openquant.fracdiff

Compiled from Rust (crates/pyopenquant). Signatures and types are from the shipped .pyi stubs; descriptions are the functions’ own docstrings, as help() shows them. All Python modules.

Functions

frac_diff

frac_diff(series: Sequence[float], diff_amt: float, thresh: float) -> list[float]

Fractionally difference a series with an expanding window.

Output t applies the first t + 1 weights of (1 - B)^d to series[0..=t] (AFML Snippet 5.2). Leading outputs whose weights on missing history exceed thresh of the total absolute weight are NaN: thresh=1.0 skips nothing (the mlfinlab default), AFML uses 0.01. The growing number of terms causes a drift (AFML 5.5.1), so prefer frac_diff_ffd for features. Pass levels (prices or log prices), not returns. Nothing is validated; a NaN input poisons every later output. Cost is O(n^2).

Parameters

series : list[float]

Levels, oldest first.

diff_amt : float

Differencing order d.

thresh : float

Share of total absolute weight allowed on missing history before an output is NaN.

Returns

list[float]

Differenced series, same length as series, with leading NaNs.

frac_diff_ffd

frac_diff_ffd(series: Sequence[float], diff_amt: float, thresh: float) -> list[float]

Fractionally difference a series with a fixed-width window (FFD).

The weights are get_weights_ffd(diff_amt, thresh, len(series)); each output is their dot product with the matching trailing window, so the first len(weights) - 1 outputs are NaN (AFML Snippet 5.3). A threshold too small for the data gives a window as long as the series and a single non-NaN output. Each output uses only values at or before its own position. Pass levels (prices or log prices), oldest first, not returns. Nothing is validated; a NaN poisons every output whose window covers it.

Parameters

series : list[float]

Levels, oldest first.

diff_amt : float

Differencing order d.

thresh : float

Minimum absolute weight kept in the window (see get_weights_ffd).

Returns

list[float]

Differenced series, same length as series, with leading NaNs.

get_weights

get_weights(diff_amt: float, size: int) -> list[float]

First size fractional-differencing weights of order diff_amt.

The weights of (1 - B)^d follow w_0 = 1, w_k = -w_{k-1} (d - k + 1) / k (AFML Snippet 5.1). They are returned oldest lag first, so the last element is w_0 = 1 and the one before it is -diff_amt. Nothing is validated.

Parameters

diff_amt : float

Differencing order d (may be fractional).

size : int

Number of weights to return.

Returns

list[float]

size weights, oldest lag first (empty when size is 0).

get_weights_ffd

get_weights_ffd(diff_amt: float, thresh: float, lim: int) -> list[float]

Fixed-width-window fractional-differencing weights of order diff_amt.

Uses the recursion of get_weights and stops before the first weight whose absolute value is below thresh, or once lim weights exist, whichever comes first (AFML Snippet 5.3). For a non-integer diff_amt the weights never reach zero, so a thresh of 0 or less (or NaN) means "cap only" and yields exactly lim weights. thresh is a floor on a single weight's magnitude, not a share of cumulative weight as in frac_diff.

Parameters

diff_amt : float

Differencing order d (may be fractional).

thresh : float

Minimum absolute weight to keep.

lim : int

Maximum number of weights.

Returns

list[float]

At most lim weights, oldest lag first (last element 1.0); empty when lim is 0.