Python implementation of the Phillips-Perron (1988) test that can be used to test for a unit root in a univariate process.

Also included here is the Monte Carlo simulation code used to generate critical values for the Z-rho statistic which makes use of the simulation code located in the repo: https://github.com/JimVaranelli/ARFIMA_sim

x : array_like, 1d
    data series
regression : {'nc', 'c','ct'}
    Constant and trend order to include in regression
    * 'nc' : no constant, no trend
    * 'c' : constant only (default)
    * 'ct' : constant and trend
trunclag : {int, None}
    number of truncation lags, default=int(sqrt(nobs)/5) (SAS, 2015)

tau : float
    Z-tau test statistic
tau_pv : float
    Z-tau p-value based on MacKinnon (1994, 2010) regression surface model
tau_cvdict : dict
    critical values for the Z-tau test statistic at the 1%, 5%, and 10% levels
rho : float
    Z-rho test statistic
rho_pv : float
    Z-tau p-value based on interpolation of simulation-derived critical values
rho_cvdict : dict
    critical values for the Z-rho test statistic at the 1%, 5%, and 10% levels
lags : int
    number of truncation lags used in covariance matrix estimation
nobs : int
     number of observations used in regression

H0 = series has a unit root (i.e., non-stationary)

Basic process is to fit the time series under test with an AR(1) model using heteroscedasticity- and autocorrelation-consistent residual covariance estimation in order to generate the Phillips-Perron Z-rho and Z-tau statistics (1988) which are asymptotically equivalent to the Dickey-Fuller (1979, 1981) rho/tau statistics. Z-tau p-values are calculated using the statsmodel implementation of MacKinnon's (1994, 2010) regression surface model. Z-rho p-values are interpolated from Monte-Carlo derived critical values. The simulation code used to estimate the Z-rho critical values is provided here.

Dickey, D.A., and 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.

Dickey, D.A., and Fuller, W.A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49: 1057-1072.

MacKinnon, J.G. (1994). Approximate asymptotic distribution functions for unit-root and cointegration tests. Journal of Business and Economic Statistics, 12: 167-176.

MacKinnon, J.G. (2010). Critical values for cointegration tests. Working Paper 1227, Queen's University, Department of Economics. Retrieved from URL: https://www.econ.queensu.ca/research/working-papers.

Newey, W.K., and West, K.D. (1994). A simple, positive semi-definite, heteroscedasticity- and autocorrelation-consistent covariance matrix. Econometrica, 20: 73-103.

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

SAS Institute Inc. (2015). SAS/ETS 14.1 User's Guide. Cary, NC: SAS Institute Inc.

Schwert, G.W. (1987). Effects of model specification on tests for unit roots in macroeconomic data. Journal of Monetary Economics, 20: 73-103.

Seabold, S., and Perktold, J. (2010). Statsmodels: econometric and statistical modeling with python. In S. van der Walt and J. Millman (Eds.), Proceedings of the 9th Python in Science Conference (pp. 57-61).

Python 3.7
Numpy 1.18.1
Statsmodels 0.11.0
Pandas 1.0.1

There are no parameters. The program is set up to access test files in the .\results directory. This path can be modified in the source file.

Please see comments in the source file for additional info including referenced output for the test files.