No, this is a mistake. First, the seasonality can be included in the ADF regression as control deterministic variables. The stochastic property of the time series will not be affected by deterministic variables.

You should not detrend your data either. This assumes that the time series has no deterministic trend, which probably is not a wise assumption.

The ADF test can test for both difference-stationary and trend-stationary at the same time. Unfortunately, it can get complicated because you have a joint hypothesis but only one equation to test it.

Let me give you some simple examples. If the t-ratio on the once-lagged variable and the t-ratio on the time trend are both not statistically significant, then there is a chance that the time series is difference-stationary. The next step is to use a simple F-test to test for the exclusion restriction (i.e., dropping both the once-lagged variable and the time trend). But, what if there is one significant t-ratio and one insignificant t-ratio, or both t-ratios are statistically significant? In this case, the original Null hypothesis is rejected in favor of the alternative hypothesis. But what is the alternative hypothesis? It is ill-defined. The practical (but not supported by any theory) step forward is to choose one of the three possibilities: 1) the time-series requires first-differencing and a time trend to render it stationary; 2) the series is a stationary series; 3) the series is trend-stationary.

Prof. Ahking

I agree with Prof Ahking. I further recommend the DFGLS test, which is a more powerful test. Here is the reference:

Elliott, G. R., Rothenberg, T.J., and Stock, J. H., (1996). Efficient tests for an autoregressive unit root. Econometrica 64: 813–836. https://doi.org/10.2307/2171846.

The only shortcoming of the DFGLS test is that the data set must not have any gaps.

According to a post on ResearchGate, it is generally recommended to remove or account for the trend and seasonality components of the time series before applying the Augmented Dickey-Fuller (ADF) test. This is because the ADF test assumes that the time series is stationary and removing trend and seasonality components can help achieve stationarity.

This is incorrect. The ADF test (or its variants) makes no such assumption. In fact, the ADF test is used to do a preliminary assessment of the stochastic property of a given time series, namely, trend-stationary vs. differenced-stationary vs. both.

Prof. Ahking

With respect to the text by Chuck A Arize reported earlier that claims that the ADF test presumes that the time series is stationary is not correct. Instead, the null hypothesis in the ADF test is that the data series has a unit root and thus is nonstationary. For an expanded discussion of these issues, please seeArticle CO 2 has significant implications for hourly ambient tempera...

Yes, it's advisable to remove trend and seasonality components before applying the Augmented Dickey-Fuller (ADF) test to ensure the stationarity of the time series data.

With all due respect, the classic Augmented Dickey-Fuller test is not always the best approach because it can fail to reject the null hypothesis of nonstationary when, in fact, it is false. Here is a link to a more useful test:https://en.wikipedia.org/wiki/ADF-GLS_test