I have a discrete-valued time series and would like to analyse it, but dont know where to start Due to some health issues, each day at about the same time, I give myself a score which represents the state of my health: specifically, fatigue, with 1 being the worst and 10 the best. In practice, the scores are between 3 and 9.
I have over three years' worth of data. I'd like to understand it: trends (if there are any) or periodic behaviour.
I have a degree in mathematics (and a PhD  in statistics, but in a very specialised area) but little specific knowledge of time series.
Can anyone suggest where I could start with analysis, before I dive in and teach myself time series analysis?
 A: I'd recommend running a number of graphical summaries. Here are a few useful examples, which you can run using the forecast package in R (even if your goal is not forecasting per se).
Specifically, I would recommend looking at the overall time series, as well as season plots - against both yearly seasonality (if you suffer from seasonal affective disorder, this should be obvious in such a plot) and weekly seasonality (to see if you are frequently tired on Monday mornings). 
With three years of daily data, the first kind of plot will be noisy (consider smoothing the data before plotting), and the second kind will be crowded (consider plotting not the raw weekly curves, but boxplots or jittered dotplots or beanplots/violinplots over each day of the week).
If your data's discreteness gives you problems, jitter each data point by a small amount, say a uniformly distributed random number between -0.2 and 0.2. Then multiple entries of 2 will turn into entries between 1.8 and 2.2 and be more easily distinguished, while still being obviously distinct from entries at 1 and 3.
Finally, a season-trend decomposition and its associated plot will be useful to see trends. Use the stl() command, and see here.
