pyhctsa.operations.symbolic.transition_p_alphabet¶

pyhctsa.operations.symbolic.transition_p_alphabet(y, num_groups=None, tau=1)¶

How transition probabilities change with alphabet size.

The time series is discretized by quantile separation into alphabets of a range of sizes, and the one-time transition matrix is computed for each. Statistics of those transition matrices are then tracked as a function of the alphabet size. The exponential fits are global least-squares fits (bf_exp_fit(), with no offset), so R^2 lies between 0 and 1; the linear fits are ordinary least squares.

Parameters:¶

y : array-like¶

The input time series.

num_groups : array-like, optional¶

The range of alphabet sizes to compare across. Must contain more than one value, each at least 2. Default is range(2, 11).

tau : int or str, optional¶

The time-delay. The time series is downsampled at this lag before being discretized. Can also be set to a string that sets it from the series: 'ac' (the first zero-crossing of the autocorrelation function), 'ac1e' (the floor of its first 1/e crossing) or 'mi' (the smaller of the first minimum of the Kraskov automutual information and the ‘ac1e’ delay; see pyhctsa.utils.get_tau()). All three are capped at floor(N/50); NaN is returned if the delay is undefined. Default is 1.

Returns:¶

The decay rate of the sum, mean, and maximum of the diagonal elements of the transition matrices, changes in symmetry, and statistics of their eigenvalues.

Return type:¶

dict