Valid choices are `"t"` for t-statistic, and `"n"` for normalized statistic, sometimes referred to as the rho-statistic. The default is `"t"`.
`trend` | a character string describing the regression from which the quantiles are to be computed. Valid choices are: `"nc"` for a regression with no intercept (constant) nor time trend, and `"c"` for a regression with an intercept (constant) but no time trend, `"ct"` for a regression with an intercept (constant) and a time trend. The default is `"c"`.

### Value

The function `padf` returns the cumulative probability of the finite sample distribution of the unit root test statistics.
The function `qadf` returns the quantiles of the finite sample distribution of the unit root test statistics, given the probabilities.
The function `punitroot` returns the cumulative probability of the asymptotic or finite sample distribution of the unit root test statistics.
The function `qunitroot` returns the quantiles of the asymptotic or finite sample distribution of the unit root test statistics, given the probabilities.

### Note

The programs `padf` and `qadf` use the tables from A. Banerjee et al. (1993).

The programs `punitroot` and `qunitroot` use Fortran routines and the tables from J.G. McKinnon (1988). Many thanks to J.G. McKinnon putting his code and tables under the GPL license, which made this implementation possible.

### Author(s)

J.G. McKinnon for the underlying Fortran routine and the tables,
Diethelm Wuertz for the Rmetrics R-port.

### References

Banerjee A., Dolado J.J., Galbraith J.W., Hendry D.F. (1993); Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data, Oxford University Press, Oxford.

Dickey, D.A., Fuller, W.A. (1979); Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association 74, 427–431.

MacKinnon, J.G. (1996); Numerical distribution functions for unit root and cointegration tests, Journal of Applied Econometrics 11, 601–618.

Phillips, P.C.B., Perron, P. (1988); Testing for a unit root in time series regression, Biometrika 75, 335–346.

### Examples

    ## SOURCE("fSeries.32A-UnitrootDistribution")

    ## qunitroot -
       # Asymptotic quantile of t-statistic
       qunitroot(0.95, trend = "nc", statistic = "t")

    ## qunitroot -
       # Finite sample quantile of n-statistic
       qunitroot(0.95, n.sample = 100, trend = "nc", statistic = "n")

    ## punitroot -
       # Asymptotic cumulative probability of t-statistic
       punitroot(1.2836, trend = "nc", statistic = "t")

    ## punitroot -
       # Finite sample cumulative probability of n-statistic
       punitroot(1.2836, n.sample = 100, trend = "nc", statistic = "n")

[Package fSeries version 221.10065 Index]