Understanding when a trend breaks in a Time Series I have a set of over 400 days within my time series, my goal is to detect when a particular trend breaks and another one begins. For example, for days 1-30, an ARIMA(0, 1, 1) will be the most appropriate, but from days 30-74 an ARIMA(2, 1, 2) will the best fit.
Is there a way I can check something like this? My understanding was the ACF function but I'm a bit confused about this now too. Could someone point me to some resources that may explain?
 A: If you google "change point analysis" you will find tons of pointers.
It is not clear to me from your question whether you want to check for
a change at a suspected, fixed point in time or rather you want to screen your time series for possible changes at some (unspecified) point of time. In the first case you might search for "intervention analysis" or "interrupted time series" (which seems to be a popular name for the same thing in medical and biological literature).
A: If you look for techniques in R, the CRAN task view on time series analysis curates a list of packages for changepoint detection and analysis (https://cran.r-project.org/web/views/TimeSeries.html). Here is the relevant excerpt:

Change point detection is provided in strucchange and strucchangeRcpp (using linear regression models) and in trend (using nonparametric tests). The changepoint package provides many popular changepoint methods, and ecp does nonparametric changepoint detection for univariate and multivariate series. changepoint.np implements the nonparametric PELT algorithm, changepoint.mv detects changepoints in multivariate time series, while changepoint.geo implements the high-dimensional changepoint detection method GeomCP. InspectChangepoint uses sparse projection to estimate changepoints in high-dimensional time series. VARDetect implements multiple change point detection in structural VAR models. Rbeast provides Bayesian change-point detection and time series decomposition. breakfast includes methods for fast multiple change-point detection and estimation.

