How to calculate Hull Moving Average in Python?

Question

I'm glad that I can share my issue with you all and looking forward to learning from you all. My current issue is with def calculating_hma where I can't get the right results:

#python27

#inputs 
period = 9
Coin_pair = "USD-BTC"
Unit = thirtyMin''

def getClosingPrices(coin_pair, period, unit):
    historical_data = api.getHistoricalData(coin_pair, period, unit)
    closing_prices = []
    for i in historical_data:
        closing_prices.append(i['C'])
    return closing_prices


def calculate_sma(coin_pair, period, unit):

    total_closing = sum(getClosingPrices(coin_pair, period, unit))
    return (total_closing / period)


def calculate_ema(coin_pair, period, unit):

    closing_prices = getClosingPrices(coin_pair, period, unit)
    previous_EMA = calculate_sma(coin_pair, period, unit)
    constant = (2 / (period + 1))
    current_EMA = (closing_prices[-1] * (2 / (1 + period))) + (previous_EMA * (1 - (2 / (1 + period))))

def calculate_hma(coin_pair, period, unit):
    """
    Hull Moving Average.
    
    Formula:
    HMA = WMA(2*WMA(n/2) - WMA(n)), sqrt(n)
    """
    
    # MY Try of calculation ?
    ma = calculate_sma(coin_pair, period, unit)
    HMA = ma(2*ma(period/2) - ma(period)), sqrt(period)
    
    # my question  ?
    # where to use the unit and pierod and coin_pair in the calculation ?  

    # check inputs above
    return hma

ema = calculate_ema(market, period=9, unit=timeframe)
sma = calculate_sma(market, period=9, unit=timeframe)
hma = calculate_sma(market, period=9, unit=timeframe) ? 

print (ema)
print (sma)
print (hma)

Answer 1

Moving averages are usually defined with a signature of ma(series) -> series. I think a big part of your confusion roots in WMA being defined to return a series, not a single value as you are expecting.

A good, formal definition of the problem can be found here: https://oxfordstrat.com/trading-strategies/hull-moving-average/

here's a python implementation of a single-point HMA:

def weighted_moving_average(series: List[float], lookback: Optional[int] = None) -> float:
    if not lookback:
        lookback = len(series)
    if len(series) == 0:
        return 0
    assert 0 < lookback <= len(series)

    wma = 0
    lookback_offset = len(series) - lookback
    for index in range(lookback + lookback_offset - 1, lookback_offset - 1, -1):
        weight = index - lookback_offset + 1
        wma += series[index] * weight
    return wma / ((lookback ** 2 + lookback) / 2)


def hull_moving_average(series: List[float], lookback: int) -> float:
    assert lookback > 0
    hma_series = []
    for k in range(int(lookback ** 0.5), -1, -1):
        s = series[:-k or None]
        wma_half = weighted_moving_average(s, min(lookback // 2, len(s)))
        wma_full = weighted_moving_average(s, min(lookback, len(s)))
        hma_series.append(wma_half * 2 - wma_full)
    return weighted_moving_average(hma_series)

Answer 2

This can be easily solved with Pandas series. The whole formula:

HMA = WMA(2*WMA(period/2) - WMA(period)), sqrt(period))

given an input series s and a period can be packed into a single line:

import pandas as pd
import numpy as np

HMA = s.rolling(period//2).apply(lambda x: ((np.arange(period//2) + 1)*x).sum()/(np.arange(period//2) + 1).sum(), raw=True).multiply(2).sub(
                        s.rolling(period).apply(lambda x: ((np.arange(period) + 1)*x).sum()/(np.arange(period) + 1).sum(), raw=True)
                ).rolling(int(np.sqrt(period))).apply(lambda x: ((np.arange(int(np.sqrt(period))) + 1)*x).sum()/(np.arange(int(np.sqrt(period))) + 1).sum(), raw=True)

But for clarity and convenience it is better to define 2 functions:

def WMA(s, period):
       return s.rolling(period).apply(lambda x: ((np.arange(period)+1)*x).sum()/(np.arange(period)+1).sum(), raw=True)

def HMA(s, period):
       return WMA(WMA(s, period//2).multiply(2).sub(WMA(s, period)), int(np.sqrt(period)))

Answer 3

solved

def calculate_hma(coin_pair, period, unit):

    HMA = ((calculate_wma(coin_pair, int(period / 2), unit) * 2 - calculate_wma(coin_pair, period, unit)) + (
        calculate_wma(coin_pair, int(math.sqrt(period)), unit))) / 2