I have time-series data, let's say a pandas series, with time (sampling frequency is hourly) as its index and temperature measurement across that time. I want some statistical/time-series principle which can tell whether a time-series is well-behaved or not.
What I mean by well behaved time-series is that, let's say the distribution of temperature for a day is same/almost identical for all 7 or even 30 days of the month. The reason for detecting even a slight deviation is to know whether some sensors that collect temperature are working properly or not. The device, whose temperature sensors are measuring every hour, has the property that it's temperature distribution for the whole day remains almost identical throughout the month.
Best Answer
Maybe start simple. If you are expecting distributions to be identical day to day, test each day's against the baseline (whatever you consider normal): http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ks2samp.htm
If you are looking to anomaly detection intraday, and you have a good model for the distribution, can you just have a probability cut-off for outliers?