ExpandingSlope

Description

The ExpandingSlope function returns the ordinary-least-squares slope of the samples seen so far against an implicit integer time axis x = 0, 1, ..., n-1. It is the whole-history analogue of RollingPoly1 with derivative_order=1. Undefined (NaN) until at least two samples have been seen. Memory is O(1).

Equation:

\[ y[t] = \frac{n\sum i\,x[i] - (\sum i)(\sum x[i])}{n\sum i^2 - (\sum i)^2}, \quad i=0..t,\; n=t+1 \]

Parameters: none.

NaN handling

Policy: ignore. A NaN in the input at index t causes the function to skip that step: output at t is NaN and internal state is unchanged. Subsequent finite samples are processed as if step t had not occurred.

Examples

Usage example

import numpy as np
from screamer import ExpandingSlope

x = np.arange(1.0, 11.0)
y = ExpandingSlope()(x)