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 formation_table(Smin, inNum, costS, cost, os, cs, MaxV, OpenD, Min_cp,
Max_tp):
LSmin = np.log(Smin) #已捨棄前16分鐘與最後五分鐘的股價取log
#LSmin = Smin
maxcompanynu = Smin.shape[1] #找出有多少檔
ind = mt.Binal_comb(range(maxcompanynu))
ind = np.hstack((ind, np.zeros([ind.shape[0], 7])))
#ind.columns = [0:S1_inx,1:S2_inx,2:opt_q, 3:Johansen intercept, 4:Johansen slope, 5:std,6:Model,7:W1,8:W2]
DailyNum = len(Smin)
cy = np.zeros([DailyNum,
ind.shape[0]]) # cy為Naturn Log共整合序列，以Capital Weight構成
cy_mean = np.zeros([DailyNum,
ind.shape[0]]) # cy_mean為共整合序列均值，以Capital Weight構成
B = np.zeros([2, ind.shape[0]]) #B為共整合係數
CapitW = np.zeros([2, ind.shape[0]]) #CW為資金權重Capital Weight
#IntegerB = np.zeros([2,ind.shape[0]]) #IB為CW整數化後的共整合係數
#start_time = time.time()
for mi in range(ind.shape[0]):
#for mi in range(1):
rowS = LSmin.iloc[0:inNum, [int(ind[mi, 0]), int(ind[mi, 1])]] #150分鐘
rowLS = LSmin.iloc[:DailyNum, [int(ind[mi, 0]),
int(ind[mi, 1])]] #250分鐘
#stock1 = Smin.iloc[inNum-1,[int(ind[mi,0])]]
#stock2 = Smin.iloc[inNum-1,[int(ind[mi,1])]]
ind[mi, 0:2] = rowS.columns.values
rowAS = np.array(rowS)
# 配適 VAR(P) 模型 ，並利用BIC選擇落後期數，max_p意味著會檢查2~max_p
try:
max_p = 5
p = order_select(rowAS, max_p)
#ADF TEST
if p < 1:
continue
# adf test
# portmanteau test
model = VAR(rowAS)
if model.fit(p).test_whiteness(nlags=5).pvalue < 0.05:
continue
# Normality test
if model.fit(p).test_normality().pvalue < 0.05:
continue
opt_model = jci.JCI_AutoSelection(rowAS, p - 1)
#如果有共整合，紀錄下Model與opt_q
ind[mi, 2] = p - 1
ind[mi, 6] = opt_model
F_a, F_b, F_ct, F_ut, F_gam, ct, omega_hat = jci.JCItestpara_spilCt(
rowAS, opt_model, p - 1)
# ind[mi,9] = F_a
# ind[mi,10] = F_b
# ind[mi,11] = F_ct
# ind[mi,12] = F_ut
# ind[mi,13] = F_gam
# ind[mi,14] = ct
# ind[mi,15] = omega_hat
Com_para = []
Com_para.append(F_a)
Com_para.append(F_b)
Com_para.extend(F_ct)
#把 arrary.shape(2,1) 的數字放進 shape(2,) 的Serires
#取出共整合係數
B[:, mi] = pd.DataFrame(F_b).stack()
#將共整合係數標準化，此為資金權重Capital Weight
CapitW[:, mi] = B[:, mi] / np.sum(np.absolute(B[:, mi]))
ind[mi, 7] = CapitW[0, mi]
ind[mi, 8] = CapitW[1, mi]
'''
#將資金權重，依股價轉為張數權重
S1 = CapitW[0][mi]/float(stock1)
S2 = CapitW[1][mi]/float(stock2)
#將張數權重，做最簡整數比，要求範圍是最大張數+1
optXY = mt.simp_frac(S1,S2,MaxV+1)
#如果最簡整數比出現[ (MaxV+1) / 1 ] or [ 1 / (MaxV+1) ] 就剃除
#張數權重整數化後，絕對值小於5的設1（通過），絕對值大於6的設0（沒通過）
if abs(optXY[0]) <= MaxV and abs(optXY[1]) <= MaxV:
ind[mi,4] = 1
