I see two reasons to answer "No." At least initially. (As my answer progresses they seem to grow in number.)
Short answer: I think the notion of anything like such predictions is more akin to incoherent than impossible or even merely impracticable, though this is hardly obvious from the outset.
Long answer. A fascinating question, that merits quite a long journey. A more rigorous treatment would probably merit a whole book.
I speak a lot of a simulator though the OP mentioned none. While prediction might be a purely mental exercise, at the scale queried it plainly requires significant extra-somatic data processing or complex analogue modelling. This I call a simulator.
First, the premise that no occurrence is random is false in every sense known to us. Chaos theory might come to mind in support of the notion that no macroscopic event has finite knowable inputs, but I don't understand that to be an ontological claim of chaos theory, which theory appears to reside in the domain of deterministic analysis, a technique which sidesteps the heart of the problem of crediting the prospect of predicting the future.
The outcome of quantum states are thoroughly described by probabilities rather than deterministically. This is not an epistemological claim (though some accounts of the uncertainty principle read that way, though, in any event, the uncertainty principle is not the sum of quantum theory). Rather, it is an ontological one. In other words, the world has randomness, it does not merely appear random.
Second, our biosphere, called Earth, is not a closed system. Nor is our solar system, nor any other scale short of the entire universe. And that is a lot of objects and states to keep track of.
And I suspect predicting your future is no less a task than predicting the whole future (of everything). Or at least the two merge asymptotically as the length your reach into the future grows. (I give short shrift to the potential that short-term predictions avoid this for most of my analysis -- but my comments on the impossibilities of collecting an initial-state data set should be construed as dispositive of the hope this is a fruitful exception to otherwise fatal problems.)
Now, if you think about it carefully, it seems you would need to keep track of the spin, charge, mass, direction, and speed of every particle in the universe to predict the future of everything. What would the record keeping look like? What would the record keeping media look like?
Actually, that's startlingly easy to imagine. The most compact record of the state of a quark would be an identical quark. Or, in our scenario the subject quark itself. Building from that observation, we quickly realize the most compact account of the present state of the universe is the present universe itself. Any independent description would have to be as large or larger. Of course, the notion an independent description (necessarily outside the universe) is essentially useless.
My point being that the universe can be accurately thought of as an analog computer that is capable of predicting its own future states in real time. In some sense, this is the only thing the universe actually "does" (other than merely being, which is really just the same thing).
The notion that anything less would suffice as a thorough predictive mechanism violates what we know about information storage. You simply cannot encode however many bits of information are needed to describe the totality of the present state of a quark into something less than a quark. (Unless the ultimate indivisible particle is smaller than a quark, then the notational limit I describe migrates down to that smaller particle.) Then these same observations all flow uphill to the larger structures of the universe which are wholly characterized by the totality of their substructures.
But is this really true. Maybe a description of the universe is compressible. But for that to be true, it seems there would have to be redundant structures in the universe, because that is ultimately what all compression algorithms leverage. That would seem to mean something like noting there are two identical molecules in the universe and I can use one as a proxy for the other. But that makes no sense. Even assuming they were identical to the most elemental level (I make no claim to the reasonableness or absurdity of such a notion), there remains the fact that it seems meaningless to assert they are fated to identical futures such that one can remain the proxy of the other. Does not data compression, in fact, work because it always has a static subject? Don't let moving pictures confuse the issue. The movie's data stream is static taken en toto. The fact that our minds view it in pieces sequentially is not the same as the data content being dynamic. It's the same movie each time you watch it. Yet nothing in reality is actually static (even digital data streams decay).
Now I admitted the future of a person in the short-term (and I have no idea how short "short-term" is) could turn on less than the state of the whole universe. But the notational problem still remains immense.
