def spread_mean(stock1, stock2, i, table):
if table.model_type.iloc[i] == 'model1':
model = 'H2'
elif table.model_type.iloc[i] == 'model2':
model = 'H1*'
elif table.model_type.iloc[i] == 'model3':
model = 'H1'
stock1 = stock1[i, :150]
stock2 = stock2[i, :150]
b1 = table.w1.iloc[i]
b2 = table.w2.iloc[i]
y = np.vstack([stock1, stock2]).T
logy = np.log(y)
# print(logy)
lyc = logy.copy()
p = order_select(logy, 5)
#print('p:',p)
_, _, para = para_vecm(logy, model, p)
logy = np.mat(logy)
y_1 = np.mat(logy[p:])
dy = np.mat(np.diff(logy, axis=0))
for j in range(len(stock1) - p - 1):
if model == 'H1':
if p != 1:
delta = para[0] * para[1].T * y_1[j].T + para[2] * np.hstack(
[dy[j:(j + p - 1)].flatten(),
np.mat([1])]).T
else:
delta = para[0] * para[1].T * y_1[j].T + para[2] * np.mat([1])
elif model == 'H1*':
if p != 1:
delta = para[0] * para[1].T * np.hstack([
y_1[j], np.mat([1])
]).T + para[2] * dy[j:(j + p - 1)].flatten().T
else:
delta = para[0] * para[1].T * np.hstack([y_1[j],
np.mat([1])]).T
elif model == 'H2':
if p != 1:
delta = para[0] * para[1].T * y_1[j].T + para[2] * dy[j:(
j + p - 1)].flatten().T
else:
delta = para[0] * para[1].T * y_1[j].T
else:
print('Errrrror')
break
dy[j + p, :] = delta.T
y_1[j + 1] = y_1[j] + delta.T
b = np.mat([[b1], [b2]])
spread = b.T * lyc[p:].T
spread_m = np.array(b.T * y_1.T).flatten()
return spread_m, spread
def get_Estd(stock1, stock2, i, table, dy=True, D=16):
if table.model_type.iloc[i] == 'model1':
model = 'H2'
elif table.model_type.iloc[i] == 'model2':
model = 'H1*'
elif table.model_type.iloc[i] == 'model3':
model = 'H1'
stock1 = stock1[i, :150]
stock2 = stock2[i, :150]
b1 = table.w1.iloc[i]
b2 = table.w2.iloc[i]
b = np.mat([[b1], [b2]])
y = np.vstack([stock1, stock2]).T
logy = np.log(y) #np.log(y)
p = order_select(logy, 5)
u, A, _ = para_vecm(logy, model, p)
constant = np.mat(A[:, 0])
A = A[:, 1:]
l = A.shape[1]
extend = np.hstack([np.identity(l - 2), np.zeros([l - 2, 2])])
newA = np.vstack([A, extend])
if not dy:
lagy = logy[p - 1:-1, :]
for i in range(1, p):
lagy = np.hstack([lagy, logy[p - 1 - i:-i - 1, :]])
MatrixA = np.mat(A)
MatrixLagy = np.mat(lagy)
Estimate_logy = MatrixA * MatrixLagy.T + constant
e = logy[p:, :].T - Estimate_logy
var = e * e.T / e.shape[1]
else:
var = u * u.T / u.shape[1]
NowCoef = np.mat(np.eye(len(newA)))
Evar = var.copy()
for i in range(149):
NowCoef = newA * NowCoef
Evar = Evar + NowCoef[:2, :2] * var * NowCoef[:2, :2].T
Evar = b.T * Evar * b
return np.sqrt(Evar)
def JB_VECM(stock1, stock2, model, p):
#eng = matlab.engine.start_matlab()
#i = 0
#j = 2
#stock1 = day1_1.iloc[:,i]
#stock2 = day1_1.iloc[:,j]
#stock1_name = day1.columns.values[i]
#stock2_name = day1.columns.values[j]
if model == 'model1':
model_name = 'H2'
elif model == 'model2':
model_name = 'H1*'
else:
model_name = 'H1'
z = (np.vstack([stock1, stock2]).T)
k = len(z.T)
z = np.log(z)
#p = order_select(z,5)
ut = para_vecm(z, model_name, p)[0]