IntegerB[:,mi] = optXY[:]
ind[mi,7] = optXY[0]
ind[mi,8] = optXY[1]
'''
#計算Spread的時間趨勢均值與標準差
Johansen_intcept, Johansen_slope = jci.Johansen_mean(
F_a, F_b, F_gam, F_ct, p - 1)
Johansen_var_correct = jci.Johansen_std_correct(
F_a, F_b, F_ut, F_gam, p - 1)
Johansen_std = np.sqrt(Johansen_var_correct)
ind[mi, 3] = Johansen_intcept
ind[mi, 4] = Johansen_slope
ind[mi, 5] = Johansen_std
SStd = Johansen_std
cy_mean[:, mi] = Johansen_intcept + Johansen_slope * np.linspace(
0, 249, 250)
#以資金權重建構Naturn Log共整合序列
cy[:, mi] = pd.DataFrame(np.mat(rowLS) *
np.mat(CapitW[:, mi]).T).stack()
#拿共整合序列拿去檢定，ADF單根檢定回傳1代表無單根（定態），0代表有單根（非定態）
#ind[mi,5] = mt.ADFtest_TR(cy[OpenD-1:inNum,mi], opt_p-1 , 0.05)
#如果收斂點在Trading Period，設為0（沒通過、不交易），反之設為1
#if converg_Point < inNum:
#ind[mi,10] = converg_Point
#Spend_time = time.time() - start_time
'''
#畫個圖確認一下
print(ind[mi,0:2])
import matplotlib.pyplot as plt
plotx = [i for i in range(DailyNum)]
CL = np.zeros((DailyNum,5))
CL [:,2] = cy_mean[:,mi]
CL [:,1] = cy_mean[:,mi]+SStd*os
CL [:,0] = cy_mean[:,mi]+SStd*cs
CL [:,3] = cy_mean[:,mi]-SStd*os
CL [:,4] = cy_mean[:,mi]-SStd*cs
plt.plot(plotx,cy[:,mi],plotx,CL)
plt.show()
'''
except:
continue
dd = np.zeros([ind.shape[0], 1])
test_Model = ind[:, 6] != 0
dd = test_Model
ind_select = ind[dd, :] #排除沒有共整合關係的配對
return ind_select
def daily_procces(Smin, inNum, costS, cost, os, cs, MaxV, OpenD, Min_cp,
Max_tp):
'''
#Debug 時使用的參數
Smin = SPmin.iloc[DailyNum*di:DailyNum*(di+1),:].to_numpy()
inNum,costS,cost,os,cs,MaxV,OpenD = indataNum,CostS,Cost,Os,Fs,MaxVolume,OpenDrop
Min_cp, Max_tp = Min_c_p, Max_t_p
'''
LSmin = np.log(Smin) #已捨棄前16分鐘與最後五分鐘的股價取log
maxcompanynu = Smin.shape[1] #找出有多少檔
ind = mt.Binal_comb(range(maxcompanynu))
ind = np.hstack((ind, np.zeros([ind.shape[0], 9])))
#ind.columns = [0:S1_inx,1:S2_inx,2:opt_q, 3:modelH Check, 4:整數 Check, 5:ADF Check,6:Model,7:IB1張數,8:IB2,9:SStd,10:converg_point Check]
DailyNum = len(Smin)
cy = np.zeros([DailyNum,
ind.shape[0]]) # cy為Naturn Log共整合序列，以Capital Weight構成
cy_mean = np.zeros([DailyNum,
ind.shape[0]]) # cy_mean為共整合序列均值，以Capital Weight構成
B = np.zeros([2, ind.shape[0]]) #B為共整合係數
CapitW = np.zeros([2, ind.shape[0]]) #CW為資金權重Capital Weight
IntegerB = np.zeros([2, ind.shape[0]]) #IB為CW整數化後的共整合係數
#start_time = time.time()
for mi in range(ind.shape[0]):
#for mi in range(1):
rowS = LSmin.iloc[0:inNum, [int(ind[mi, 0]), int(ind[mi, 1])]]
