The simple rule is: If you use a singular noun that is not a proper noun (i.e. the name of someone or something), it must be preceded by an article (a/the), a possessive pronoun (my/his/etc), or one of a small set of other adjectives (like "one").

This rule is unaffected by any other adjectives that may happen to be present. That is, for example, "dog" requires an article, like "the dog". If you say "big brown furry dog", it still requires an article: "THE big brown furry dog".

But if you used the dog's name, then there should not be an article. "Rover buried his bone", NOT "The Rover ..."

Don't get distracted by the words "according to". These have nothing to do with it. The rule would be the same regardless of what other words surround it.

So example 1 is correct. The noun is "specification". This is singular, and so requires an article.

Example 2 is incorrect. The noun is "forecast", which is singular, and so it should be "According to a Bank of Russia forecast ..."

I think the writer in example 2 was tripped up by the presence of the phrase "Bank of Russia". This is being used as an adjective to modify "forecast". What kind of forecast? A Bank of Russia forecast. But the writer may have seen the proper name here and thought that this meant there should not be an article.

It's also possible that an editor changed the sentence incorrectly. If the writer had left out the word "forecast" and used "Bank of Russia" as the noun, then there should be no article. "According to Bank of Russia, ..." If someone -- whether the original writer or someone else -- later said, "We really should specify that it's a forecast and not the current state", and so added the word forecast, they might have failed to realize that they now also needed to add an article.