Which model to use?

Hi all,

I am attempting to model some data but it has been a while since I completed my masters so my statistical skills are not what they used to be :(

Right so, I have some data that gets reported on a weekly basis - this could either be a 4 weeks or 5 week cycle. So let's say for example as of 1 Apr 2016:-

Week 4 Snapshot, Week 8 Snapshot, Week 13 Snapshot, Week 17 Snapshot, Week 21 Snapshot, Week 26 Snapshot, Week 30 Snapshot

So what I am wanting to do is forecast performance moving forward. However, the main issue is that what gets reported on each of these weeks is very much dependent on another variable which works on the basis of a payment cycle so e.g. week 1 - big rise.. lowers again until week 5.. big rise.. so that being in the 5 week cycle there could be two big rises but in a 4 week cycle there will be one that could fall in an early week up until the actual snapshot week.

I think this is best explained visually so I have attached an image. I am wanting to predict Y at a particular time using historic Y data but also take into account the timing of Z i.e. if Z occurred in the same week as the time of reporting (highlighted in yellow) then I expect a big rise in Y, but also if Z occurred in the previous week then also a rise but a less significant effect. However (refer to screenshot for this) if Z occured in Week 1 then I am expecting a low number for Y as at Time = 4, but for Week 13 I am expecting a really high number because of the occurrence of Z at Weeks 9 and 13.

I was thinking it could be time series modelling that would help me achieve this? For example, if it's a sales model there will be peaks in certain periods then it will calm and peak again - possibly seasonal modelling? And then of course I am wanting to apply this using a statistical package - most likely R which I am familiar with.

Any help of course is much appreciated,