MACD Indicator with Bitcoin¶

In this playground, I'm using Python and Pandas to create the MACD indicator for Daily bitcoin prices.

The MACD indicator is used to spot changes in trends in an asset. But, as it is a lagging indicator, it's hardly useful to spot any real trend changes and its usage as an investment technique is discouraged.

To calculate it, we just need to calculate "Exponential moving average" (EMA) of a given asset price.

Let's take it step by step!

Do you want to try this by yourself? Copy this Playground to get started! You'll get the same dataset and my original notebook.

In [5]:

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt

import matplotlib.dates as mdates

First, let's start by reading the Data:

In [6]:

df = pd.read_csv('/data/bitstamp-btcusd-daily-historic/btcusd_daily.csv', index_col='timestamp', parse_dates=True)

Explore it:

In [7]:

df.head()

Out[7]:

	open	high	low	close	volume
timestamp
2015-01-01 00:00:00+00:00	321.00	321.00	312.60	313.81	3087.436554
2015-01-02 00:00:00+00:00	313.81	317.01	311.96	315.42	3468.281375
2015-01-03 00:00:00+00:00	315.42	316.58	280.00	282.00	21752.719146
2015-01-04 00:00:00+00:00	280.00	289.39	255.00	264.00	41441.278553
2015-01-05 00:00:00+00:00	264.55	280.00	264.07	276.80	9528.271002

For our MACD Indicator, I'll use the Close price, so I create a new empty dataframe:

In [8]:

close_df = df[['close']].copy()

In [9]:

close_df.head()

Out[9]:

	close
timestamp
2015-01-01 00:00:00+00:00	313.81
2015-01-02 00:00:00+00:00	315.42
2015-01-03 00:00:00+00:00	282.00
2015-01-04 00:00:00+00:00	264.00
2015-01-05 00:00:00+00:00	276.80

Calculating MACD¶

MACD has 3 main Time Series:

The MACD Series
The Signal Line
The difference between 1 and 2, often called the "divergence" series.

1. The MACD Series¶

The MACD Series is the difference between a "fast" (short period) exponential moving average (EMA), and a "slow" (longer period) EMA of the price series. Usually, the values chosen are 12 for the fast one, and 26 for the fast one. So let's start calculating these EMAs:

In [10]:

close_df['EMA_12'] = close_df['close'].ewm(span=12, adjust=False).mean()
close_df['EMA_26'] = close_df['close'].ewm(span=26, adjust=False).mean()

close_df.head()

Out[10]:

	close	EMA_12	EMA_26
timestamp
2015-01-01 00:00:00+00:00	313.81	313.810000	313.810000
2015-01-02 00:00:00+00:00	315.42	314.057692	313.929259
2015-01-03 00:00:00+00:00	282.00	309.125740	311.564129
2015-01-04 00:00:00+00:00	264.00	302.183318	308.040860
2015-01-05 00:00:00+00:00	276.80	298.278192	305.726722

Now, we can calculate teh MACD series, which is just the difference between EMA_12 and EMA_26:

In [11]:

close_df['MACD'] = close_df['EMA_12'] - close_df['EMA_26']
close_df.head()

Out[11]:

	close	EMA_12	EMA_26	MACD
timestamp
2015-01-01 00:00:00+00:00	313.81	313.810000	313.810000	0.000000
2015-01-02 00:00:00+00:00	315.42	314.057692	313.929259	0.128433
2015-01-03 00:00:00+00:00	282.00	309.125740	311.564129	-2.438389
2015-01-04 00:00:00+00:00	264.00	302.183318	308.040860	-5.857542
2015-01-05 00:00:00+00:00	276.80	298.278192	305.726722	-7.448530

2. The Signal Line¶

The signal line is just an EMA of the MACD series itself. Usually, 9 periods are used:

In [12]:

close_df['Signal_Line'] = close_df['MACD'].ewm(span=9, adjust=False).mean()
close_df.head()

Out[12]:

	close	EMA_12	EMA_26	MACD	Signal_Line
timestamp
2015-01-01 00:00:00+00:00	313.81	313.810000	313.810000	0.000000	0.000000
2015-01-02 00:00:00+00:00	315.42	314.057692	313.929259	0.128433	0.025687
2015-01-03 00:00:00+00:00	282.00	309.125740	311.564129	-2.438389	-0.467129
2015-01-04 00:00:00+00:00	264.00	302.183318	308.040860	-5.857542	-1.545211
2015-01-05 00:00:00+00:00	276.80	298.278192	305.726722	-7.448530	-2.725875

3. The divergence series¶

And finally, we can calculate the divergence series, which is just the difference between the two:

In [13]:

close_df['Divergence'] = close_df['MACD'] - close_df['Signal_Line']
close_df.head()

