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2092 lines (1615 loc) · 104 KB
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import pandas as pd
from pandas_datareader import data
import numpy as np, numpy.random
from numpy import mean
import random
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib import cm
from datetime import datetime
from scipy.stats import norm
from scipy.stats import shapiro
from scipy.stats import kstest
from scipy.stats import skew
from scipy.stats import kurtosis
from scipy import stats
from statsmodels.tsa.stattools import adfuller
from statsmodels.graphics.tsaplots import plot_pacf
from statsmodels.graphics.tsaplots import plot_acf
import pmdarima
import arch
#Based loosely on https://towardsdatascience.com/how-to-simulate-financial-portfolios-with-python-d0dc4b52a278
def extract_prices(start_date,end_date,symbols,portfolioWeights,portfolioValue,backtestduration=0):
dim=len(symbols)
for symbol in symbols:
dfprices = data.DataReader(symbols, start=start_date, end=end_date, data_source='yahoo')
dfprices = dfprices[['Adj Close']]
dfprices.columns=[' '.join(col).strip() for col in dfprices.columns.values]
priceAtEndDate=[]
for symbol in symbols:
priceAtEndDate.append(dfprices[[f'Adj Close {symbol}']][-(backtestduration+1):].values[0][0])
noOfShares=[]
portfolioValPerSymbol=[x * portfolioValue for x in portfolioWeights]
for i in range(0,len(symbols)):
noOfShares.append(portfolioValPerSymbol[i]/priceAtEndDate[i])
noOfShares=[round(element, 5) for element in noOfShares]
listOfColumns=dfprices.columns.tolist()
dfprices["Adj Close Portfolio"]=dfprices[listOfColumns].mul(noOfShares).sum(1)
share_split_table=dfprices.tail(1).T
share_split_table=share_split_table.iloc[:-1]
share_split_table["Share"]=symbols
share_split_table["No Of Shares"]=noOfShares
share_split_table.columns=["Price At "+end_date,"Share Name","No Of Shares"]
share_split_table["Value At "+end_date]=share_split_table["No Of Shares"]*share_split_table["Price At "+end_date]
share_split_table.index=share_split_table["Share Name"]
share_split_table=share_split_table[["Share Name","Price At "+end_date,"No Of Shares","Value At "+end_date]]
share_split_table=share_split_table.round(3)
share_split_table=share_split_table.append(share_split_table.sum(numeric_only=True), ignore_index=True)
share_split_table.at[len(symbols),'No Of Shares']=np.nan
share_split_table.at[len(symbols),'Price At '+end_date]=np.nan
share_split_table.at[len(symbols),'Share Name']="Portfolio"
share_split_table["Weights"]=portfolioWeights+["1"]
share_split_table = share_split_table[['Share Name', 'Weights', 'Price At '+end_date, 'No Of Shares', "Value At "+end_date]]
print(f"Extracted {len(dfprices)} days worth of data for {len(symbols)} counters with {dfprices.isnull().sum().sum()} missing data")
return dfprices, noOfShares, share_split_table
def plotprices(dfprices,symbols,imagecounter,targetfolder):
dfprices.plot(subplots=True, figsize=(15,7.5*len(symbols)))
plt.savefig(f'static/{targetfolder}/{imagecounter}_02adjclosingprices.png')
def plotpiechart(symbols,portfolioWeights,imagecounter,targetfolder):
labels = symbols
sizes = portfolioWeights
fig1, ax1 = plt.subplots()
ax1.pie(portfolioWeights, labels=symbols, autopct='%1.1f%%',
shadow=True, startangle=90)
ax1.axis('equal') # Equal aspect ratio ensures that pie is drawn as a circle.
