# Identifying periods of non random behavior in time series

Im looking for some pointers on which topics I should be looking into in order to identify periods (of non fixed length) which deviate from randomness. I have a feeling hypothesis testing may be what I'm looking for though I haven't covered it yet. My stats knowledge is limited hence any suggested books / websites would also be appreciated.

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I don't quite follow the premise of your question. Are you asking how to know if your time-series data are stationary? That's a very fundamental issue in ts analysis. Are you wanting to identify seasonality, or regime changes? – gung Dec 15 '12 at 17:40
No, i dont believe so. Im trying to determine how its possible to "identify some deviation from randomness by inspecting some standardized statistical output and observing some anomaly." any ideas? – Hans Rudel Dec 15 '12 at 17:52

Periods which deviate from randomness are called Unspecified Interventions, waiting to be discovered. If the period is 1, it is called a pulse. If the period is >1 and the "size" of the non-randomness has the same magnitude for all the values in the time range this is called a step/level. If the non=randomness has the same magnitude for periods that are "S time points apart", this is called a Seasonal Pulse. If the non-randomness follows a linear trend this is called a Time Trend. Software to do this can be found in SAS, SPSS, AUTOBOX (which I am involved with) in varying degrees of "correctness". You might pursue "automatic intervention detection" to get some reading material.

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+1, this is a nice layout of the options. – gung Dec 15 '12 at 18:10
are you aware of any books which may cover this topic, or will i have to look into papers? Ive had a scan on google/amazon but havent been able to find any. +1 for addressing all the possible scenarios. – Hans Rudel Dec 15 '12 at 18:14
I would begin by reading unc.edu/~jbhill/tsay.pdf . I would then read amazon.com/Time-Analysis-Univariate-Multivariate-Methods/dp/… for more on Intervention Detection ( not simply Intervention Modelling ). As I mentioned AUTOBOX (autobox.com) has a 30 day free trial which you can download and use in expanding your knowledge in this area. After the 30 day period is up you can still use it and learn by example how these approaches work for thousands of text-book time series. It is a good way to learn. You could also read many of my posts here at SE. – IrishStat Dec 15 '12 at 20:27

If your measure of non-randomness is autocorrelation then you might find the ideas expressed here useful.

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+1 thanks for the link, ill check it out. – Hans Rudel Dec 15 '12 at 19:50
Thanks I should have mentioned that and also the idea that non-randomness can sometimes be attributed to changing parameters over time or changing error variance over time, both of which I often address myself to. – IrishStat Dec 15 '12 at 20:30