Phillips Perron Test - rileywheadon/ffa-framework GitHub Wiki

The PP Test is used to identify if an autoregressive time series $y_t$ has a unit root.

• Null hypothesis: $y_{t}$ has a unit root and is thus non-stationary.
• Alternative hypothesis: $y_{t}$ does not have a unit root and is trend-stationary.

Precisely, let $x_{t}$ be an AR(1) model. Let $y_{t}$ be a stochastic process through $x_{t}$ with drift $\mu$ and trend $\alpha t$.

$$ \begin{align} y_{t} &= \mu + \alpha t + x_{t} \\ x_{t} &= \rho x_{t-1} + \epsilon_{t} \end{align} $$

• If $\rho = 1$, then $x_t$ and hence $y_t$ has a unit root (null hypothesis).
• If $\rho < 1$, then $y_t$ is trend stationary (alternative hypothesis).

This test is implemented using R package aTSA with the following settings:

• lag.short = TRUE, since AMS data has minimal autocorrelation.
• We consider type3 results since we are assuming the presence of drift and trend.

For more information, see the documentation.

Warning: The implementation of the PP test in the aTSA package interpolates the p-value using a table from Fuller, W. A. (1996). This table only contains significance thresholds for $0.01$, $0.05$ and $0.10$. Therefore, p-values below $0.01$ and above $0.10$ will be truncated.