plt.title("Portfolio Weights")
plt.savefig(f'static/{targetfolder}/{imagecounter}_01portfolioweights.png')
#Modified from https://medium.com/swlh/generating-candlestick-charts-from-scratch-ef6e1d3cf0e9
# Function to draw candlestick
def draw_candlestick(axis, data, color_up, color_down):
# Check if stock closed higher or not
if data['Close'] > data['Open']:
color = color_up
else:
color = color_down
# Plot the candle wick
axis.plot([data['day_num'], data['day_num']], [data['Low'], data['High']], linewidth=2, color='black', solid_capstyle='round', zorder=2)
# Draw the candle body
rect = mpl.patches.Rectangle((data['day_num'] - 0.5, data['Open']), 1.0, (data['Close'] - data['Open']), facecolor=color, edgecolor='black', linewidth=1, zorder=3)
# Add candle body to the axis
axis.add_patch(rect)
# Return modified axis
return axis
# Function to draw all candlesticks
def draw_all_candlesticks(axis, data, color_up='white', color_down='black'):
for day in range(data.shape[0]):
axis = draw_candlestick(axis, data.iloc[day], color_up, color_down)
return axis
def plot_candlesticks(symbols,start_date,end_date,imagecounter,targetfolder):
for i in range(0,len(symbols)):
tkr_str = str(symbols[i])
tkr_history = data.DataReader(tkr_str, start=start_date, end=end_date, data_source='yahoo')
tkr_history['Date']=tkr_history.index
base_date = tkr_history['Date'][0]
tkr_history['day_num'] = tkr_history['Date'].map(lambda date:(date - base_date).days)
# Create figure and axes
fig = plt.figure(figsize=(20, 10), facecolor='white')
ax = fig.add_subplot(111)
# Colors for candlesticks
colors = ['#00FF00', '#FF0000']
# Grid lines
ax.grid(linestyle='-', linewidth=4, color='white', zorder=1)
# Draw candlesticks
ax = draw_all_candlesticks(ax, tkr_history, colors[0], colors[1])
# Set ticks to every 5th day
ax.set_xticks(list(tkr_history['day_num'])[::15])
ax.set_xticklabels(list(tkr_history['Date'].dt.strftime('%Y-%m-%d'))[::15])
ax.tick_params(labelsize=14)
plt.xticks(rotation=50)
# # Add dollar signs
# formatter = mpl.ticker.FormatStrFormatter('$%.2f')
# ax.yaxis.set_major_formatter(formatter)
# Append ticker symbol
ax.text(0, 1.05, tkr_str, va='baseline', ha='left', size=20, transform=ax.transAxes)
# Set axis limits
ax.set_xlim(-1, tkr_history['day_num'].iloc[-1] + 1)
# Show plot
plt.savefig(f'static/{targetfolder}/{imagecounter}_candlestick{i}.png')
#plt.show()
#Modified from https://tcoil.info/compute-bollinger-bands-for-stocks-with-python-and-pandas/
# n = smoothing length eg 20
# m = number of standard deviations away from MA eg 2
def bollinger_bands(start_date,end_date,symbol, n, m,i):
df=data.DataReader(symbol, start=start_date, end=end_date, data_source='yahoo')
#typical price
TP = (df['High'] + df['Low'] + df['Close']) / 3
# but we will use Adj close instead for now, depends
datax = TP
#data = df['Adj Close']
# takes one column from dataframe
B_MA = pd.Series((datax.rolling(n, min_periods=n).mean()), name='B_MA')
sigma = datax.rolling(n, min_periods=n).std()
BU = pd.Series((B_MA + m * sigma), name='BU')
BL = pd.Series((B_MA - m * sigma), name='BL')
df = df.join(B_MA)
df = df.join(BU)