rowLS = LSmin.iloc[:DailyNum, [int(ind[mi, 0]), int(ind[mi, 1])]]
stock1 = Smin.iloc[inNum - 1, [int(ind[mi, 0])]]
stock2 = Smin.iloc[inNum - 1, [int(ind[mi, 1])]]
ind[mi, 0:2] = rowS.columns.values
rowAS = np.array(rowS)
# 配適 VAR(P) 模型 ，並利用BIC選擇落後期數，max_p意味著會檢查2~max_p
try:
max_p = 5
p = order_select(rowAS, max_p)
opt_model = jci.JCI_AutoSelection(rowAS, p - 1)
#如果有共整合，紀錄下Model與opt_q
ind[mi, 2] = p - 1
ind[mi, 6] = opt_model
if opt_model == 4 or opt_model == 5:
F_a, F_b, F_ct, F_ut, F_gam, ct, omega_hat = jci.JCItestpara_spilCt(
rowAS, opt_model, p - 1)
Com_para = []
Com_para.append(F_a)
Com_para.append(F_b)
Com_para.extend(F_ct)
#把 arrary.shape(2,1) 的數字放進 shape(2,) 的Serires
#取出共整合係數
B[:, mi] = pd.DataFrame(F_b).stack()
#將共整合係數標準化，此為資金權重Capital Weight
CapitW[:, mi] = B[:, mi] / np.sum(np.absolute(B[:, mi]))
#將資金權重，依股價轉為張數權重
S1 = CapitW[0][mi] / float(stock1)
S2 = CapitW[1][mi] / float(stock2)
#將張數權重，做最簡整數比，要求範圍是最大張數+1
optXY = mt.simp_frac(S1, S2, MaxV + 1)
#如果最簡整數比出現[ (MaxV+1) / 1 ] or [ 1 / (MaxV+1) ] 就剃除
#張數權重整數化後，絕對值小於5的設1（通過），絕對值大於6的設0（沒通過）
if abs(optXY[0]) <= MaxV and abs(optXY[1]) <= MaxV:
ind[mi, 4] = 1
IntegerB[:, mi] = optXY[:]
ind[mi, 7] = optXY[0]
ind[mi, 8] = optXY[1]
#計算Spread的時間趨勢均值與標準差
Johansen_intcept, Johansen_slope = jci.Johansen_mean(
F_a, F_b, F_gam, F_ct, p - 1)
Johansen_var_correct = jci.Johansen_std_correct(
F_a, F_b, F_ut, F_gam, p - 1)
Johansen_std = np.sqrt(Johansen_var_correct)
ind[mi, 9] = Johansen_std
cy_mean[:,
mi] = Johansen_intcept + Johansen_slope * np.linspace(
0, 249, 250)
#以資金權重建構Naturn Log共整合序列
cy[:, mi] = pd.DataFrame(
np.mat(rowLS) * np.mat(CapitW[:, mi]).T).stack()
#拿共整合序列拿去檢定，ADF單根檢定回傳1代表無單根（定態），0代表有單根（非定態）
#ind[mi,5] = mt.ADFtest_TR(cy[OpenD-1:inNum,mi], opt_p-1 , 0.05)
#如果收斂點在Trading Period，設為0（沒通過、不交易），反之設為1
#if converg_Point < inNum:
#ind[mi,10] = converg_Point
#Spend_time = time.time() - start_time
except:
continue
dd = np.zeros([ind.shape[0], 1])
test_Inter = ind[:, 4] == 1
#test_ADF = ind[:,5]==1
test_Model = ind[:, 6] >= 4 #挑出model4&5交易
#test_converg = ind[:,10]>0
#dd = test_Inter & test_ADF & test_Model & test_converg
dd = test_Inter & test_Model
OMinx = ind[dd, :]
cy = cy[:, dd]
cy_mean = cy_mean[:, dd]
IntegerB = IntegerB[:, dd]
DailyResult = np.zeros((OMinx.shape[0], 17))
DailyResult[:, 0:2] = OMinx[:, 0:2]
DailyResult[:, 2:5] = OMinx[:, 6:9]
DailyResult[:, 5] = OMinx[:, 10]
#DailyResult=[S1,S2,model,SFx資金權重,SFy,Cconverg_point收斂點,...
