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.