df = df.join(BL)
return df
def plot_bollingerbands(symbols,start_date,end_date,n,m,imagecounter,targetfolder):
for i in range(0,len(symbols)):
df=bollinger_bands(start_date,end_date,str(symbols[i]), n, m,i)
# plot correspondingRSI values and significant levels
plt.figure(figsize=(15,5))
plt.title(symbols[i]+': Bollinger Bands For Smoothing Length Of '+str(n)+' Days & '+str(m)+' Std Devs From MA')
plt.plot(df.index, df['Adj Close'])
plt.plot(df.index, df['BU'], alpha=0.3)
plt.plot(df.index, df['BL'], alpha=0.3)
plt.plot(df.index, df['B_MA'], alpha=0.3)
plt.fill_between(df.index, df['BU'], df['BL'], color='grey', alpha=0.1)
plt.savefig(f'static/{targetfolder}/{imagecounter}_bollingerband{i}.png')
#plt.show()
#Modified from https://stackoverflow.com/questions/20526414/relative-strength-index-in-python-pandas
def calcRSI(start_date,end_date,symbol,time_window,RSItype="EWMA"):
df=data.DataReader(symbol, start=start_date, end=end_date, data_source='yahoo')
diff = df["Adj Close"].diff(1).dropna() # diff in one field(one day)
#this preservers dimensions off diff values
up_chg = 0 * diff
down_chg = 0 * diff
# up change is equal to the positive difference, otherwise equal to zero
up_chg[diff > 0] = diff[ diff>0 ]
# down change is equal to negative deifference, otherwise equal to zero
down_chg[diff < 0] = diff[ diff < 0 ]
# check pandas documentation for ewm
# https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.ewm.html
# values are related to exponential decay
# we set com=time_window-1 so we get decay alpha=1/time_window
if RSItype=="EWMA":
up_chg_avg = up_chg.ewm(com=time_window-1 , min_periods=time_window, adjust=False).mean()
down_chg_avg = down_chg.ewm(com=time_window-1 , min_periods=time_window, adjust=False).mean()
elif RSItype=="SMA":
# Calculate the SMA
up_chg_avg = up_chg.rolling(time_window).mean()
down_chg_avg = down_chg.abs().rolling(time_window).mean()
rs = abs(up_chg_avg/down_chg_avg)
rsi = 100 - 100/(1+rs)
df["RSI"]=rsi
return df
def plot_RSI(symbols,start_date,end_date,time_window,RSItype,imagecounter,targetfolder):
for i in range(0,len(symbols)):
dfrsi=calcRSI(start_date,end_date,str(symbols[i]),time_window,RSItype)
plt.figure(figsize=(15,5))
dfrsi['Adj Close'][time_window::].plot()
plt.title(str(symbols[i])+": Adj Close Price")
plt.savefig(f'static/{targetfolder}/{imagecounter}_{i}adjclosingprice.png')
#plt.show
plt.figure(figsize=(15,5))
dfrsi["RSI"].plot()
plt.axhline(0, linestyle='--', alpha=0.1)
plt.axhline(20, linestyle='--', alpha=0.5)
plt.axhline(30, linestyle='--')
plt.axhline(70, linestyle='--')
plt.axhline(80, linestyle='--', alpha=0.5)
plt.axhline(100, linestyle='--', alpha=0.1)
plt.title(str(symbols[i])+": RSI Plot: "+RSItype+" With Period Of "+str(time_window)+" Days")
plt.savefig(f'static/{targetfolder}/{imagecounter}_{i}relativestrengthindex.png')
#plt.show()
def calcMACD(start_date,end_date,symbol,timeperiod1,timeperiod2,timeperiod3,imagecounter,targetfolder):
df=data.DataReader(symbol, start=start_date, end=end_date, data_source='yahoo')
df["EWMA "+str(timeperiod1)+" Days"]=df["Adj Close"].ewm(span=timeperiod1,min_periods=timeperiod1,adjust=False,ignore_na=False).mean()
