pmdarima.utils.diff_inv

pmdarima.utils.diff_inv(x, lag=1, differences=1, xi=None)

Inverse the difference of an array.

A python implementation of the R diffinv function [1]. This computes the inverse of lag differences from an array given a lag and differencing term.

If x is a vector of length \(n\), lag=1 and differences=1, then the computed result is equal to the cumulative sum plus left-padding of zeros equal to lag * differences.

Parameters:

x : array-like, shape=(n_samples, [n_features])

The array to difference.

lag : int, optional (default=1)

An integer > 0 indicating which lag to use.

differences : int, optional (default=1)

An integer > 0 indicating the order of the difference.

Returns:

res : np.ndarray, shape=(n_samples, [n_features])

The result of the inverse of the difference arrays.

References

[R94]

https://stat.ethz.ch/R-manual/R-devel/library/stats/html/diffinv.html

Examples

Where lag=1 and differences=1:

>>> x = c(10, 4, 2, 9, 34)
>>> diff_inv(x, 1, 1)
array([ 0., 10., 14., 16., 25., 59.])

Where lag=1 and differences=2:

>>> x = c(10, 4, 2, 9, 34)
>>> diff_inv(x, 1, 2)
array([  0.,   0.,  10.,  24.,  40.,  65., 124.])

Where lag=3 and differences=1:

>>> x = c(10, 4, 2, 9, 34)
>>> diff_inv(x, 3, 1)
array([ 0.,  0.,  0., 10.,  4.,  2., 19., 38.])

Where lag=6 (larger than the array is) and differences=1:

>>> x = c(10, 4, 2, 9, 34)
>>> diff_inv(x, 6, 1)
array([ 0.,  0.,  0.,  0.,  0.,  0., 10.,  4.,  2.,  9., 34.])

For a 2d array with lag=1 and differences=1:

>>> import numpy as np
>>>
>>> x = np.arange(1, 10).reshape((3, 3)).T
>>> diff_inv(x, 1, 1)
array([[ 0.,  0.,  0.],
       [ 1.,  4.,  7.],
       [ 3.,  9., 15.],
       [ 6., 15., 24.]])