Examples/references for not changing tense when using reported speech

Solution 1:

Careful writers will report He said, 'I'm going on holiday next week' as He said he was going on holiday the following week. (Note the three changes: I > he, 'm > was, next > following.) However, in speech and in informal writing often only the personal pronoun will change, with no change in meaning.

EDIT

Today is Monday 23 April. If I want to refer to the week beginning Monday 30 April I will say next week and not the next week. So I might say, for example, I’m going on holiday next week and not I’m going on holiday the next week. If someone reports what I say at some time in the future, then it will be He said he was going on holiday the following week, although He said he was going on holiday the next week is just about possible. However, if someone reports what I said soon after I say it, then it’s He said he was going on holiday next week.

Solution 2:

It is perfectly ok not to change the tense if what the speaker says is still true and you have no reason to doubt the reliability or veracity of the statement. It is also correct to backshift the tense in such circumstances, and this is what older pedagogic grammars might prescribe.

The backshift becomes the more usual choice however if you want imply that you consider the statement dubious or unreliable in some way. In such circumstances of course you would often go on to say why.