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 tau-step 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 lag of the transitions: the pairs (s[t], s[t + tau]) of the discretized series, for every t. An integer, or a rule 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), or one of these computed from the ranks of the series ('ac-rank', 'ac1e-rank', 'mi-rank'); see pyhctsa.utils.get_tau(). With a rank-based rule, the result is unchanged by a strictly increasing transformation of the series. NaN is returned if the delay is undefined or leaves no transition. 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