Out[13]:

	close	EMA_12	EMA_26	MACD	Signal_Line	Divergence
timestamp
2015-01-01 00:00:00+00:00	313.81	313.810000	313.810000	0.000000	0.000000	0.000000
2015-01-02 00:00:00+00:00	315.42	314.057692	313.929259	0.128433	0.025687	0.102746
2015-01-03 00:00:00+00:00	282.00	309.125740	311.564129	-2.438389	-0.467129	-1.971261
2015-01-04 00:00:00+00:00	264.00	302.183318	308.040860	-5.857542	-1.545211	-4.312331
2015-01-05 00:00:00+00:00	276.80	298.278192	305.726722	-7.448530	-2.725875	-4.722655

Plotting MACD¶

It's sometimes useful to plot the MACD indicator along with the original price to understand the changes of trends. To do so, I'll start first by only getting the prices of 2023 onwards, and then creating two axes:

The first one contains the price itself with the EMA12 and EMA26. The second one, contains the Signal Line and the MACD along with a barchar of the Divergence

In [14]:

df_2023 = close_df.loc['2023':].copy()

In [12]:

fig = plt.figure(figsize=(14, 12), constrained_layout=True)

gs = fig.add_gridspec(2, 1, height_ratios=[2, 1])


ax1 = fig.add_subplot(gs[0, 0])
ax2 = fig.add_subplot(gs[1, 0])

df_2023['close'].plot(ax=ax1, color='blue', label='Close')
df_2023['EMA_12'].plot(ax=ax1, color='black', label='EMA_12')
df_2023['EMA_26'].plot(ax=ax1, color='red', label='EMA_26')


ax2.bar(df_2023.index, df_2023['Divergence'], label='MACD Histogram', color='grey')

ax2.plot(df_2023.index, df_2023['MACD'], label='MACD', color='blue', alpha=.5)
ax2.plot(df_2023.index, df_2023['Signal_Line'], label='Signal Line', color='red', alpha=.5)

for ax in (ax1, ax2):
    ax.xaxis.set_major_locator(mdates.MonthLocator())
    ax.xaxis.set_major_formatter(mdates.DateFormatter('%b %Y'))
    ax.tick_params(axis='x', which='major', labelrotation=45)

ax1.set_title('Close Price including EMA 12 and 26')
ax2.set_title('MACD')

ax1.legend()
ax2.legend(loc='upper left')

plt.tight_layout()

/tmp/ipykernel_14/3985725785.py:30: UserWarning: The figure layout has changed to tight
  plt.tight_layout()

What does MACD tells us?¶

EMA 12 vs EMA 26¶

We can start by just analyzing the EMAs. In theory, when EMA_12 crosses EMA_26 could be considered a bullish signal, while the opposite (EMA_26 crossing over EMA_12) could be considered a bearish market. Let's take a look!

First I'll extract only the EMAs in a single dataframe:

In [15]:

analysis_df = df_2023[['EMA_12', 'EMA_26']].copy()
analysis_df.head()

Out[15]:

	EMA_12	EMA_26
timestamp
2023-01-01 00:00:00+00:00	16701.523922	16838.578239
2023-01-02 00:00:00+00:00	16697.135626	16826.313184
2023-01-03 00:00:00+00:00	16692.960915	16814.734430
2023-01-04 00:00:00+00:00	16716.966928	16817.272620
2023-01-05 00:00:00+00:00	16733.741247	16817.919093

We can then shift both EMAs to compare them with the day before:

In [16]:

analysis_df['EMA_12_prev'] = analysis_df['EMA_12'].shift(1)
analysis_df['EMA_26_prev'] = analysis_df['EMA_26'].shift(1)

And then compare the times where EMA_12 crossed over EMA_26 and the other way around:

In [17]:

positive_flips = (analysis_df['EMA_12_prev'] < analysis_df['EMA_26_prev']) & (analysis_df['EMA_12'] > analysis_df['EMA_26'])
negative_flips = (analysis_df['EMA_26_prev'] < analysis_df['EMA_12_prev']) & (analysis_df['EMA_26'] > analysis_df['EMA_12'])

In [18]:

analysis_df.loc[positive_flips.loc[positive_flips].index - pd.Timedelta(days=1)]

Out[18]:

	EMA_12	EMA_26	EMA_12_prev	EMA_26_prev
timestamp
2023-01-08 00:00:00+00:00	16844.333909	16857.325500	16794.394620	16836.391540
2023-03-14 00:00:00+00:00	22603.703225	22660.892063	22213.467447	22493.763428
2023-06-20 00:00:00+00:00	26610.391812	26669.514586	26300.463050	26537.875753
2023-09-19 00:00:00+00:00	26463.337800	26518.750666	26326.853763	26463.130719
2023-09-28 00:00:00+00:00	26522.229408	26530.428801	26430.634755	26490.783105

In [19]:

analysis_df.loc[negative_flips.loc[negative_flips].index - pd.Timedelta(days=1)]

Out[19]:

	EMA_12	EMA_26	EMA_12_prev	EMA_26_prev
timestamp
2023-03-05 00:00:00+00:00	23087.328435	23086.354448	23207.206332	23139.022804
2023-05-08 00:00:00+00:00	28663.309955	28623.164825	28840.275402	28697.818011
2023-07-24 00:00:00+00:00	29941.999726	29888.027428	30081.090585	29944.909622
2023-09-23 00:00:00+00:00	26569.991342	26566.414817	26567.626132	26565.088002