#DailyResult(:,6:11)
# ...,總獲利,平倉獲利,停損獲利,換日強停獲利,換日強停虧損,...
#DailyResult(:,11:17)
# ...,開倉次數,平倉次數,停損次數,換日強停獲利次數,換日強停虧損次數,向上(1)/向下(-1)]
for pi in range(OMinx.shape[0]):
SStd = OMinx[pi, 9] #標準差
mean_slope = cy_mean[inNum, pi] - cy_mean[0, pi]
#Con_Point = int(DailyResult[pi,5])
smin = Smin[[str(int(OMinx[pi, 0])),
str(int(OMinx[pi, 1]))]][inNum:DailyNum]
'''
#畫個圖確認一下
import matplotlib.pyplot as plt
plotx = [i for i in range(DailyNum)]
CL = np.zeros((DailyNum,5))
CL [:,2] = cy_mean[:,pi]
CL [:,1] = cy_mean[:,pi]+SStd*os
CL [:,0] = cy_mean[:,pi]+SStd*cs
CL [:,3] = cy_mean[:,pi]-SStd*os
CL [:,4] = cy_mean[:,pi]-SStd*cs
plt.plot(plotx,cy[:,pi],plotx,CL)
'''
if SStd * os <= costS:
continue
elif SStd * os > costS and mean_slope > 0: #and Con_Point < Min_cp:
print(
mt.trade_up(cy[inNum:DailyNum, pi],
cy_mean[inNum:DailyNum, pi], np.array(smin),
IntegerB[:, pi], SStd, cost, os, cs, Max_tp))
# DailyResult[pi, 6:11]=ProfitU
# DailyResult[pi, 11:16]=CountU
# DailyResult[pi, 16] = 1
elif SStd * os > costS and mean_slope < 0: # and Con_Point < Min_cp:
print(
mt.trade_down(cy[inNum:DailyNum, pi], cy_mean[inNum:DailyNum,
pi],
np.array(smin), IntegerB[:, pi], SStd, cost, os,
cs, Max_tp))
# DailyResult[pi, 6:11]=ProfitD
# DailyResult[pi, 11:16]=CountD
# DailyResult[pi, 16] = -1
return DailyResult
def cointegration_weight(stock1, stock2):
# 開啟matlab引擎
#eng=matlab.engine.start_matlab()
# 選擇適合的 VECM model，並且檢定 formation period 是否有結構性斷裂，並刪除該配對，其餘配對則回傳共整合係數。
#rank = 1
#t1 = int(len(min_price)*3/4) # 一天的時間長度(偵測兩天中間是否有結構性斷裂)
local_select_model = []
local_weight = []
local_name = []
local_pval = []
# stock1 = min_price.iloc[:,i]
# stock2 = min_price.iloc[:,j]
# stock1_name = min_price.columns.values[i]
# stock2_name = min_price.columns.values[j]
z = (np.vstack([stock1, stock2]).T)
model = VAR(z)
p = order_select(z, 5)
#p = int(model.select_order(5).bic)
# VAR 至少需落後1期
if p < 1:
return 0, 0
# portmanteau test
if model.fit(p).test_whiteness(nlags=5).pvalue < 0.05:
return 0, 0
# Normality test
if model.fit(p).test_normality().pvalue < 0.05:
return 0, 0
#r1 = eng.rank_jci( matlab.double(z.tolist()) , 'H2' , (p-1) )
#r2 = eng.rank_jci( matlab.double(z.tolist()) , 'H1*' , (p-1))
#r3 = eng.rank_jci( matlab.double(z.tolist()) , 'H1' , (p-1) )
r1 = rank(pd.DataFrame(z), 'H2', p)
r2 = rank(pd.DataFrame(z), 'H1*', p)
r3 = rank(pd.DataFrame(z), 'H1', p)
#r4 = rank( pd.DataFrame(z) , 'H*' , p )
if r3 > 0: # 在 model 3 上有 rank
if r2 > 0: # 在 model 2 上有 rank
if r1 > 0: # select model 1 and model 2 and model 3
#lambda_model2 = eng.eig_jci( matlab.double(z.tolist()) , 'H1*' , (p-1) , r2 )
#lambda_model3 = eng.eig_jci( matlab.double(z.tolist()) , 'H1' , (p-1) , r2 )
lambda_model2 = eig(pd.DataFrame(z), 'H1*', p, r2)
lambda_model3 = eig(pd.DataFrame(z), 'H1', p, r2)
test = np.log(
lambda_model2 / lambda_model3) * (len(stock1) - p)
if test <= 0:
raise ValueError('test value error')
if test > 3.8414:
#bp1 = chow_test( z , t1 , p , 'H1' , r3 )
#if bp1 == 0:
local_select_model.append('model3')
return weigh(pd.DataFrame(z), 'H1', p, r3)
