Pytorch Fractional Differencing

!pip install torch numpy pandas python-binance

import pandas as pd
import numpy as np

def get_weights_floored(d, num_k, floor=1e-3):
    r"""Calculate weights ($w$) for each lag ($k$) through
    $w_k = -w_{k-1} \frac{d - k + 1}{k}$ provided weight above a minimum value
    (floor) for the weights to prevent computation of weights for the entire
    time series.

    Args:
        d (int): differencing value.
        num_k (int): number of lags (typically length of timeseries) to calculate w.
        floor (float): minimum value for the weights for computational efficiency.
    """
    w_k = np.array([1])
    k = 1

    while k < num_k:
        w_k_latest = -w_k[-1] * ((d - k + 1)) / k
        if abs(w_k_latest) <= floor:
            break

        w_k = np.append(w_k, w_k_latest)

        k += 1

    w_k = w_k.reshape(-1, 1) 

    return w_k

def frac_diff(df, d, floor=1e-3):
    r"""Fractionally difference time series via CPU.

    Args:
        df (pd.DataFrame): dataframe of raw time series values.
        d (float): differencing value from 0 to 1 where > 1 has no FD.
        floor (float): minimum value of weights, ignoring anything smaller.
    """
    # Get weights window
    weights = get_weights_floored(d=d, num_k=len(df), floor=floor)
    weights_window_size = len(weights)

    # Reverse weights
    weights = weights[::-1]

    # Blank fractionally differenced series to be filled
    df_fd = []

    # Slide window of time series, to calculated fractionally differenced values
    # per window
    for idx in range(weights_window_size, df.shape[0]):
        # Dot product of weights and original values
        # to get fractionally differenced values
        date_idx = df.index[idx]
        df_fd.append(np.dot(weights.T, df.iloc[idx - weights_window_size:idx]).item())

    # Return FD values and weights
    df_fd = pd.DataFrame(df_fd)

    return df_fd, weights

import torch
def get_weights_floored(d, num_k, floor=1e-3):
    r"""Calculate weights ($w$) for each lag ($k$) through
    $w_k = -w_{k-1} \frac{d - k + 1}{k}$ provided weight above a minimum value
    (floor) for the weights to prevent computation of weights for the entire
    time series.
    
    Args:
        d (int): differencing value.
        num_k (int): number of lags (typically length of timeseries) to calculate w.
        floor (float): minimum value for the weights for computational efficiency.
    """
    w_k = torch.DoubleTensor([1.])
    k = 1
    
    while k < num_k:
        w_k_latest = -w_k[-1] * ((d - k + 1)) / k
        if abs(w_k_latest) <= floor:
            break

        w_k = torch.cat((w_k, w_k_latest.unsqueeze(0)))
        
        k += 1
    
    return w_k.flip(0)

def frac_diff_fast(df, d, floor=1e-3, weights=None):
    r"""Fractionally difference time series via CPU.
    
    Args:
        df (pd.DataFrame): dataframe of raw time series values.
        d (float): differencing value from 0 to 1 where > 1 has no FD.
        floor (float): minimum value of weights, ignoring anything smaller.
    """
    # Get weights window
    if weights is None:
        weights = get_weights_floored(d=d, num_k=len(df), floor=floor)
    weights_window_size = len(weights)

    

    df_fd = torch.DoubleTensor([])
    for idx in range(weights_window_size, df.shape[0] + 1):
        df_fd = torch.cat((df_fd, torch.dot(weights, df[idx - weights_window_size:idx]).unsqueeze(0)))

    

from binance.client import Client
client = Client()
klines = client.get_historical_klines('BTCUSDT', Client.KLINE_INTERVAL_1HOUR, "1 Jan, 2019")
df = pd.DataFrame(klines, columns=['opentime', 'open', 'high', 'low', 'close', 'volume', 'closetime', 'assetvol', 'numbertrades', 'takerbasevol', 'takerquotevol', 'ignore']).astype(np.float64)
df.head()

import time
start = time.time()
frac_diff(df[['close']], d=0.5)
duration = time.time() - start
f"Numpy Frac Diff took {duration}"

start = time.time()
data = torch.DoubleTensor(df[['close']].values).flatten()
frac_diff_fast(data, d=0.5)
duration = time.time() - start
f"Pytorch Frac Diff took {duration}"