How the HMM works with sequential or time series data

In this post, we are going to analyze the data of stock market, step by step, to get an idea about how the HMM works with sequential or time series data.

Import the necessary packages as shown below:

import datetime
import warnings

Now, use the stock market data from the matpotlib.finance package, as shown here:

import numpy as np
from matplotlib import cm, pyplot as plt
from matplotlib.dates import YearLocator, MonthLocator
try:
from matplotlib.finance import quotes_historical_yahoo_och1
except ImportError:
from matplotlib.finance import (
quotes_historical_yahoo as quotes_historical_yahoo_och1)
from hmmlearn.hmm import GaussianHMM

Load the data from a start date and end date, i.e., between two specific dates as shown here:

start_date = datetime.date(1995, 10, 10)
end_date = datetime.date(2015, 4, 25)
quotes = quotes_historical_yahoo_och1('INTC', start_date, end_date)

In this step, we will extract the closing quotes every day. For this, use the following command:

closing_quotes = np.array([quote[2] for quote in quotes])

Now, we will extract the volume of shares traded every day. For this, use the following command:

volumes = np.array([quote[5] for quote in quotes])[1:]

Here, take the percentage difference of closing stock prices, using the code shown below:

diff_percentages = 100.0 * np.diff(closing_quotes) / closing_quotes[:-]
dates = np.array([quote[0] for quote in quotes], dtype=np.int)[1:]
training_data = np.column_stack([diff_percentages, volumes])

In this step, create and train the Gaussian HMM. For this, use the following code:

hmm = GaussianHMM(n_components=7, covariance_type='diag', n_iter=1000)
with warnings.catch_warnings():
warnings.simplefilter('ignore')
hmm.fit(training_data)

Now, generate data using the HMM model, using the commands shown:

num_samples = 300
samples, _ = hmm.sample(num_samples)

Finally, in this step, we plot and visualize the difference percentage and volume of shares traded as output in the form of graph.

Use the following code to plot and visualize the difference percentages:

plt.figure()
plt.title('Difference percentages')
plt.plot(np.arange(num_samples), samples[:, 0], c='black')

Use the following code to plot and visualize the volume of shares traded:

plt.figure()
plt.title('Volume of shares')
plt.plot(np.arange(num_samples), samples[:, 1], c='black')
plt.ylim(ymin=0)

plt.show()