How can I check when I can (statistically) fly to given locations most cheaply? [duplicate]

You can use Google Flights to perform such a search.

By clicking on the date icon (departure or return date) and then on the histogram icon, you can see how the prices vary during the year:

You approach might not completely make sense. How do you define those historical prices? The cheapest fare ever sold on the plane? The average price paid by people who took it? The cheapest fare available shortly before departure?

Since fares universally go up as a plane gets fuller and the departure date nears, average price is going to be higher for fully booked flights but that's trivial and not so relevant to your purpose. Maybe there was an ultra-cheap fare on that flight too and it simply sold earlier (it's also possible there wasn't but a simple average won't tell you that).

What about flexibility? If you are on a flight with many business travellers that don't pay for their tickets themselves and prefer flexible fares with lots of miles, the average price paid by all passengers on the plane will be higher but it does not mean that the cheapest available fare at any given time was more expensive.

Same thing for short-haul flights to large hubs. Sometimes, a person flying directly to a hub will pay more than someone else on the same flight who then connects to another flight. With some crazy routings and other tricks (cf. fuel dumping), you can even save money by going somewhere else and flying through your departure point to some other far away destination. What's the meaning of the average fare on this feeder flight?

Instead of looking at statistical trends or past data, you might be best served by checking what fares are available right not and booking the cheapest one you can find. See How can I do a "broad" search for flights? for tools to do that.

You could use Google Trends Google Trends and select the travel section. After pick your destination and enter

flights to Spain

, you will be able to see when that queries is getting more and more popular and when it decrease. You could cross compare those trends with the price you found with Google Flights. Hope that information can help you.