You might have heard of Fourier transforms. Any time-series can be transformed into its sinusoidal components, even if a composition of waves is not a good model.
It's possible, and in my opinion more likely, that the business cycle is not a cycle at all.
Consider my mind blown - thank you !
If you look at trends over an arbitrary period, they may look useful.
If you look at the similar trends over a larger period, they look different.
Therefore, the smaller periods are just random variations relative to the larger periods.
For example, sometimes it rains, and sometimes the sun shines. Is the weather cyclical? Depends on the place, time, and time-scale you're considering.
Maybe a better example is roulette. If you watch the "cycles" of red and black, you might imagine you could make predictions. Gamblers are often fooled by this randomness.
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.