FRAMA: Fractal Adaptive Moving Average

References

Definition

  • The Fractal Adaptive Moving Average (FRAMA) was developed by John Ehlers.
  • The indicator is constructed on the EMA exponential moving average algorithm, with a smoothing factor calculated on the basis of the current fractal dimension of the price.
  • The advantage of the indicator is the ability to track strong trend movements and market consolidation moments.

Read the indicator

The interpretation of the indicator is identical to the interpretation of moving averages

  • The FRAMA line is relatively “flat” in periods of horizontal range trading. It could therefore be used to avoid many false signals when it is desired to use a technique of the crossing of moving averages.
  • The FRAMA line has a greater reactivity to changes in trends than moving averages, making it possible to take a much earlier position on a breakout of the horizontal channel.
Load basic packages 
import pandas as pd
import numpy as np
import os
import gc
import copy
from pathlib import Path
from datetime import datetime, timedelta, time, date

#this package is to download equity price data from yahoo finance
#the source code of this package can be found here: https://github.com/ranaroussi/yfinance/blob/main
import yfinance as yf

pd.options.display.max_rows = 100
pd.options.display.max_columns = 100

import warnings
warnings.filterwarnings("ignore")

import pytorch_lightning as pl
random_seed=1234
pl.seed_everything(random_seed)

Global seed set to 1234





1234

#S&P 500 (^GSPC),  Dow Jones Industrial Average (^DJI), NASDAQ Composite (^IXIC)
#Russell 2000 (^RUT), Crude Oil Nov 21 (CL=F), Gold Dec 21 (GC=F)
#Treasury Yield 10 Years (^TNX)

#benchmark_tickers = ['^GSPC', '^DJI', '^IXIC', '^RUT',  'CL=F', 'GC=F', '^TNX']

benchmark_tickers = ['^GSPC']
tickers = benchmark_tickers + ['GSK', 'NVO', 'AROC', 'GKOS']

#https://github.com/ranaroussi/yfinance/blob/main/yfinance/base.py
#     def history(self, period="1mo", interval="1d",
#                 start=None, end=None, prepost=False, actions=True,
#                 auto_adjust=True, back_adjust=False,
#                 proxy=None, rounding=False, tz=None, timeout=None, **kwargs):

dfs = {}

for ticker in tickers:
    cur_data = yf.Ticker(ticker)
    hist = cur_data.history(period="max", start='2000-01-01')
    print(datetime.now(), ticker, hist.shape, hist.index.min(), hist.index.max())
    dfs[ticker] = hist

2022-09-10 22:19:15.989643 ^GSPC (5710, 7) 1999-12-31 00:00:00 2022-09-09 00:00:00
2022-09-10 22:19:16.349383 GSK (5710, 7) 1999-12-31 00:00:00 2022-09-09 00:00:00
2022-09-10 22:19:16.721121 NVO (5710, 7) 1999-12-31 00:00:00 2022-09-09 00:00:00
2022-09-10 22:19:16.968170 AROC (3791, 7) 2007-08-21 00:00:00 2022-09-09 00:00:00
2022-09-10 22:19:17.186939 GKOS (1816, 7) 2015-06-25 00:00:00 2022-09-09 00:00:00

ticker = 'GKOS'
dfs[ticker].tail(5)
Open High Low Close Volume Dividends Stock Splits
Date
2022-09-02 49.590000 50.900002 48.419998 48.830002 650900 0 0
2022-09-06 49.200001 49.200001 47.630001 48.099998 334400 0 0
2022-09-07 52.759998 60.919998 51.490002 57.009998 4560500 0 0
2022-09-08 56.439999 59.599998 56.439999 58.380001 1106900 0 0
2022-09-09 58.369999 58.529999 55.860001 56.299999 1291100 0 0
Define FRAMA calculation function 
#https://github.com/peerchemist/finta/blob/master/finta/finta.py
def cal_frama(series: pd.Series, period: int = 16, batch: int=10) -> pd.Series:
        """Fractal Adaptive Moving Average
        :period: Specifies the number of periods used for FRANA calculation
        :batch: Specifies the size of batches used for FRAMA calculation
        """

        assert period % 2 == 0, print("FRAMA period must be even")

        window = batch * 2

        hh = series.rolling(batch).max()
        ll = series.rolling(batch).min()

        n1 = (hh - ll) / batch
        n2 = n1.shift(batch)

        hh2 = series.rolling(window).max()
        ll2 = series.rolling(window).min()
        n3 = (hh2 - ll2) / window

        # calculate fractal dimension
        D = (np.log(n1 + n2) - np.log(n3)) / np.log(2)
        alp = np.exp(-4.6 * (D - 1))
        alp = np.clip(alp, .01, 1).values

        filt = series.values
        for i, x in enumerate(alp):
            cl = series.values[i]
            if i < window:
                continue
            filt[i] = cl * x + (1 - x) * filt[i - 1]

        return pd.Series(filt, index=series.index, name=f"FRAMA{period}")
Calculate FRAMA 
df = dfs[ticker][['Open', 'High', 'Low', 'Close', 'Volume']]
df = df.round(2)

df_ta = cal_frama(df['Close'], period = 16, batch = 10)
df = df.merge(df_ta, left_index = True, right_index = True, how='inner' )

del df_ta
gc.collect()

