MacKinnonPValues {urca} | R Documentation

## MacKinnon's Unit Root p Values

### Description

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

The functions are:

`punitroot` | the returns cumulative probability,
`qunitroot` | the returns quantiles of the unit root test statistics,
`unitrootTable` | tables p values from MacKinnon's response surface.

### Usage

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

    unitrootTable(trend = c("c", "nc", "ct", "ctt"), statistic = c("t", "n"))

### Arguments

`N` | the number of observations in the sample from which the quantiles are to be computed.
`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 `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 function `punitroot` and `qunitroot` use Fortran routines and the response surface approach from J.G. MacKinnon (1988). Many thanks to J.G. MacKinnon putting his code and tables under the GPL license, which made this implementation possible.

### Author(s)

J.G. MacKinnon for the underlying Fortran routine and the tables,
Diethelm Wuertz for the formerly Rmetrics R-port and Bernhard Pfaff for the porting to urca.

### References

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

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

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

    ## Mac Kinnon's unitrootTable -
       unitrootTable(trend = "nc")

[Package urca version 1.2-3 Index]