Is Bach's brain a Markov chain? Recurrence quantification to assess Markov order for short, symbolic, musical compositions.

It is rarely possible to precisely characterise the system underlying a series of observations. Hypothesis testing, which involves assessing simple assumptions about driving mechanisms, provides hope that we can at least rule out certain possibilities regarding the nature of the system. Unfortunately, the brevity, nonstationarity, and symbolic nature of certain time series of interest undermines traditional hypothesis tests.