MA Process

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import statsmodels.api as sm
import numpy as np
import matplotlib.pyplot as plt

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def create_MAdata(thetas=[0.1], mu=1, N=400, init=1, c=1, sigma=0.3):
    """GGenerate MA Process data"""
    epsilon = np.random.normal(loc=0, scale=sigma, size=N)
    data = np.zeros(N)
    data[0] = init

    for t in range(2, N):
        res = mu + epsilon[t]
        for j, theta_j in enumerate(thetas):
            res += theta_j * epsilon[t - j - 1]
        data[t] = res
    return data

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plt.figure(figsize=(12, 6))
thetas = [0.5]
ma1_1 = create_MAdata(thetas=thetas)
plt.plot(ma1_1)
plt.show()

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plt.figure(figsize=(12, 6))
thetas = [0.5, 0.5]
ma1_2 = create_MAdata(thetas=thetas)
plt.plot(ma1_1)
plt.show()

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plt.figure(figsize=(12, 6))
thetas = [0.5 for _ in range(10)]
ma1_5 = create_MAdata(thetas=thetas)
plt.plot(ma1_5)
plt.show()