I solve Rubik's cubes as a hobby. I record the time it took me to solve the cube using some software, and so now I have data from thousands of solves. The data is basically a long list of numbers representing the time each sequential solve took (e.g. 22.11, 20.66, 21.00, 18.74, ...)
The time it takes me to solve the cube naturally varies somewhat from solve to solve, so there are good solves and bad solves.
I want to know whether I "get hot" - whether the good solves come in streaks. For example, if I've just had a few consecutive good solves, is it more likely that my next solve will be good?
What sort of analysis would be appropriate? I can think of a few specific things to do, for example treating the solves as a Markov process and seeing how well one solve predicts the next and comparing to random data, seeing how long the longest streaks of consecutive solves below the median for the last 100 are and comparing to what would be expected in random data, etc. I am not sure how insightful these tests would be, and wonder whether there are some well-developed approaches to this sort of problem.