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