ut_cov = np.dot(ut, ut.T) / len(ut.T)
#ut = eng.res_jci( matlab.double(z.tolist()) , model , (p-1) , 1 )
#ut_cov = eng.cov_jci( matlab.double(z.tolist()) , model , (p-1) , 1 )
L = np.linalg.cholesky(ut_cov)
w = pd.DataFrame(np.dot(np.linalg.inv(L), np.array(ut))).T
b1 = w.apply(lambda x: np.mean(x**3), axis=1)
b2 = w.apply(lambda x: np.mean(x**4), axis=1)
lambda_s = np.dot(b1, b1.T) * len(w) / 6
lambda_k = np.dot(b2 - 3, (b2 - 3).T) * len(w) / 24
lambda_sk = lambda_s + lambda_k
#print(lambda_sk)
#eng.quit()
if lambda_sk > float(chi2.ppf(0.95, 2 * k)):
return 1 # 拒絕虛無假設，表示殘差不是常態
else:
return 0
def fore_chow(stock1, stock2, stock1_trade, stock2_trade, model):
#eng = matlab.engine.start_matlab()
#stock1 = day1_1.iloc[:,0]
#stock2 = day1_1.iloc[:,2]
#stock1_trade = day1.iloc[0:210,0]
#stock2_trade = day1.iloc[0:210,2]
#model_name = 'H1'
if model == 'model1':
model_name = 'H2'
elif model == 'model2':
model_name = 'H1*'
else:
model_name = 'H1'
y = (np.vstack([stock1, stock2]).T)
day1 = (np.vstack([stock1_trade, stock2_trade]).T)
k = len(y.T) # 幾檔股票
n = len(y) # formation period 資料長度
y = np.log(y)
day1 = np.log(day1)
h = len(day1) - n
p = order_select(y, 5) # 計算最佳落後期數
#ut , A = VAR_model(y , p) # 計算VAR殘差共變異數與參數
at, A = para_vecm(y, model_name, p)
ut = np.dot(at, at.T) / len(at.T)
#A = pd.DataFrame(A)
A = A.T
phi_0 = np.eye(k)
A1 = np.delete(A, 0, axis=0).T
phi = np.hstack((np.zeros([k, 2 * (p - 1)]), phi_0))
sigma_t = np.dot(np.dot(phi_0, ut), phi_0.T) # sigma hat
ut_h = []
for i in range(1, h + 1):
lag_mat = day1[len(day1) - i - p - 1:len(day1) - i, :]
lag_mat = np.array(lag_mat[::-1])
if p == 1:
ut_h.append(lag_mat[0].T -
(A[0].T + np.dot(A[1:k * p + 1].T, lag_mat[1:2].T)).T)
else:
ut_h.append(lag_mat[0].T - (A[0].T + np.dot(
A[1:k * p + 1].T, lag_mat[1:k * p - 1].reshape([k * p, 1]))).T)
for i in range(h - 1):
a = phi[:, i * 2:len(phi.T)]
phi_i = np.dot(A1, a.T)
sigma_t = sigma_t + np.dot(np.dot(phi_i, ut), phi_i.T)
phi = np.hstack((phi, phi_i))
phi = phi[:, ((p - 1) * k):len(phi.T)]
ut_h = np.array(ut_h).reshape([1, h * 2])
e_t = np.dot(phi, ut_h.T)
# 程式防呆，如果 sigma_t inverse 發散，則回傳有結構性斷裂。
try:
tau_h = np.dot(np.dot(e_t.T, np.linalg.inv(sigma_t)), e_t) / k
except:
return 1
else:
if tau_h > float(f.ppf(
0.99, k, n - k * p + 1)): #tau_h > float(chi2.ppf(0.99,k)):
return 1 # 有結構性斷裂
else:
return 0
def fore_chow(stock1, stock2, model, Flen, give=False, p=0, A=0, ut=0, maxp=5):
#Flen:formation length
if model == 1:
model_name = 'H2'
elif model == 2:
model_name = 'H1*'
else:
model_name = 'H1'
day1 = (np.vstack([stock1, stock2]).T)
day1 = np.log(day1)
h = len(day1) - Flen
k = 2 # 幾檔股票
n = Flen # formation period 資料長度
if give == False:
y = (np.vstack([stock1[0:Flen], stock2[0:Flen]]).T)
y = np.log(y)
p = order_select(y, maxp)
at, A, _ = para_vecm(y, model_name, p)
# at , A = para_vecm(y,model_name,p)
ut = np.dot(at, at.T) / len(at.T) #sigma_u
Remain_A = A.copy()
