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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$\begingroup$ 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? $\endgroup$– gung - Reinstate MonicaDec 15, 2012 at 17:40
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$\begingroup$ 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? $\endgroup$– Hans RudelDec 15, 2012 at 17:52
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2 Answers
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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.
answered Dec 15, 2012 at 18:00
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$\begingroup$ 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. $\endgroup$ Dec 15, 2012 at 18:14
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$\begingroup$ 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. $\endgroup$ Dec 15, 2012 at 20:27
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If your measure of non-randomness is autocorrelation then you might find the ideas expressed here useful.
answered Dec 15, 2012 at 18:19
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$\begingroup$ 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. $\endgroup$ Dec 15, 2012 at 20:30