信息处理 - Hankel 矩阵 SVD 去噪 - 吾爱随笔录

我已经执行了汉克尔矩阵奇异值分解去噪以平滑我的单变量时间序列。它是欧元/美元汇率的收盘价。这是一张图片：

我遇到的问题是数据的结尾似乎是错误的。我该如何解决这个问题，或者有更好的方法来对我的时间序列进行去噪，例如卡尔曼滤波器或小波变换。这是我的 Python 代码的主要部分：

import numpy as np
import pandas_datareader as pdr
from datetime import datetime 
from scipy.linalg import hankel
import matplotlib.pyplot as plt

symbol = "EURUSD=X"
df = pdr.DataReader(symbol, "yahoo", datetime(2000, 1, 1),
                        datetime.now()).drop(columns=["Adj Close", "Volume"])

hankel_matrix = hankel(df.Close)

U, S, VT = np.linalg.svd(hankel_matrix)

first_k_singulars = 40
S = [0 if i > first_k_singulars else j for i, j in zip(range(len(S)), S)]

close = U @ np.diag(S) @ VT

max_col = len(close[0])
max_row = len(close)
fdiag = [[] for _ in range(max_row + max_col - 1)]

for x in range(max_col):
    for y in range(max_row):
        fdiag[x + y].append(close[y][x])

avg_fdiag = []  
for i, j in zip(fdiag, range(1, len(fdiag)+1)):
    avg_fdiag.append(np.sum(i)/j)

close = avg_fdiag[:len(df)] # take this length of our avg_fdiag as it is a hankel matrix

Python代码

import numpy as np import pandas_datareader as pdr from datetime import datetime from scipy.linalg import hankel import matplotlib.pyplot as plt symbol = "EURUSD=X" df = pdr.DataReader(symbol, "yahoo", datetime(2000, 1, 1), datetime.now()).drop(columns=["Adj Close", "Volume"]) subset = np.concatenate((df.Close.values, df.Close.values[-1:]*np.ones(100))) hankel_matrix = hankel(subset) U, S, VT = np.linalg.svd(hankel_matrix) first_k_singulars = 90 S = [0 if i > first_k_singulars else j for i, j in zip(range(len(S)), S)] close = U @ np.diag(S) @ VT max_col = len(close[0]) max_row = len(close) fdiag = [[] for _ in range(max_row + max_col - 1)] for x in range(max_col): for y in range(max_row): fdiag[x + y].append(close[y][x]) avg_fdiag = [] for i, j in zip(fdiag, range(1, len(fdiag)+1)): avg_fdiag.append(np.sum(i)/j) close = avg_fdiag[:len(subset)] # take this length of our avg_fdiag as it is a hankel matrix plt.plot(subset) plt.plot(close)