ありがとうございます。is standard full sentence. ありがとうございました。is past tense sentence. ありがとう。is abbreviated/shortened sentence.
Whatever language we speak, mentioning full standard sentence is formal and therefore gives polite impression. If you make speech at formal occasions, you had better avoid omission/abbreviation, deformation, phonetic changes and any other deviations because it would give impression to audiences that speaker is showing a sincere attitude.
At informal situation, you may freely use those deviations with people you feel near and intimate.
About the tense for ありがとうございます, there seems two factors which will make speaker to choose ます form or ました form.
1. tense of topic or object for which speaker wants to express his gratitude. ます for on-going matter and ました for past matter. ⇒ こんなかけがえのないものを下さるなんて、ありがとうございます。 ⇒ あの時は困っていた私を助けてくださり、ありがとうございました。
2. speaker's psychological attitude to the matter. Whenever speaker wants to show his gratitude as current and existing emotion even though its object took place many years ago, ます will be chosen. ⇒ ５年前に力を貸して頂いたおかげで、私はここまで発展することができました。お力添えを片時も忘れたことはございません。誠にありがとうございます。
On the contrary, speaker may express ました form against on-going kindness. For example, someone unexpectedly fallen in difficulty and foreigner extended his hand for help. But this kind foreigner seems belonging socially disrespected class and this someone doesn't feel easy to be seen the situation by passers by. So even though the help has not been completed, he/she would say: ⇒ どうもありがとうございました。あとはもう自分でやりますから、はい、はい。ありがとうございました。
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