#weight.append( eng.coin_jci( matlab.double(z.tolist()) , 'H1' , (p-1) , r3 ) )
# local_weight.append( weigh( pd.DataFrame(z) , 'H1' , p , r3 ) )
# local_name.append([stock1_name,stock2_name])
# local_pval.append( vecm_pvalue('model3', vecm( pd.DataFrame(z),'H1',p)[0][0] ) )
else:
#lambda_model1 = eng.eig_jci( matlab.double(z.tolist()) , 'H2' , (p-1) , r1 )
lambda_model1 = eig(pd.DataFrame(z), 'H2', p, r1)
test = np.log(
lambda_model1 / lambda_model2) * (len(stock1) - p)
if test > 3.8414:
#bp1 = chow_test( z , t1 , p , 'H1*' , r2 )
#if bp1 == 0:
# local_select_model.append('model2')
#weight.append( eng.coin_jci( matlab.double(z.tolist()) , 'H1*' , (p-1) , r2 ) )
return weigh(pd.DataFrame(z), 'H1*', p, r2)
# local_weight.append( weigh( pd.DataFrame(z) , 'H1*' , p , r2 ) )
# local_name.append([stock1_name,stock2_name])
# local_pval.append( vecm_pvalue('model2',vecm(pd.DataFrame(z),'H1*',p)[0][1] ) )
else:
#bp1 = chow_test( z , t1 , p , 'H2' , r1 )
#if bp1 == 0:
# local_select_model.append('model1')
#weight.append( eng.coin_jci( matlab.double(z.tolist()) , 'H2' , (p-1) , r1 ) )
return weigh(pd.DataFrame(z), 'H2', p, r1)
# local_weight.append( weigh( pd.DataFrame(z) , 'H2' , p , r1 ) )
# local_name.append([stock1_name,stock2_name])
# local_pval.append( vecm_pvalue('model1',vecm(pd.DataFrame(z),'H2',p)[0][0] ) )
else: # select model 2 and model 3
#lambda_model2 = eng.eig_jci( matlab.double(z.tolist()) , 'H1*' , (p-1) , r2 )
#lambda_model3 = eng.eig_jci( matlab.double(z.tolist()) , 'H1' , (p-1) , r2 )
lambda_model2 = eig(pd.DataFrame(z), 'H1*', p, r2)
lambda_model3 = eig(pd.DataFrame(z), 'H1', p, r2)
test = np.log(
lambda_model2 / lambda_model3) * (len(stock1) - p)
if test <= 0:
raise ValueError('test value error')
if test > 3.8414:
#bp1 = chow_test( z , t1 , p , 'H1' , r3 )
#if bp1 == 0:
# local_select_model.append('model3')
#weight.append( eng.coin_jci( matlab.double(z.tolist()) , 'H1' , (p-1) , r3 ) )
return weigh(pd.DataFrame(z), 'H1', p, r3)
# local_weight.append( weigh( pd.DataFrame(z) , 'H1' , p , r3 ) )
# local_name.append([stock1_name,stock2_name])
# local_pval.append( vecm_pvalue('model3',vecm(pd.DataFrame(z),'H1',p)[0][0] ) )
else:
#bp1 = chow_test( z , t1 , p , 'H1*' , r2 )
#if bp1 == 0:
# local_select_model.append('model2')
#weight.append( eng.coin_jci( matlab.double(z.tolist()) , 'H1*' , (p-1) , r2 ) )
return weigh(pd.DataFrame(z), 'H1*', p, r2)
# local_weight.append( weigh( pd.DataFrame(z) , 'H1*' , p , r2 ) )
# local_name.append([stock1_name,stock2_name])
# local_pval.append( vecm_pvalue('model2',vecm(pd.DataFrame(z),'H1*',p)[0][1] ) )
else: # 只在 model 3 上有rank
#bp1 = chow_test( z , t1 , p , 'H1' , r3 )
#if bp1 == 0:
# local_select_model.append('model3')
#weight.append( eng.coin_jci( matlab.double(z.tolist()) , 'H1' , (p-1) , r3 ) )
return weigh(pd.DataFrame(z), 'H1', p, r3)
# local_weight.append( weigh( pd.DataFrame(z) , 'H1' , p , r3 ) )
# local_name.append([stock1_name,stock2_name])
# local_pval.append( vecm_pvalue('model3',vecm(pd.DataFrame(z),'H1',p)[0][0] ) )
return 0, 0