Is the month ordinal or nominal variable? I read in some article that the month of the year was being considered as qualitative nominal variable, but for me the month of the year has a clearly ordered structure and should therefore be considered as qualitative ordinal. Am I right?
On the same article it was said that the year was a qualitative ordinal variable. I am OK with that, but I also wanted to ask if it was possible to consider the year as quantitative discrete.
 A: I find it hard to believe that there are grounds for regarding year or month as qualitative. You don't give a precise reference and you don't report the argument, so further comment on that view is difficult for me. 
A year variable with values such as 2018 is evidently quantitative and numeric (I don't distinguish between those) and ordered (2018 > 2017 > 2016) and also interval in so far as differences such as 2017 $-$ 1947 are well defined (as indeed we all know from childhood in working with people's ages). It's not a ratio scale in so far as the zero point is arbitrary. The test is that ratios such as 2017/1947 make no substantive sense. (Detail: There was in history, even in retrospect, no year zero; 1 BC/BCE is deemed to have been followed immediately by 1 AD/CE; no one complained at the time if only because the labelling was introduced much later. Recall that zero took some time to be accepted as a basic mathematical idea.) 
(The illustration here uses the "Western" calendar; the same arguments apply to any other calendar, so far as I am aware.) 
It's not even essential to regard year as discrete. Whenever in physical or environmental science (for example) something varies continuously with time, so we have (e.g.) monthly or daily measurements, so too time can be regarded as continuous: 2017.5 is well defined as half-way through 2017. 
The case of month is interesting. First, we need to be clear that monthly dates such as January 2018 are quantitative, numeric, ordered and interval insofar as for the purposes of CV they will generally be handled in terms of a count of months before and after some origin used by particular software. Good software arranges that dates are shown conventionally, but calculations are based on integers on a defined scale. 
Month of the year January to December or 1 to 12, say, is quantitative and numeric and ordered in so far as no person who completed elementary education reasonably well has a problem in putting the months in order. But the order is circular, in so far as a particular 12 is necessarily followed by another particular 1. 
This may clash with any narrow definition of ordinal scale you encounter, but such a clash just shows lack of imagination and experience on the part of the definer, or more charitably an attempt to keep things simple by leaving out complications from some introduction or elementary treatment. Ordinal, I suggest, means "can be placed in a definite and repeatable order" and doesn't exclude that order being circular. 
Evidently it's just a convention to start with January: we all know at least a little about calendars associated with particular religions or say academic, financial and hydrological years. So, to spell it out, month of year is not a ratio scale as the origin is quite arbitrary. And indeed it can be convenient, even natural, to think that years "start" in months other than January. 
Circular scales are all around you.... A full and busy statistically-based career could conceivably include no need to work with circular scales, but 


*

*seasons: spring, summer, autumn (fall), winter 

*months: December January ... December January ... 

*day of year 1 to 365 or 366 (complicated by leap years)

*compass direction (aspect, azimuth) 
are some basic examples. Circular scales usually need care and attention, so for example the mean of directions 1 degree (just East of North) and 359 degrees (just West of North) is not sensibly 180 degrees (South).
The unequal lengths of months may or may not be important detail. In practice (at least in fields I know about) people with monthly data usually treat the months as equally spaced and as equally long, even though that's not quite right. This is a matter of convenience rather than a denial of fact. 
A: Month should be considered qualitative nominal data. With years, saying an event took place before or after a given year has meaning on its own. There is no doubt that a clear order is followed in which given two years you can say with certainty, which year precedes which.
As for months, on their own, you cannot. I agree that there is, in some sense, an order to months but the order or relative positions (without the years the months correspond to) provide no information on their own. For example, if someone deduces that car accidents are most likely to occur in May of all the months by looking at historical data, the relative position of the months have nothing to do with the pattern. I think it is fundamentally incorrect to think of months as a circular scale. In theory, January 2018 can be distinct from January 2019 in every conceivable way. There is no weight in saying that there is a circularity in months. They are labels, arbitrarily chosen by humans, to literally 'nominate' time.
