# pp.test: Phillips-Perron Test In aTSA: Alternative Time Series Analysis

## Description

Performs the Phillips-Perron test for the null hypothesis of a unit root of a univariate time series `x` (equivalently, `x` is a non-stationary time series).

## Usage

 `1` ```pp.test(x, type = c("Z_rho", "Z_tau"), lag.short = TRUE, output = TRUE) ```

## Arguments

 `x` a numeric vector or univariate time series. `type` the type of Phillips-Perron test. The default is `Z_rho`. `lag.short` a logical value indicating whether the parameter of lag to calculate the statistic is a short or long term. The default is a short term. `output` a logical value indicating to print the results in R console. The default is `TRUE`.

## Details

Compared with the Augmented Dickey-Fuller test, Phillips-Perron test makes correction to the test statistics and is robust to the unspecified autocorrelation and heteroscedasticity in the errors. There are two types of test statistics, Z_{ρ} and Z_{τ}, which have the same asymptotic distributions as Augmented Dickey-Fuller test statistic, `ADF`. The calculations of each type of the Phillips-Perron test can be see in the reference below. If the `lag.short = TRUE`, we use the default number of Newey-West lags floor(4*(length(x)/100)^0.25), otherwise floor(12*(length(x)/100)^0.25) to calculate the test statistics. In order to calculate the test statistic, we consider three types of linear regression models. The first type (`type1`) is the one with no drift and linear trend with respect to time:

x[t] = ρ*x[t-1] + e[t],

where e[t] is an error term. The second type (`type2`) is the one with drift but no linear trend:

x[t] = μ + ρ*x[t-1] + e[t].

The third type (type3) is the one with both drift and linear trend:

x[t] = μ + α*t + ρ*x[t-1] + e[t].

The p.value is calculated by the interpolation of test statistics from the critical values tables (Table 10.A.1 for `Z_rho` and 10.A.2 for `Z_tau` in Fuller (1996)) with a given sample size n = length(`x`).

## Value

A matrix for test results with three columns (`lag`,`Z_rho` or `Z_tau`, `p.value`) and three rows (`type1`, `type2`, `type3`). Each row is the test results (including lag parameter, test statistic and p.value) for each type of linear equation.

## Note

Missing values are removed.

Debin Qiu

## References

Phillips, P. C. B.; Perron, P. (1988). Testing for a Unit Root in Time Series Regression. Biometrika, 75 (2): 335-346.

Fuller, W. A. (1996). Introduction to statistical time series, second ed., Wiley, New York.

`adf.test`, `kpss.test`, `stationary.test`

## Examples

 ```1 2 3 4 5 6``` ```# PP test for ar(1) process x <- arima.sim(list(order = c(1,0,0),ar = 0.2),n = 100) pp.test(x) # PP test for co2 data pp.test(co2) ```

### Example output

```Attaching package: 'aTSA'

The following object is masked from 'package:graphics':

identify

Phillips-Perron Unit Root Test
alternative: stationary

Type 1: no drift no trend
lag Z_rho p.value
3 -97.8    0.01
-----
Type 2: with drift no trend
lag Z_rho p.value
3 -97.7    0.01
-----
Type 3: with drift and trend
lag Z_rho p.value
3 -97.6    0.01
---------------
Note: p-value = 0.01 means p.value <= 0.01
Phillips-Perron Unit Root Test
alternative: stationary

Type 1: no drift no trend
lag Z_rho p.value
5 0.141   0.723
-----
Type 2: with drift no trend
lag Z_rho p.value
5 -2.14   0.752
-----
Type 3: with drift and trend
lag Z_rho p.value
5 -92.7    0.01
---------------
Note: p-value = 0.01 means p.value <= 0.01
```

aTSA documentation built on May 29, 2017, 11:44 a.m.