df["EWMA "+str(timeperiod2)+" Days"]=df["Adj Close"].ewm(span=timeperiod2,min_periods=timeperiod2,adjust=False,ignore_na=False).mean()
df["MACD"]=df["EWMA "+str(timeperiod1)+" Days"]-df["EWMA "+str(timeperiod2)+" Days"]
df["Signal Line"]=df["MACD"].ewm(span=timeperiod3,min_periods=timeperiod3,adjust=False,ignore_na=False).mean()
df[['Adj Close',"EWMA "+str(timeperiod1)+" Days","EWMA "+str(timeperiod2)+" Days"]].plot(figsize=(15,5))
plt.title(symbol+": MACD ("+str(timeperiod1)+","+str(timeperiod2)+","+str(timeperiod3)+") - EWMAs & Adj Close Price")
plt.savefig(f'static/{targetfolder}/{imagecounter}_{symbol}_1_MACD.png')
df[["MACD","Signal Line"]].plot(figsize=(15,5))
plt.title(symbol+": MACD ("+str(timeperiod1)+","+str(timeperiod2)+","+str(timeperiod3)+") - MACD & Signal Line")
plt.savefig(f'static/{targetfolder}/{imagecounter}_{symbol}_2_MACD.png')
df["Histogram"]=df["MACD"]-df["Signal Line"]
df.plot.bar(y='Histogram',figsize=(15,5))
tick_spacing = 28
plt.gca().xaxis.set_major_locator(plt.AutoLocator())
plt.title(symbol+": MACD ("+str(timeperiod1)+","+str(timeperiod2)+","+str(timeperiod3)+") - MACD Histogram")
#plt.savefig(f'static/{targetfolder}/{imagecounter}_{symbol}_3_MACD.png')
def plot_MACD(start_date,end_date,symbols,timeperiod1,timeperiod2,timeperiod3,imagecounter,targetfolder):
for symbol in symbols:
calcMACD(start_date,end_date,symbol,timeperiod1,timeperiod2,timeperiod3,imagecounter,targetfolder)
def calc_returns(dfprices,symbols):
dfreturns=pd.DataFrame()
columns = list(dfprices)
mean=[]
stdev=[]
for column in columns:
dfreturns[f'Log Daily Returns {column}']=np.log(dfprices[column]).diff()
mean.append(dfreturns[f'Log Daily Returns {column}'][1:].mean())
stdev.append(dfreturns[f'Log Daily Returns {column}'][1:].std())
dfreturns=dfreturns.dropna()
if len(dfreturns.columns)==1:
df_mean_stdev=pd.DataFrame(list(zip(symbols,mean,stdev)),columns =['Stock', 'Mean Log Daily Return','StdDev Log Daily Return'])
else:
df_mean_stdev=pd.DataFrame(list(zip(symbols+["Portfolio"],mean,stdev)),columns =['Stock', 'Mean Log Daily Return','StdDev Log Daily Return'])
return dfreturns ,df_mean_stdev
def convertReturnsToPrices(dfreturns,startingrefprice):
stockprices=pd.DataFrame()
stockprices=np.exp(dfreturns)
stockprices=stockprices.cumprod()
stockprices=stockprices.mul(startingrefprice.values)
stockprices.columns=stockprices.columns.str.lstrip('Log Daily Returns ')
firstrow=pd.DataFrame(startingrefprice)
stockprices=pd.concat([firstrow,stockprices])
return stockprices
def plotreturns(dfreturns,imagecounter,targetfolder):
dfreturns.plot(subplots=True, figsize=(15,7.5*len(dfreturns.columns)))
plt.savefig(f'static/{targetfolder}/{imagecounter}_03Dailyreturns.png')
#Correlations which are within the blue bands are not statistically significant
def plotACFPACF(series,imagecounter,targetfolder):
for i in range(0,len(series.columns)):
plt.figure(figsize=(15,5))
Prices=series[series.columns[i]].plot()
plt.title(series.columns[i])
plt.savefig(f'static/{targetfolder}/{imagecounter}_{i}_Price.png')
