need advise

What methodology exists to analyze whether a process that gives a time
series has changed? In other words,consider the process occurring in a
black box,all we see is the time series,and we know if at some point
the process has changed. Is there a way to tell how many data points
one must have to be sure there has been a change? Is the moving
average the most sensitive way to detect a change? Or is there some
other method? If one models the process with ARIMA, what approach
could you take to decide if the model has suddenly become in
adequate,how long would you have to wait to tell? I'm afraid this has
a simple answer but I can't find it in my book on time series. Thanks
for any help. jk
.

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