have been arriving

arrive可用作 continuous tense 嗎?
當然可以，
- The fans are arriving early to get free admission.
- I will be arriving in Paris this time tomorrow.


你的句子在修詞上有一些問題。
late 是副詞 ，應該放在動詞arrive之後
Since the summer he has been arriving (really) late for training.


自(今年)夏天以來，他一直都遲到了培訓。

If the above Chinese expression is really what you mean, there are better expressions in English:

Since this summer he has been late for training.
Since this summer he has been late in arriving at the training site.

late 是形容詞

2015-06-14 15:29:01 補充：
late for school 上學遲到
late for work 上班遲到
late for meeting 開會遲到
late for meeting 訓練遲到
e.g Nicklas Bendtner missed Wolfsburg 's Bundesliga game with Schalke at the weekend because he was late for training on Friday.

2015-06-14 15:30:47 補充：
late for training 訓練遲到

2015-06-14 23:26:17 補充：
You're right! 到達 是 一刻子的動作
所以，以下兩句都錯:
He has been arriving since the summer.
He has arrived in Hong Kong since last Monday.

2015-06-14 23:46:42 補充：
The expression "arrive late/early" has a shift of an action (arrive) to a status (being late) in meaning.

So, I won't be surprised to hear somebody saying "He has been arriving late for work ..."

But, I insist on using "has been late" (100% stative verb).

2015-06-15 14:58:36 補充：
"have been arriving" + "late" represents a serious of repeated events of being late in arriving.

2015-06-15 14:59:35 補充：
typo above: a series of repeated events

2015-06-15 15:07:07 補充：
Present perfect continuous can sometimes be used to express the meaning of a series of repeated events as indicated by the Event verb.

He has been arriving late for work for 10 years.

"arriving late for work" was a series of repeated events in the past 10 years.

2015-06-15 23:04:02 補充：
will arrive = your plan is on a fixed schedule
will be arriving = there is an uncertainty about your plan

2015-06-15 23:29:34 補充：
will be playing (durative) = an event in progress at a particular point in the future

你兩句子都是錯, arrive 不是 durative verb.
"arrive" is not normally used in continuous tense.
但有例外
"The fans are arriving early to get free admission"
"fans" 是 plural, 他們先後到達, 在不同的時間,
有點像川流不息, 所以用 continuous tense

2015-06-15 06:14:28 補充：
"The guests are arriving." ~ ABC news

When a continuous tense is used, the interpretation is that a reference is being made to the approach of the event.

Joe told Mary that Pia’s plane was arriving.
It means that although Pia’s plane had not yet arrived, it would arrive very soon.