fig1, ax1 = plt.subplots(figsize=(15, 5))
ACFplot=plot_acf(series[series.columns[i]], lags=30, ax=ax1)
plt.title(series.columns[i]+' ACF')
plt.savefig(f'static/{targetfolder}/{imagecounter}_{i}_PriceACF.png')
fig2, ax2 = plt.subplots(figsize=(15, 5))
PACFplot=plot_pacf(series[series.columns[i]], lags=30,ax=ax2)
plt.title(series.columns[i]+' PACF')
plt.savefig(f'static/{targetfolder}/{imagecounter}_{i}_PricePACF.png')
def compareStartMidEnd(dfreturns,df_mean_stdev):
#print ('Size of dataFrame=', len(dfreturns.index))
desired_number_of_groups = 3
group_size = int(len(dfreturns.index) / (desired_number_of_groups))
#print("group_size=", group_size)
remainder_size = len(dfreturns.index) % group_size
#print("remainder_size=", remainder_size)
df_split_list = [dfreturns.iloc[i:i + group_size] for i in range(0, len(dfreturns) - group_size + 1, group_size)]
#print("Number of split_dataframes=", len(df_split_list))
if remainder_size > 0:
df_remainder = dfreturns.iloc[-remainder_size:len(dfreturns.index)]
df_split_list.append(df_remainder)
#print("Revised Number of split_dataframes=", len(df_split_list))
#print("Splitting complete, verifying counts")
count_all_rows_after_split = 0
for index, split_df in enumerate(df_split_list):
#print("split_df:", index, " size=", len(split_df.index))
count_all_rows_after_split += len(split_df.index)
if count_all_rows_after_split != len(dfreturns.index):
raise Exception('rows_after_split = ', count_all_rows_after_split," but original CSV DataFrame has count =", len(dfreturns.index))
columns =['Stock','Start Mean', 'Start StdDev','Middle Mean','Middle StdDev','End Mean','End StdDev']
anothertable=[]
for i in range(0,len(dfreturns.columns)):
boxplotsplit=pd.DataFrame()
boxplotsplit["Start"]=df_split_list[0].iloc[:,i].values
boxplotsplit["Middle"]=df_split_list[1].iloc[:,i].values
boxplotsplit["End"]=df_split_list[2].iloc[:,i].values
#means = [boxplotsplit["Start"].mean(),boxplotsplit["Middle"].mean(),boxplotsplit["End"].mean()]
#std = [boxplotsplit["Start"].std(),boxplotsplit["Middle"].std(),boxplotsplit["End"].std()]
meanstdev=[dfreturns.columns[i],boxplotsplit["Start"].mean(),boxplotsplit["Start"].std(),\
boxplotsplit["Middle"].mean(),boxplotsplit["Middle"].std(),\
boxplotsplit["End"].mean(),boxplotsplit["End"].std()]
anothertable.append(meanstdev)
yetanothertable=pd.DataFrame(anothertable,columns=columns)
yetanothertable["Overall Mean"]=df_mean_stdev["Mean Log Daily Return"]
yetanothertable["Overall StdDev"]=df_mean_stdev["StdDev Log Daily Return"]
yetanothertable=yetanothertable[['Stock','Overall Mean', 'Start Mean','Middle Mean','End Mean',\
'Overall StdDev','Start StdDev','Middle StdDev','End StdDev']]
return yetanothertable
def fit_test_normal(dfreturns,symbols,imagecounter,targetfolder):
columnlist=dfreturns.columns
KSTestResults=[]
KSPValResults=[]
for column in columnlist:
data=(dfreturns[column])
normed_data=(data-dfreturns[column].mean())/dfreturns[column].std()
KSTestResults.append(kstest(normed_data, 'norm')[0])
KSPValResults.append(kstest(normed_data, 'norm')[1])
if len(dfreturns.columns)==1:
KSTestResultsDF=pd.DataFrame([dfreturns.columns,KSTestResults,KSPValResults]).T
