Inferring present and the future states or events from past states and events - the kind of activity you appear to have in mind in your opening sentences - is a form of induction. Popper on induction is a tangled topic but, to express a standard interpretation, Popper finds no proper use for induction in science :
[As an empiricist he] interpret[s] empiricism - 'the thesis that experiment alone can
decide upon the truth or falsity of scientific statements' - as being satisfied by
falsifiability alone, for 'the method of falsification presupposes no inductive
inference. (Andrew J. Swann, 'Popper on Induction', The British Journal for the Philosophy of Science, Vol. 39, No. 3 (Sep., 1988), pp.
Falsifiability can be explained as follows. You can verify - find confirming instances of - a universal statement indefinitely but however many confirmations you find, unless you can enumerate the class concerned, you can never tell if there are instances you have not examined and which falsify - refute - the universal statement. Verification is useless to the extent that it fails to cover, in the typical scientific situation, the whole class of objects that fall under the universal statement. Falsification in contrast is very useful. One contrary instance, one object in the relevant class for which the universal statement fails, refutes the universal statement.
Induction has no place in science
". . . It is from universal statements in conjunction with initial conditions [GT: the situation in or to which the universal statement is applied for testing] that we deduce the singular statement, 'this thread will break'.
We call this statement a specific or singular prediction." (Popper, The Logic of
Scientific Discovery, London, 1959, p. 60.)
.. . If the singular conclusions turn out to be acceptable, or verified,
then the theory has, for the time being, passed its test: we have found
no reason to discard it. But if . . . the conclusions have been falsified,
then their falsification also falsifies the theory from which they were
logically deduced." (op. cit., p. 33).
The mode of reasoning is entirely deductive. (K. K. Lee, 'Popper's Falsifiability and Darwin's Natural Selection', Philosophy, Vol. 44, No. 170 (Oct., 1969), pp. 291-302: 292.)
Science and history
Two points are relevant. The first is that concepts such as 'revolution', 'political change', 'dictatorship', 'democracy', 'populism' - the kind of descriptions I take it you are concerned with - are too imprecise and contestable to
form the subjects of rigorous, falsifiable universal statements (or 'theories', as Popper also calls them).
The second point is one that Popper makes in the Intro to The Poverty of Historicism (1957) - a title that takes a nice dig at Marx's The Poverty of Philosophy (1847. Namely, that the future is impossible to predict in the form of universal statements because there will be unknowable future inventions the effects of which we are unable to take into account in formulating such statements. This is true now about the future, and it will be true of all future futures.
One might wonder on what basis, save that of induction, Marx can infer that since there have been unpredicable or at least unpredicted inventions in the past, there will also be such inventions in the future.
I have probably explained ideas such as falsifiability with which you are already perfectly familiar. I've included them just in case they are new to some members.