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# Create an HMM object with two hidden states
model = hmm.GaussianHMM(n_components = 2, covariance_type = "diag", n_iter = 100, random_state = 42)

# Create an array input for the HMM model
X = data[['R']].values

# Estimate the HMM model
results = model.fit(X)

# Use the Viterbi algorithm to find the fitted hidden states

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# Count number of downward and upward events
data['Event'].value_counts()

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# Set the figure size
plt.figure(figsize=(15,7))

# Plot the R indicator
plt.plot(data.index, data['R'], label = "R")

# Set the title of the graph
plt.title('Time-Adjusted Return of DC', fontsize=16)

# Set the x- and y- axis labels and ticks sizes

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# Compute the DC indicators
data = directional_change_events(data, theta=0.004)

# Drop NaN values
data.dropna(inplace=True)

# Present the data
data

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# Download the GBPUSD data from 2003 to 2013
data = yf.download('GBPUSD=X', start='2003-12-01', end='2023-10-06', auto_adjust=True)

# Compute the log returns
data['returns'] = np.log(data['Close']/data['Close'].shift(1))

# Print the data
data

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# Function to create the DC indicators provided by Chen and Tsang (2021)
def directional_change_events(data, theta=0.2):

    # Copy the dataframe
    data = data.copy()

    # Create the necessary columns and variables
    data["Event"] = 0.0

    # Set the initial event variable value

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# For data manipulation
import numpy as np
import pandas as pd
import yfinance as yf
import pyfolio as pf
from hmmlearn import hmm
from sklearn.utils import check_random_state

# For data visualization
import matplotlib.pyplot as plt

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# Set the figure size
plt.figure(figsize=(15,7))

# Plot the residuals
plt.plot(arfima_residuals.index, arfima_residuals, label = "Best d ARFIMA Residuals")

# Set the title of the graph
plt.title('Residuals from the Best d ARFIMA model', fontsize=16)

# Set the x- and y- axis labels and ticks sizes

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# Estimate ARFIMA residuals with optimal d
arfima_residuals = fracDiff_FFD(np.log(data['Close']),d)

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# Get the optimal ARFIMA d parameter
d = optimal_d(data, 0.04, 0, 1)