# Can a time series be stationary and still have seasonality?

Would there be a case that a time series does have seasonality but, ADF test fails to point it out. I want to be sure of it being stationary so that I can use it in a regression and be sure that the results are not spurious.

• You seem to equate a statistical test with a property of an underlying process. Although the distinction may seem subtle, it's important. So, what exactly do you mean by "be stationary"? – whuber Nov 27 '19 at 22:52
• A time series with a seasonal component is non-stationary. If your target variable is stationary, it doesn't have a seasonal component, and therefore it seems unlikely to me that a seasonal time series is really an appropriate regressor. The fact that you think it is causes me to wonder, along with @whuber, what exactly you mean by "be stationary". See stats.stackexchange.com/questions/131092/…, which your question may be a duplicate of. – jbowman Nov 27 '19 at 23:10
• Note that the first answer, despite being accepted, got a pretty negative score and a lot of disagreement. However, mea culpa; this stats.stackexchange.com/questions/174741/… one is a better quick reference. – jbowman Nov 28 '19 at 1:03
• Why not refer to Rob Hyndman's explanation on otexts.com/fpp2/stationarity.html#fn14? "A stationary time series is one whose properties do not depend on the time at which the series is observed. Thus, time series with trends, or with seasonality, are not stationary — the trend and seasonality will affect the value of the time series at different times." There's a footnote to this definition though. – Isabella Ghement Nov 28 '19 at 5:25
• @whisperer, if I read your last comment correctly, you seem to read the ADF test as an omnibus test against all sorts of possible violations of stationarity (e.g. the ones mentioned by Isabella). It definitely cannot do that. It is, broadly speaking, a test of the null of a stochastic trend against the alternative of mean reversion. – Christoph Hanck Nov 28 '19 at 8:50