# Confusion with Augmented Dickey Fuller test

I am working on the data set electricity available in R package TSA. My aim is to find out if an arima model will be appropriate for this data and eventually fit it. So I proceeded as follows:

1st: Plot the time series which resulted if the following graph:

2nd: I wanted to take log of electricity to stabilize variance and afterward differenced the series as appropriate, but just before doing so, I tested for stationarity on the original data set using the adf (Augmented Dickey Fuller) test and surprisingly, it resulted as follows:

### Code and Results:

adf.test(electricity)

Augmented Dickey-Fuller Test
data:  electricity
Dickey-Fuller = -9.6336, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary
Warning message: In adf.test(electricity) : p-value smaller than printed p-value


Well, as per my beginner’s notion of time series, I suppose it means that the data is stationary (small p-value, reject null hypothesis of non-stationarity). But looking at the ts plot, I find no way that this can be stationary. Does anyone has a valid explanation for this?

Since you take the default value of k in adf.test, which in this case is 7, you’re basically testing if the information set of the past 7 months helps explain $x_t - x_{t-1}$. Electricity usage has strong seasonality, as your plot shows, and is likely to be cyclical beyond a 7-month period. If you set k=12 and retest, the null of unit root cannot be rejected,
> adf.test(electricity, k=12)