There are many dedicated Timestamping Services for this Use-Case, one that has been around since '95 and with a corrrespondingly solid reputation IMHO is http://www.itconsult.co.uk/stamper/stampinf.htm. But there are other services as well, just search for "Timestamping Service"... I'd steer clear of the Bitcoin-based ones, they tend to be... enthusiastic but not too proffessional.
OriginStamp is a Bitcoin-based service that seems to be solid.
It’s used by, for example, namespace’s Project Registration Database. (I built a custom PmWiki plug-in for this purpose, that allows any wiki page (or any wiki page you want) to automatically be OriginStamp’d upon creation. I haven’t released the code yet, but if anyone’s interested, I will.)
Proving you made the statement at a given time is as simple as getting a trusted signed timestamp or inserting it in some blockchain-like ledger, but that's not even close to making yourself accountable for predictive accuracy.
Be sure to publish *all* your predictions so we don't get file-drawered (except on you as a person which we probably can't help).
A common technique is to publish a secure hash of your prediction rather than the text (in case you want to avoid it being self-fulfilled or anti-fulfilled or otherwise traded on) (crypto signed w/ your identity, too).
But if we don't see a stream of plaintext reveals and a means of identifying all such hashes you've published, we might suspect you of planting both positive and negative predictions.
Most people prefer to publish their prediction (+reasoning) clear-text because they want to persuade and they want credit for being smart before the verdict is in.
I guess the best way is just to post on a bunch of platforms and have those web pages back-up by various archiving services (notably the Wayback Machine).
Publishing a book is probably too much work for most used cases.
I've also heard one could publish text on the Bitcoin blockchain for example, but I'm not sure how well that works.
I guess the best way is just to post on a bunch of platforms and have those web pages back-up by various archiving services (notably the Wayback Machine).
Note that you can also set up your writing to be automatically archived via archive.is (example).
It's important to specify what you want to prove, to what standards of evidence, to whom, and how far in the future?
There are a few answers about how you can timestamp or archive things in ways that provide pretty good timestamp and content evidence. None of the suggestions so far provide identity evidence (that it was you who said it, not someone claiming to be you), and it's unclear who'll accept the evidence later.
For legal purposes, go lower-tech. File a statement with a court or court-recognized agent, notarized or certified by an agent registered to do so. This is more about chain-of-trust and assertion of timing and identity than about any technological or math trickery.
For casual/social "proof" over reasonably short timeframes (a few years), twitter is probably good enough.
With an asymmetric cryptographic key you can sign messages to prove that those messages came from the same specific private key. You can then create strong evidence of the identity of the key (that you have the key) by using systems/accounts that are identified to you and that only you have access to share other signed messages that proves that the owner of the account has the private key in question. This is probably more convenient and trusted world wide (some people might not trust authorities of unknown countries but might trust some online systems that are known worldwide) while offering a comparable level of security/trust to my opinion. The traditional channels of law/notary/governments have their benefits too (like physical inspection to match a government provided ID) but it looks like to me that they also have bigger costs (harder to access the data (probably not digitalized or protected from public acces) , higher fees, potentially less recognized worldwide)
If you create a new twitter account (and make the first tweet(s) include your name and some quotes from the intro of https://books.google.com/books/about/The_Prophecies.html?id=neZvDwAAQBAJ&printsec=frontcover&source=kp_read_button ) and then put all your predictions, and only your predictions, in it - that would be an easy time stamped record.
An important use case would be for tracking predictions reliability.
Ideally this should also reduce risks of positive bias.