If you have daily data over the past 20 years, then, while it is technically not continuous (in that you can’t be halfway between Jan 1 and Jan 2), it would be absurd to treat it as categorical. But if you only have a few dates, then it might make sense to treat date as a category.

Are dates interval data?

Dates themselves are interval, but I could see cases where they could be any of those four. Then you will transpose the date into day and that could be nominal. Often, you will treat dates as ordinal, e.g. if you are looking at something and want to model it in terms of who was president at the time.

Is month a continuous or categorical variable?

What type of variable is ‘month’? The correct answer is c) Categorical. This is because months of the year are divided into distinct categories.

Month should be considered qualitative nominal data.