Remain_ut = ut.copy()
Remain_p = p
#LUKE pg184
A = A.T
phi_0 = np.eye(k)
A1 = np.delete(A, 0, axis=0).T
phi = np.hstack((np.zeros([k, 2 * (p - 1)]), phi_0))
sigma_t = np.dot(np.dot(phi_0, ut), phi_0.T) # sigma hat
ut_h = []
for i in range(1, h + 1):
lag_mat = day1[len(day1) - i - p - 1:len(day1) - i, :]
lag_mat = np.array(lag_mat[::-1])
if p == 1:
ut_h.append(lag_mat[0].T -
(A[0].T + np.dot(A[1:k * p + 1].T, lag_mat[1:2].T)).T)
else:
ut_h.append(lag_mat[0].T - (A[0].T + np.dot(
A[1:k * p + 1].T, lag_mat[1:k * p - 1].reshape([k * p, 1]))).T)
for i in range(h - 1):
a = phi[:, i * 2:len(phi.T)]
phi_i = np.dot(A1, a.T)
sigma_t = sigma_t + np.dot(np.dot(phi_i, ut), phi_i.T)
phi = np.hstack((phi, phi_i))
phi = phi[:, ((p - 1) * k):len(phi.T)]
ut_h = np.array(ut_h).reshape([1, h * 2])
e_t = np.dot(phi, ut_h.T)
# 程式防呆，如果 sigma_t inverse 發散，則回傳有結構性斷裂。
try:
tau_h = np.dot(np.dot(e_t.T, np.linalg.inv(sigma_t)), e_t) / k
except:
return Remain_p, Remain_A, Remain_ut, 1
else:
if tau_h > float(f.ppf(
0.99, k, n - k * p + 1)): #tau_h > float(chi2.ppf(0.99,k)):
return Remain_p, Remain_A, Remain_ut, 1 # 有結構性斷裂
else:
return Remain_p, Remain_A, Remain_ut, 0
def spread_mean(output, i, model, D, ini=0, future=True, order=False):
'''
if model == 'model1':
model = 'H2'
elif model == 'model2':
model = 'H1*'
elif model == 'model3':
model = 'H1'
'''
if model == 1:
model = 'H2'
elif model == 2:
model = 'H1*'
elif model == 3:
model = 'H1'
stock1 = output[2 * i, 8:158]
stock2 = output[(2 * i + 1), 8:158]
b1 = output[2 * i, 3]
b2 = output[(2 * i + 1), 3]
spread = output[2 * i, 3] * np.log(output[2 * i, 8:(274 - D)]) + output[
(2 * i + 1), 3] * np.log(output[(2 * i + 1), 8:(274 - D)])
y = np.vstack([stock1, stock2]).T
logy = np.log(y)
p = order_select(logy, 5)
#print('p:',p)
_, _, para = para_vecm(logy, model, p)
logy = np.mat(logy)
y_1 = np.mat(logy[p + ini:])
dy = np.mat(np.diff(logy, axis=0)[ini:, :])
for j in range(len(stock1) - p - 1 - ini):
if model == 'H1': #MODEL3
if p != 1:
delta = para[0] * para[1].T * y_1[j].T + para[2] * np.hstack(
[dy[j:(j + p - 1)].flatten(),
np.mat([1])]).T
else:
delta = para[0] * para[1].T * y_1[j].T + para[2] * np.mat([1])
elif model == 'H1*': #MODEL2
if p != 1:
delta = para[0] * para[1].T * np.hstack([
y_1[j], np.mat([1])
]).T + para[2] * dy[j:(j + p - 1)].flatten().T
else:
delta = para[0] * para[1].T * np.hstack([y_1[j],
np.mat([1])]).T
elif model == 'H2': #MODEL1
if p != 1:
delta = para[0] * para[1].T * y_1[j].T + para[2] * dy[j:(
j + p - 1)].flatten().T
else:
delta = para[0] * para[1].T * y_1[j].T
else:
print('Errrrror')
break
dy[j + p, :] = delta.T
y_1[j + 1] = y_1[j] + delta.T
b = np.mat([[b1], [b2]])
spread_m = np.array(b.T * y_1.T).flatten()
if future:
if order:
return spread_m, spread[p + ini:], p
else:
return spread_m, spread[p + ini:]
else:
if order:
return spread_m, spread[p + ini:150], p
else:
return spread_m, spread[p + ini:150]