Now, putting altogether:

In [20]:

fig, ax = plt.subplots(figsize=(14, 7))


df_2023['close'].plot(ax=ax, color='blue', label='Close')
df_2023['EMA_12'].plot(ax=ax, color='black', label='EMA_12')
df_2023['EMA_26'].plot(ax=ax, color='red', label='EMA_26')

for ts in positive_flips.loc[positive_flips].index - pd.Timedelta(days=1):
    ax.axvline(pd.Timestamp(ts), color='red')

for ts in negative_flips.loc[negative_flips].index - pd.Timedelta(days=1):
    ax.axvline(pd.Timestamp(ts), color='blue')

In [21]:

df_2023.head()

Out[21]:

	close	EMA_12	EMA_26	MACD	Signal_Line	Divergence
timestamp
2023-01-01 00:00:00+00:00	16615.0	16701.523922	16838.578239	-137.054317	-122.929765	-14.124552
2023-01-02 00:00:00+00:00	16673.0	16697.135626	16826.313184	-129.177558	-124.179323	-4.998235
2023-01-03 00:00:00+00:00	16670.0	16692.960915	16814.734430	-121.773515	-123.698162	1.924646
2023-01-04 00:00:00+00:00	16849.0	16716.966928	16817.272620	-100.305692	-119.019668	18.713975
2023-01-05 00:00:00+00:00	16826.0	16733.741247	16817.919093	-84.177846	-112.051303	27.873457

Signal-line crossover¶

In this case, what we can analyze is the Divergence. In theory, when the Divergence series crosses above 0, we're in a bull market, and when it drops below zero, we're in a bearish market.

In [22]:

div_df = df_2023[['Divergence']].copy()
div_df.head()

Out[22]:

	Divergence
timestamp
2023-01-01 00:00:00+00:00	-14.124552
2023-01-02 00:00:00+00:00	-4.998235
2023-01-03 00:00:00+00:00	1.924646
2023-01-04 00:00:00+00:00	18.713975
2023-01-05 00:00:00+00:00	27.873457

To calculate it, we'll follow a similar process as the previous one. We'll first calculate the shifted value:

In [23]:

div_df['Shifted'] = div_df['Divergence'].shift(1)
div_df.head()

Out[23]:

	Divergence	Shifted
timestamp
2023-01-01 00:00:00+00:00	-14.124552	NaN
2023-01-02 00:00:00+00:00	-4.998235	-14.124552
2023-01-03 00:00:00+00:00	1.924646	-4.998235
2023-01-04 00:00:00+00:00	18.713975	1.924646
2023-01-05 00:00:00+00:00	27.873457	18.713975

In [30]:

!jupyter nbextension enable spellchecker/main

Enabling notebook extension spellchecker/main...
      - Validating: OK

And now, for positive crossover, we can just identify the points in which the previous value was negative, and the current one is positive. For negative crossover, is just the oposite. If the value was positive before and now it's negative, we identify it as a negative crossover.

In [25]:

positive_crossover = (
    (div_df['Shifted'] < 0) & (div_df['Divergence'] > 0)
)
negative_crossover = (
    (div_df['Shifted'] > 0) & (div_df['Divergence'] < 0)
)

In [26]:

positive_crossover.loc[positive_crossover]

Out[26]:

timestamp
2023-01-03 00:00:00+00:00    True
2023-02-17 00:00:00+00:00    True
2023-03-14 00:00:00+00:00    True
2023-04-11 00:00:00+00:00    True
2023-05-27 00:00:00+00:00    True
2023-06-06 00:00:00+00:00    True
2023-06-17 00:00:00+00:00    True
2023-08-08 00:00:00+00:00    True
2023-08-29 00:00:00+00:00    True
2023-10-16 00:00:00+00:00    True
2023-11-10 00:00:00+00:00    True
2023-12-02 00:00:00+00:00    True
dtype: bool

And we can plot it to verify it:

In [29]:

ax = div_df['Divergence'].plot(figsize=(14, 7))
ax.axhline(0, color='green')

for ts in positive_crossover.loc[positive_crossover].index:
    ax.axvline(ts, color='red')
    
for ts in negative_crossover.loc[negative_crossover].index:
    ax.axvline(ts, color='blue')

Finally, we can combine it with the price and the EMAs:

In [32]:

fig, ax = plt.subplots(figsize=(14, 7))


df_2023['close'].plot(ax=ax, color='black', label='Close')
df_2023['EMA_12'].plot(ax=ax, color='green', label='EMA_12', alpha=.5)
df_2023['EMA_26'].plot(ax=ax, color='orange', label='EMA_26', alpha=.5)

for ts in positive_crossover.loc[positive_crossover].index:
    ax.axvline(ts, color='red')
    
for ts in negative_crossover.loc[negative_crossover].index:
    ax.axvline(ts, color='blue')

Conclusion¶

As we can clearly see from the previous chart, the MACD indicator doesn't look as a great indicator to use as an investment tool. But hey! At least we can use it to practice some Pandas!

Building a MACD indicator using Python and Pandas