!pip install yfinance

import yfinance as yf
import datetime as dt 

end = dt.datetime.today()
start = dt.datetime(end.year-10, end.month, end.day)

df = yf.download('005930.KS', start, end)

df

import numpy as np
import matplotlib.pyplot as plt

plt.figure(figsize=(14,9), dpi=100)
plt.plot(df['Adj Close'], label='Samsung Electronics')
plt.xlabel('date')
plt.ylabel('stock price')
plt.grid()
plt.legend()
plt.show()

import numpy as np
import matplotlib.pyplot as plt

y = df['Adj Close'].values
y -= np.mean(y)
y /= np.std(y)

n = len(y)

plt.figure(figsize=(14,9), dpi=100)
plt.plot(y, label='Samsung Electronics')
plt.xlabel('days')
plt.ylabel('normalized price')
plt.grid()
plt.legend()
plt.show()

lam = 1e5

A = np.eye(n)

D = np.zeros((n-2,n))
for i in range(D.shape[0]):
  D[i,i:i+3] = [1, -2, 1]

A_tilde = np.vstack((A,np.sqrt(lam)*D))
y_tilde = np.hstack((y,np.zeros(n-2)))

xhat = np.linalg.lstsq(A_tilde,y_tilde,rcond=None)[0]

plt.figure(figsize=(14,9), dpi=100)
plt.plot(y, alpha=0.4, label='Samsung Electronics')
plt.plot(xhat,linewidth=3, label=r'$\ell_2$ trend filter')
plt.xlabel('days')
plt.ylabel('normalized price')
plt.grid()
plt.legend()
plt.show()

import scipy.sparse as ssp
import scipy.sparse.linalg as sla

lam = 1e5

As = ssp.eye(n)

Ds = ssp.spdiags([np.ones(n), -2*np.ones(n), np.ones(n)], [0, 1, 2], n-2, n)

As_tilde = ssp.vstack((As, np.sqrt(lam)*Ds))
y_tilde = np.hstack((y, np.zeros(n-2)))

xhats = sla.lsqr(As_tilde,y_tilde)[0]

plt.figure(figsize=(14,9), dpi=100)
plt.plot(y, alpha=0.4, label='Samsung Electronics')
plt.plot(xhats,linewidth=3, label=r'$\ell_2$ trend filter (sparse)')
plt.xlabel('days')
plt.ylabel('normalized price')
plt.grid()
plt.legend()
plt.show()

import cvxpy as cp

x = cp.Variable(n)
obj = cp.Minimize( cp.norm(y-As@x,1) + 100*cp.norm(Ds@x,1) )
prob = cp.Problem(obj)
prob.solve(solver=cp.ECOS, verbose=False, max_iters=100)

plt.figure(figsize=(14,9), dpi=100)
plt.plot(y, alpha=0.4, label='Samsung Electronics')
plt.plot(xhats,linewidth=4, alpha=0.6, label=r'$\ell_2$ trend filter')
plt.plot(x.value,linewidth=3, label=r'$\ell_1$ trend filter')
plt.xlabel('days')
plt.ylabel('normalized price')
plt.grid()
plt.legend()
plt.show()

z = 10*np.random.randn(n)

for i in range(n):
  if np.random.rand() > 0.01:
    z[i] = 0
    
y_cor = y + z

plt.figure(figsize=(14,9), dpi=100)
plt.plot(y_cor, alpha=0.4, label='Samsung Electronics (corrupted)')
plt.xlabel('days')
plt.ylabel('normalized price')
plt.ylim(-1.5,3.5)
plt.grid()
plt.legend()
plt.show()

b_tilde_cor = np.hstack((y_cor, np.zeros(n-2)))
xhats_cor = sla.lsqr(As_tilde,b_tilde_cor)[0]

plt.figure(figsize=(14,9), dpi=100)
plt.plot(y_cor, alpha=0.4, label='Samsung Electronics (corrupted)')
plt.plot(xhats,linewidth=4, alpha=0.6, label=r'$\ell_2$ trend filter (on clean data)')
plt.plot(xhats_cor,linewidth=4, alpha=0.6, label=r'$\ell_2$ trend filter (on corrupted data)')
plt.xlabel('days')
plt.ylabel('normalized price')
plt.ylim(-1.5,3.5)
plt.grid()
plt.legend()
plt.show()

x_cor = cp.Variable(n)
obj = cp.Minimize( cp.norm(y_cor-As@x_cor,1) + 100*cp.norm(Ds@x_cor,1) )
prob = cp.Problem(obj)
prob.solve(solver=cp.ECOS, verbose=False, max_iters=100)

plt.figure(figsize=(14,9), dpi=100)
plt.plot(y_cor, alpha=0.4, label='Samsung Electronics')
plt.plot(x.value, linewidth=4, label=r'$\ell_1$ trend filter (on clean data)')
plt.plot(x_cor.value, linewidth=3, label=r'$\ell_1$ trend filter (on corrupted data)')
plt.xlabel('days')
plt.ylabel('normalized price')
plt.ylim(-1.5,3.5)
plt.grid()
plt.legend()
plt.show()