80

display(df.head(5))
display(df.tail(5))
Open High Low Close Volume FRAMA16
Date
2015-06-25 29.11 31.95 28.00 31.22 7554700 31.22
2015-06-26 30.39 30.39 27.51 28.00 1116500 28.00
2015-06-29 27.70 28.48 27.51 28.00 386900 28.00
2015-06-30 27.39 29.89 27.39 28.98 223900 28.98
2015-07-01 28.83 29.00 27.87 28.00 150000 28.00
Open High Low Close Volume FRAMA16
Date
2022-09-02 49.59 50.90 48.42 50.322998 650900 50.322998
2022-09-06 49.20 49.20 47.63 50.267480 334400 50.267480
2022-09-07 52.76 60.92 51.49 50.951297 4560500 50.951297
2022-09-08 56.44 59.60 56.44 51.928922 1106900 51.928922
2022-09-09 58.37 58.53 55.86 52.504161 1291100 52.504161 
#https://github.com/matplotlib/mplfinance
#this package help visualize financial data
import mplfinance as mpf
import matplotlib.colors as mcolors

# all_colors = list(mcolors.CSS4_COLORS.keys())#"CSS Colors"
all_colors = list(mcolors.TABLEAU_COLORS.keys()) # "Tableau Palette",
# all_colors = list(mcolors.BASE_COLORS.keys()) #"Base Colors",


#https://github.com/matplotlib/mplfinance/issues/181#issuecomment-667252575
#list of colors: https://matplotlib.org/stable/gallery/color/named_colors.html
#https://github.com/matplotlib/mplfinance/blob/master/examples/styles.ipynb

def plot_3panels(main_data, add_data=None, mid_panel=None, chart_type='candle', names=None, 
                  figratio=(14,9)):


    style = mpf.make_mpf_style(base_mpf_style='yahoo',  #charles
                               base_mpl_style = 'seaborn-whitegrid',
#                                marketcolors=mpf.make_marketcolors(up="r", down="#0000CC",inherit=True),
                               gridcolor="whitesmoke", 
                               gridstyle="--", #or None, or - for solid
                               gridaxis="both", 
                               edgecolor = 'whitesmoke',
                               facecolor = 'white', #background color within the graph edge
                               figcolor = 'white', #background color outside of the graph edge
                               y_on_right = False,
                               rc =  {'legend.fontsize': 'small',#or number
                                      #'figure.figsize': (14, 9),
                                     'axes.labelsize': 'small',
                                     'axes.titlesize':'small',
                                     'xtick.labelsize':'small',#'x-small', 'small','medium','large'
                                     'ytick.labelsize':'small'
                                     }, 
                              )   

    if (chart_type is None) or (chart_type not in ['ohlc', 'line', 'candle', 'hollow_and_filled']):
        chart_type = 'candle'
    len_dict = {'candle':2, 'ohlc':3, 'line':1, 'hollow_and_filled':2}    
        
    kwargs = dict(type=chart_type, figratio=figratio, volume=True, volume_panel=1, 
                  panel_ratios=(4,2), tight_layout=True, style=style, returnfig=True)
    
    if names is None:
        names = {'main_title': '', 'sub_tile': ''}
    


    added_plots = { 
  
        'FRAMA16': mpf.make_addplot(add_data['FRAMA16'], panel=0, color='dodgerblue', secondary_y=False), 
#         'AO-SIGNAL': mpf.make_addplot(mid_panel['AO']-mid_panel['SIGNAL'], type='bar',width=0.7,panel=1, color="pink",alpha=0.65,secondary_y=False),
    }

                         

    fig, axes = mpf.plot(main_data,  **kwargs,
                         addplot=list(added_plots.values()),
                        )
    # add a new suptitle
    fig.suptitle(names['main_title'], y=1.05, fontsize=12, x=0.135)

    axes[0].set_title(names['sub_tile'], fontsize=10, style='italic',  loc='left')
    
    

    
    #set legend

#     axes[0].legend([None]*6)
#     handles = axes[0].get_legend().legendHandles
#     print(handles)
#     axes[0].legend(handles=handles[4:],labels=['MAMA', 'FAMA'])
    #axes[2].set_title('AO', fontsize=10, style='italic',  loc='left')
#     axes[0].set_ylabel('MAMA')
    
    

#     axes[0].set_ylabel(names['y_tiles'][0])
    return fig, axes
   


start = -100
end = df.shape[0]

names = {'main_title': f'{ticker}', 
         'sub_tile': 'FRAMA: Fractal Adaptive Moving Average'}


aa_, bb_ = plot_3panels(df.iloc[start:end][['Open', 'High', 'Low', 'Close', 'Volume']], 
             df.iloc[start:end][[ 'FRAMA16']],
             None, 
             chart_type='hollow_and_filled',
                     names = names, 
                    )

png