This is a good observation that I upvoted because it's very relevant. A lot of things look like cycles but have no oscillating dynamic, it's true.
But you could suppose that business cycles are caused by a build-up of bad debt. Things to well, debts can be paid, collateral gets worth more, more investment, etc. This can't go on forever and the reverse cycle then occurs, often as rates come up. Soros store about this and called it reflexivity.
Of course I'm not saying business cycles are definitely caused by this, there's probably more to it than that. But it's a common explanation.
Why does it build up? A generalized autoregressive model explains that just as well as an oscillator does. The key difference is how predictable the periods are. The more waves you're composing to force the oscillator model to fit, the less likely it's appropriate.
But you could suppose that business cycles are caused by a build-up of bad debt. Things to well, debts can be paid, collateral gets worth more, more investment, etc. This can't go on forever and the reverse cycle then occurs, often as rates come up. Soros store about this and called it reflexivity.
Of course I'm not saying business cycles are definitely caused by this, there's probably more to it than that. But it's a common explanation.