Detect periodic events within data I have a collection of card transactions, each with a date, amount, card identifier and merchant. I want to determine if a card is making periodic payments to a given merchant. The issue is that the period is unknown, there may be some variance (i.e. different days in a month, sometimes the bill is paid a few days late), and there may be interspersed events that do not match the cycle.
Ultimately I want to extract the subset of transactions that are found to be periodic (if any exists)
I think to start with I would just use the date vs binary payments (i.e. whether a payment was made or not, disregarding amount)
Could someone point me to some approaches to this? My background is not in statistics and so far my googling has proved inadequate. Thanks
 A: I would not recommend turning the data into 0/1 . I have had a lot of experience with daily  bank payment data , ATM access , deposits etc.. If the payments are systematic/regular to a particular day of the month then its is fairly straightforward to identify these patterns. If however the data is non-systematic then I would suggest a two stage approach. Stage 1 would identify pulses and record the date and the magnitude of the pulse. The second stage would require a rule-based approach where you took the pulses and the data es that were associated with them and pooled/analyzed them according to your specification i.e. things 1 day apart or 2 days apart from regular should be considered/classified as part of the same family. Another way is to use the size of the pulse/unusual value as the qualified for grouping. Detecting unusual activity requires a model that incorporates the routine e.g. day-of-the-week effects, holiday effects, weekly effects, monthly effects and any auto-correlative structure evidenced in your data. Commercially available software may have to  customized/improved to deal with this potentially thorny issue but that's typical of how software develops as a result of it's documented current inadequacy. 
