経済・ファイナンスデータの計量時系列分析 2章 MA過程

MA過程を描いてみる。

import matplotlib.pyplot as plt
import numpy as np

def ma(n, mu, theta, sigma):
    """
    1次の移動平均過程を返す
    """
    epsilon = (np.random.rand(n) * 2 - 1) * sigma
    y = []
    for i in range(n):
        if i == 0:
            yi = mu + epsilon[i]
        else:
            yi = mu + epsilon[i] + theta * epsilon[i-1]
        y.append(yi)
    return np.array(y)


# MA 過程のグラフ
n = 100

params = [(0, 0.8, 1), (2, 0.5, 0.5), (-2, 0.3, 2), (0, -0.3, 1), (2, -0.5, 0.5), (-2, -0.8, 2)]
row = 3
col = 2

fig, ax = plt.subplots(row, col, figsize=(10, 8))
for i, (mu, theta, sigma) in enumerate(params):
    i_row = i // col 
    i_col = i % col 
    print(i_row, i_col)

    x = range(n)
    y = ma(n, mu, theta, sigma)

    ax[i_row][i_col].plot(x, y)
    ax[i_row][i_col].set_title(f"mu: {mu}, theta: {theta}, sigma: {sigma}")
    

plt.tight_layout()
plt.show()