I'm starting to familiarize myself with ARIMA models to better understand time series analysis, and my question is: is time-series analysis essentially a complex regression model where time is the sole independent variable?

What is the approach if I want to include time/periodicity/seasonality as one element (read: of a larger analysis?

I was thinking of an example where I'm trying to predict the optimal inventory level at my clothing store. Of course time-series analysis is a big part of this, but what if I want to incorporate some categorical variables that potentially drive my outcome?

Thanks for the thoughts! I'm not expecting anyone to "solve" anything here, more just point me to resources or concepts I can research further.