There are a number of possible models at a variety of levels of complexity. These include
(some are very closely related):
Time series regression with lagged variables
Lagged regression models. See also distributed lag models
Regression with autocorrelated errors
Transfer function modelling /lagged regression with autocorrelated errors
ARMAX models
Vector autoregressive models
State-space/dynamic linear models can incorporate both autocorrelated and regression components
Because your input series is 0/1 you may want to look at lagged regression with autocorrelated errors, but watch for seasonal and calendar effects (like holidays).
So simple-ish models might perhaps look something like
$\qquad\text{ Sales}_t = \phi_0+\phi_1\,\text{Sales}_{t-1} +\beta_3\,\text{job}_{t-3}+\beta_4\,\text{job}_{t-4}+\epsilon_t$
or perhaps something like
$\qquad\text{ Sales}_t = \alpha +\beta_3\,\text{job}_{t-3}+\beta_{12}\,\text{job}_{t-12}+\text{seasonal}_{t}+\eta_t$
where $\eta_t$ is in turn some ARMA model for the noise term (though you may well want more lags in there than just one) -- or a variety of other possibilities. [The seasonal term above doesn't have a parameter because it's likely to have several components, and so several parameters; consider it a placeholder for a model for that component of the data. Neither of those models are likely to be sufficient, they're just to get a general sense of what a simple model might look like]
You may also want to consider whether the binary job-status variable needs a model itself (if you want to forecast further than the smallest lag involving it, it may well be essential to at least consider whether there are any such effects there -- see transfer function models, but you have to consider the special nature of the binary variable)
Once you have an appropriate model for sales that captures the main features well, you can look as testing. You should have enough data (looks like several years) to hold some data out for out-of-sample model testing and validation. I'd start by considering the features of sales alone - is it stationary? Autocorrelated? Does it experience any seasonal/cyclical or calendar components? Are there other major drivers to consider?
Since you mention R, note that the function tslm
in the package forecast
can be handy for including seasonal or trend components in regression models.
A book that discusses nearly all of those topics is Shumway and Stoffer Time Series Analysis and its Applications (3rd ed is at Stoffer's page here). Another highly recommended text is Forecasting Principles and Practice, Hyndman and Athanasopoulos, here, which covers some of the things I mentioned (but not as many).
Best Answer
In terms of practical down-to-earth examples , I might suggest reviewing some of my 583 replies to time-series model building questions. It is the only subject that I know and feel competent to comment on and thus is the only area that I do so. @gung nicely pointed to one of them in his response. Most are real data case studies where the data is delivered by the OP and procedural issues are raised.
In terms of theory/overview I can recommend a presentation that I made 8 years ago to the International Society of Forecasters ( http://www.autobox.com/stack/dpr-isf27.ppt ) . In particular on slide 41 I presented an analysis of monthly ice cream sales from Norway. As shown it is a univariate (non-causal) model whereas when temperature is incorporated (not shown) the "seasonality" vanishes as temperature is the driver and then needs to be forecasted in order to forecast ice cream sales.