Could blockchain technology prove that time travel is possible?
No... Those two are totally different concepts...
The patterns would be similar to the patterns that occur in insider trading. The time traveler's trading activity would show that he is making the right bet more often than is statistically likely. However, a smart time traveler would probably change his address after each trade or bet, so it would be impossible to link his various transactions together. In this way, block chain technology would make it more difficult to prove time travel, as it makes it easier for the time traveler to hide his tracks.
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Why would blockchains make this any easier than any other technology? Most of the trading activity that happens with blockchains happens on exchanges. Why would it make any difference whether the trading was with cryptocurrencies or with traditional securities on an ordinary exchange like CME or NASDAQ?

In other words, I don't see why blockchains would help give us any information about time travel.
Blockchain technology is the result of technological advances, and is born due to artificial intelligence, blockchain is relatively inpossible for time travel is possible. Yet it is possible through the supernatural, only through the supernatural able to defeat artificial intelligence.
This is a very easy question to answer. You'd only need to look for the mandela effect. Slight changes in the letters of the exchanges. Instead of Bittrex .. you may see Bitrex.

This would be due to tears and shifts in parallel universes. So it wouldn't be so much time travel happened with the tech. As much as it would be the overlapping of other universes and earths now using the tech. So as the both universes would be so similar you'd hardly notice any difference at all. So look for slight changes like that.