Fracdiff

class fracdiff.sklearn.Fracdiff(d=1.0, window=10, mode='same', window_policy='fixed')

A scikit-learn transformer to compute fractional differentiation.

Parameters:

• d (float, default 1.0) – The order of differentiation.

• window (int > 0 or None, default 10) – Number of observations to compute each element in the output.

• mode ({"same", "valid"}, default "same") – See fracdiff.fdiff() for details.

• window_policy ({"fixed"}, default "fixed") –

  “fixed” (default) :

  Fixed window method. Every term in the output is evaluated using window observations. In other words, a fracdiff operator, which is a polynominal of a backshift operator, is truncated up to the window-th term. The beginning window_ - 1 elements in output are filled with numpy.nan.

  ”expanding” (not available) :

  Expanding window method. Every term in fracdiff time-series is evaluated using at least window observations. The beginning window - 1 elements in output are filled with numpy.nan.

coef_

Sequence of coefficients in the fracdiff operator.

Type:

numpy.array, shape (window,)

Examples

>>> from fracdiff.sklearn import Fracdiff
>>> X = numpy.arange(10).reshape(5, 2)
>>> fracdiff = Fracdiff(0.5, window=3)
>>> fracdiff.fit_transform(X)
array([[0.   , 1.   ],
       [2.   , 2.5  ],
       [3.   , 3.375],
       [3.75 , 4.125],
       [4.5  , 4.875]])
>>> fracdiff.coef_
array([ 1.   , -0.5  , -0.125])

>>> fracdiff = Fracdiff(0.5, window=3, mode="valid")
>>> fracdiff.fit_transform(X)
array([[3.   , 3.375],
       [3.75 , 4.125],
       [4.5  , 4.875]])

>>> X = numpy.array([1, 0, 0, 0]).reshape(-1, 1)
>>> fracdiff = Fracdiff(0.5, window=4)
>>> fracdiff.fit_transform(X)
array([[ 1.    ],
       [-0.5   ],
       [-0.125 ],
       [-0.0625]])

fit(X, y=None)

Fit the model with X.

Parameters:

• X (array_like, shape (n_samples, n_features)) – Time-series to perform fractional differentiation. Here n_samples is the number of samples and n_features is the number of features.

• y (array_like, optional) – Ignored.

Returns:

self – Returns the instance itself.

Return type:

object

transform(X, y=None)

Return the fractional differentiation of X.

Parameters:

• X (array_like, shape (n_samples, n_series)) – Time-series to perform fractional differentiation. Raises ValueError if n_samples < self.window.

• y (array_like, optional) – Ignored.

Returns:

fdiff – The fractional differentiation of X.

Return type:

numpy.array, shape (n_samples, n_series)