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I have collected performance data at fixed time intervals from a 'shared system' with the aim of investigating the affect of the sharing on the performance of my 'slice' of the system. The performance as claimed should be consistent over time, the actions of the neighbors are unobserved apart from the affect on my performance.

Unfortunately I cant post time plots collected (over a two week period) or the plot of differences as I'm new here.

There is no reason to believe that the series should have any deterministic trends and my initial belief is that a good model would be 

P(t)=constant + random variation

However, the performance series certainly appears non-stationary (and rejects a KPSS test of stationary with no trend) and the correlogram decays very slowly whilst the pacf shows no non-significant correlations after 15 lags. Looking at my time plot and the differenced series the variance appears to be changing. I'm new to time series analysis and would appreciate any pointers and what might be a useful direction to take the analysis in. My understanding (which may well be wrong) is that non constant variance together with serial correlation in a series gives rise to local trends - stochastic trends? Would a ARCH/GARCH model be applicable here or should I try ARIMA models first?

I'm less interested in forecasting future performance and more interested in understanding the structure of the data.

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  • $\begingroup$ What is the fixed interval at which measurements are taken? Does there appear to be seasonality (e.g. weekends different from weekdays, business hours different from off-hours, etc)? Also, what kind of data is "performance data": times, counts, percentages, etc? $\endgroup$
    – Wayne
    Commented Apr 1, 2013 at 15:54
  • $\begingroup$ The performance data is a (standard) CPU benchmark which times how long a task takes to complete -taken at fixed intervals of 15 minutes. There is no periodicity in the data, there are also no 'global' linear trends but some of the experiments showed some local ones - so performance got better linearly over a period of 3 days in one case. But in general the data is non-stationary but with no cycles or trends. $\endgroup$
    – user23774
    Commented Apr 1, 2013 at 16:22
  • $\begingroup$ actually don't think what I am asking makes much sense in terms of the ARMA/GARCH since the residuals (or innovations) in an ARMA model are either purely random white noise (iid zero mean and constant variance) or modeled using GARCH which allows the unconditional variance to vary? So I guess having obtained a stationary series through differencing I should try to fit an ARMA model to it. I imagine there are then tests to see if the variance of the residuals should be constant or not? $\endgroup$
    – user23774
    Commented Apr 2, 2013 at 0:21

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