# How can I determine if a time-series is statistically stable?

I have time-series data that tracks the number of sydromics records my organization receives each week. The number of records had been steadily increasing as more organizations started sending us data and now I'm trying to figure out if the number of messages we see each week has begun to stabilize around a mean over the past few months. Could I simply test if the time series has become stationary? Or use a control chart? I am very stumped as to what tests/techniques to use so I would greatly appreciate some help.

Thank you.

There exist various approaches to testing whether a time series is stationary. One of the most popular approaches is based on unit root test family of tests, which include Augmented_Dickey-Fuller (ADF) test (available in R as tseries::adf.test()), Zivot-Andrews test (available in R as urca::ur.za()) and several others (see the links in the unit root test Wikipedia article). Another approach is to use the KPSS test, which is considered complimentary to unit root testing. Finally, there are approaches, based on spectrum analysis, which include Priestley-Subba Rao (PSR) test and wavelet spectrum test. Some theoretic discussion and examples are available via the previous link as well as in corresponding section of the online textbook "Forecasting: principles and practice" by professors Rob J. Hyndman and George Athana­sopou­los: http://www.otexts.org/fpp/8/1.