# Given time series data, how to model the frequency of someone changes his job?

I am given a time series data vector (ordered by months and years),which contains only 0s and 1s. 1 s represent a person changes his job at a particular a month.

Questions: What model can i use to determine model how frequently this person change his job ? In addition, this model should be able to predict the probability of this person changing his in the next 6 months.

A poisson process ? (I have studied poisson process before however I have no idea when and how to apply it). Any assumptions that data need to meet before applying the poisson process ?

Would love to gather more information on how to model something like this. Thanks

• Transform your data to be a list of number of month between events (in Matlab this would be diff(find(V)) where V is your current time series vector. Then try to fit an exponential distribution to this by estimating the rate parameter. rate, would be a decent metric of the frequency of job changes. The exponential distribution should show how the probability will increase with time since the last event. You also might want to test for a goodness of fit after estimating rate: – Dan Jul 17 '14 at 9:41
• what is the equivalent of diff(find(V)) in R ? – user1769197 Jul 17 '14 at 10:22
• I don't know much R but I'll explain the Matlab code: find return the element number of the 1s, diff returns the difference between each consecutive number. Hence that line just returns a vector of the number of months between each job change. – Dan Jul 17 '14 at 10:46
• I'll point back to this link again: stats.stackexchange.com/questions/76994/… looks like r has a fitdistr function – Dan Jul 17 '14 at 16:00
• actually, i just manually computed the MLE of $\lambda$ of exponential distribution. – user1769197 Jul 17 '14 at 16:08

## 2 Answers

A simple and perhaps somewhat naive approach would be to assume that a person changes jobs at a constant rate and that previous job changes have no influence on future ones. Under these assumptions you could model the job changes as a Poisson process and estimate the rate parameter using MLE (http://en.wikipedia.org/wiki/Poisson_process and http://en.wikipedia.org/wiki/Poisson_distribution).

Of course one should explore how well these assumptions hold in the data. To do this, you could study whether or not job changes are independent of one another by computing the correlation between events at various lags (http://en.wikipedia.org/wiki/Correlation). You could also plot the distribution of time between job change events. If the process is Poisson-like then you should observe little to no correlation between events at any number of lags and the distribution of time between job change events should be exponentially distributed (http://en.wikipedia.org/wiki/Exponential_distribution).

Take a look at the R package tscount. The first 13 pages are very theoretical, so skip ahead to the examples: https://goo.gl/D7hZPH