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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.

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  • $\begingroup$ Out of curiosity, what data would you use to "predict the optimal inventory level at [your] clothing store"? Is the optimal level observable? $\endgroup$
    – Adrian
    Commented Feb 12, 2016 at 16:48
  • $\begingroup$ I suppose the "optimal level" would be defined as minimizing the risk of running out of stock. In addition to time I might want to incorporate the occurrence of an event near my store (if I sold sport-team apparel) or non-seasonal promotions. Sorry this is pretty hypothetical. I'm just wondering about explaining the variance of a process with variables other than time. $\endgroup$
    – Austin T
    Commented Feb 12, 2016 at 16:55
  • $\begingroup$ I changed "IV" to "independent variable" because "IV" has a very common meaning of "instrumental variable". $\endgroup$
    – Richard Hardy
    Commented Feb 12, 2016 at 19:39

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<...> is time-series analysis essentially a complex regression model where time is the sole independent variable?

I had some trouble defining what a regression model is; you may see the relevant thread here. Hence, I am not sure whether a time series model such as ARIMA (with a non-empty MA part) or GARCH may be considered regression models (for example, they both involve some latent variables that are nontrivial to recover, and GARCH does not even have an error term in the conditional variance equation).

But superficially you seem to have the right intuition. There is the dependent variable and perhaps a linear time trend or some other function of time. There may also be seasonal effects, e.g. seasonal dummies or certain autoregressive moving-average structures as found in SARIMA models. There may also be other exogenous regressors. Actually, if there are "a lot of" exogenous variables but the autoregressive moving-average structure is "simple", then the model may look quite similar to a regular regression. For example, there exists a model called regression with ARMA errors. It is a regression with one extra trick: model residuals are not i.i.d. (as in an ordinary regression) but follow an ARMA process.

<...> time-series analysis is a big part of this, but what if I want to incorporate some categorical variables that potentially drive my outcome?

You can do that by including these variables just like you include seasonal dummies or time trends.

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  • $\begingroup$ This is great info, thank you. I will look at Regression with ARMA errors. Thanks for understanding the hypothetical nature of my question! $\endgroup$
    – Austin T
    Commented Feb 12, 2016 at 19:42
  • $\begingroup$ Just to make sure: I am not advertising any models, they were given as examples. Whether they fit your needs or not is a different question. $\endgroup$
    – Richard Hardy
    Commented Feb 12, 2016 at 19:44
  • $\begingroup$ Of course, they'll set me down the path to the right solution with no guarantees how many steps I'll have to take to get there! :) $\endgroup$
    – Austin T
    Commented Feb 12, 2016 at 19:51
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To answer your title question:

Is Time the only independent variable?

No

In Multivariate Time Series Models, time is not the only independent variable. Here are some references:

http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc45.htm

Is it possible to do a time series analysis with more than one explanatory variable?

Building a time series model using more than independent variables

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