pyhctsa.operations.pre_process.preproc_model_fit¶

pyhctsa.operations.pre_process.preproc_model_fit(y, model='ar', order=2, random_seed=None)¶

How the error of an AR model changes after preprocessing the series.

Fits an autoregressive (AR) model to the time series and to a set of preprocessed versions of it, and returns the in-sample root-mean-square (RMS) one-step prediction error for each preprocessed version as a ratio of the RMS prediction error for the original series. Every version is z-scored before the model is fitted. The AR model is fitted by forward-backward least squares.

Only one representative of each family of preprocessings (from hctsa’s PP_PreProcess) is fitted, as the other candidates were found to correlate at r >= 0.95 with one of these:

• d1: incremental differencing (first differences)

• d2: second differences

• p1_20: a straight line removed in each of 20 equal segments (piece-wise linear detrending)

• p2_5: a quadratic removed in each of 5 equal segments (piece-wise quadratic detrending)

• rmgd: the values replaced by Gaussian values of the same rank (rank mapping to a Gaussian distribution)

Parameters:¶

y : array-like¶

The input time series.

model : str, optional¶

The time-series model to fit to the transformed series (currently 'ar' is the only option).

order : int, optional¶

The order of the AR model to fit. Default is 2.

random_seed : int, 'default', 'none' or None, optional¶

The seed of the random draws used by rmgd (hctsa’s BF_RandomSeed): an integer, 'default' or None for seed 0, or 'none' for a seed drawn from NumPy’s global random state. The draws come from the portable generator pyhctsa.robust.bf_random(), so they are hctsa’s for the same seed.

Returns:¶

The ratios of the RMS prediction error of the AR model for the preprocessed series to that for the original series: stderat_d1, stderat_d2, stderat_p1_20, stderat_p2_5, stderat_rmgd. A ratio above 1 means the preprocessing left the series harder to predict, as when it removes a trend or slow dynamics that the model had been exploiting.

Return type:¶

dict