And the computational model is perhaps even more so. The maximum scale of complex physical systems that can be modeled (or simulated) in real time with infinitesimal precision presently is stunning small. To be honest, I am not entirely sure there is any scale we can model this way in real time. There are no examples I can think of where we have complete momentary data describing a starting point absolutely outside of those experiments in particle physics utilizing chambered high energy collisions. And frankly, the most detailed accounts I have seen of those suggest they are not based on complete knowledge notwithstanding the minuscule scope of those highly isolated "worlds." Analyses of these experiments are peppered with references to statistical methods, a seeming indication of less than absolute knowledge.
Another substantial wrinkle is that the most energetic particles can pass through as much as a light-year thick layer of lead. Unless these cast no influence upon "history" the notion that one can isolate analysis to some "manageable" subset of the near universe seems quite delusional.
Still another problem with predictions is that inasmuch as a simulator is essential, that requires knowledge of how the modeled system works. Plainly predicting the future of a person requires, among countless things, predicting the future of their mind. But our knowledge of the mind's workings is not even 3% what would be necessary to model it.
Further, we need a thorough account of an initial state to feed our prediction engine. Is not the crux of all interpretations of Heisenberg's uncertainty principle that one cannot collect a fine-scaled complete account of anything?
On top of all the above, how does one power such a grand simulator? Does the existence of the simulator not become a factor that needs simulation? Can a simulator be conceived of which simulates both the world (or even some subset of it) outside of itself and itself? I don't mean can such a simulator be conceived, I mean could such a conception be coherent or is it inherently nonsensical?
Ultimately, the notion of such predictive engines sounds no less absurd and nonsensical than the notion of the mind of an omniscient god. And is not the penultimate play of those clinging to such notions that the actuality of god transcends reason?
The more I reason this through the more convinced I am that I am converging on the conclusion that the only simulation that can predict the outcome of any non-trivial subset of existing reality is reality (the universe) itself.
PS: The is also the question of data integrity. As our capacity to store ever larger data sets grow we are coming to see the ever expanding complexity of maintaining a static account of a static data set (a subset of the problem of a reliable account of a dynamic data set). And this is in a world limited to nothing achieving even yottabit storage. I don't know off the top of my head what size a petabyte account of subatomic particles amounts to, but I suspect it's not even person-scaled.
This problem of data "decay" is external to the simulation and a defect that makes the scale of the simulation problem larger. The only scale at which it is manageable is at the scale of universe-as-a-predictor-of-history, because that simulation seems to move data decay inside the simulation where it manifests as quantum uncertainty, a causal element in history rather than mere noise.
PPS: Fantasies of predicting the future always seem pinned to hopes the world can be saved from quantum mechanics and returned to the comfortable deterministic model of nineteenth-century science. This is symptomatic of the admission that quantum mechanics has historic influence. But if QM has historic influence, does this not doom a simulator to have the requirement of matching the scale of what it models? Otherwise, the simulator will experience materially greater randomness than the subject.
Of course raising this objection suggests I am ignoring the more basic problem that a simulator even at matching-scale is doomed to experience different randomness than the subject, thus corrupting it conclusions.
Indeed, if the simulator worked, it would seem an epistemological apocalypse (1), as the production of a correct prediction could only seem to follow if either the randomness experienced by the simulator and the subject were the same (thus violating the definition of randomness and refuting a core tenet of QM) or the significance of QM in the causality of macroscopic phenomenon was trivial (violating a tenet of determinism -- which would be even more catastrophic to our understanding of the world than the collapse of quantum theory).
PPS: The subject of data integrity oddly raises perhaps the best tangible example of the interface of subatomic particles and macroscopic effects for our purposes. Some accounts of the subject identify energetic stray subatomic particles as among the causes of corruption of isolated bits within a data stream. If these claims are accurate, they strongly validate the notion that a predictive engine is a self-defeating objective more akin to perpetual motion machines than anything worthy of serious attempts. This conclusion builds on the notion that a predictive engine cannot differ in scale from the phenonmenon it models as noted above, a consequence of which is that attempts at error correction are intrinsically self-defeating in this endeavor as they grow the scale of the simulator.
(1) I am startled to learn from Google that no less than 109 people beat me to the punch coining that word pairing.