# P-value of Augmented Dickey-Fuller test and KPSS test

I would like to test if the time series of the US 3-month treasury bills (monthly data from 1934 to 2015) is stationary. I'm using the ADF test in R (from the package tseries), but I get contradictory results: if I change the alternative hypothesis the p-value is always high.

Augmented Dickey-Fuller Test

data: x Dickey-Fuller = -2.0698, Lag order = 9, p-value = 0.5488 alternative hypothesis: stationary

Augmented Dickey-Fuller Test

data: x Dickey-Fuller = -2.0698, Lag order = 9, p-value = 0.4512 alternative hypothesis: explosive

The same thing happen if I use the KPSS test (p-value is always low):

KPSS Test for Level Stationarity

data: x KPSS Level = 3.3275, Truncation lag parameter = 7, p-value = 0.01

KPSS Test for Trend Stationarity

data: x KPSS Trend = 2.1869, Truncation lag parameter = 7, p-value = 0.01

What am I doing wrong?

With ADF, what you do is to test both the null of a unit root against a stationary process as well as against an explosive process, i.e., in a model like $y_t=\rho y_{t-1}+\epsilon_t$, that $\rho=1$ against $|\rho|<1$ or against $\rho>1$.