else:
KSTestResultsDF=pd.DataFrame([dfreturns.columns,KSTestResults,KSPValResults]).T
KSTestResultsDF.columns=["Share Name","KS Test Statistic","KS Test P-Value"]
KSTestResultsDF["Accept/Reject At 5% Signif Lvl"]=np.where(KSTestResultsDF['KS Test P-Value']> 0.05, "Data looks normal (Fail to reject H0)", "Data does NOT look normal (Reject H0)")
ShapiroWilkTestStats=[]
ShapiroWilkTestPValue=[]
for column in columnlist:
data=(dfreturns[column])
stat, pvalue = shapiro(data)
ShapiroWilkTestStats.append(stat)
ShapiroWilkTestPValue.append(round(pvalue,6))
ShapiroWilkTestResultsDF=pd.DataFrame([ShapiroWilkTestStats,ShapiroWilkTestPValue]).T
if len(dfreturns.columns)==1:
ShapiroWilkTestResultsDF["Share Name"]=dfreturns.columns
else:
ShapiroWilkTestResultsDF["Share Name"]=dfreturns.columns
ShapiroWilkTestResultsDF.columns=["SW Test Statistic","SW Test P-Value","Share Name"]
ShapiroWilkTestResultsDF=ShapiroWilkTestResultsDF[["Share Name","SW Test Statistic","SW Test P-Value"]]
ShapiroWilkTestResultsDF["Accept/Reject At 5% Signif Lvl"]=np.where(ShapiroWilkTestResultsDF['SW Test P-Value']> 0.05, "Data looks normal (Fail to reject H0)", "Data does NOT look normal (Reject H0)")
ADFTestStats=[]
ADFTestCritValue=[]
for column in columnlist:
data=(dfreturns[column])
ADFTest_result = adfuller(data)
ADFTestStats.append(ADFTest_result[0])
ADFTestCritValue.append(ADFTest_result[4]['5%'])
ADFTestResultsDF=pd.DataFrame([ADFTestStats,ADFTestCritValue]).T
ADFTestResultsDF["Share Name"]=dfreturns.columns
ADFTestResultsDF.columns=["ADF Test Statistic","ADF Test Stat Crit Value At 5% Signif Lvl","Share Name"]
ADFTestResultsDF=ADFTestResultsDF[["Share Name","ADF Test Statistic","ADF Test Stat Crit Value At 5% Signif Lvl"]]
ADFTestResultsDF["Accept/Reject At 5% Signif Lvl"]=np.where(ADFTestResultsDF['ADF Test Statistic']> ADFTestResultsDF['ADF Test Stat Crit Value At 5% Signif Lvl'] , "Time series is NON-stationary (Reject H0)", "Time series is stationary (Fail To Reject H0)")
skewArray=[]
kurtosisArray=[]
for column in columnlist:
data=(dfreturns[column])
skewArray.append(skew(data))
kurtosisArray.append(kurtosis(data))
mu = np.mean(data)
sigma = np.std(data)
plt.figure(figsize = (15, 5))
plt.hist(data, bins=50, density=True, alpha=0.6, color='g')
# Plot the PDF.
xmin, xmax = plt.xlim()
x = np.linspace(xmin, xmax, 100)
p = norm.pdf(x, mu, sigma)
plt.plot(x, p, 'k', linewidth=2)
title = column+" Histogram vs Best Fit Normal Distribution Mu = %.3f, Sigma = %.3f" % (mu, sigma)
plt.title(title)
plt.savefig(f'static/{targetfolder}/{imagecounter}_04histogram{column}.png')
Kurtosis_Skew=pd.DataFrame(list(zip(skewArray, kurtosisArray)),
index=columnlist,columns =['Skew','Kurtosis'])
# If the skewness is between -0.5 and 0.5, the data are fairly symmetrical.
# If the skewness is between -1 and – 0.5 or between 0.5 and 1, the data are moderately skewed.
# If the skewness is less than -1 or greater than 1, the data are highly skewed.
def skewconditions(s):
if (s['Skew'] > 1) :
return "Highly Positively Skewed"
elif (s['Skew'] <= 1) and (s['Skew'] > 0.5) :
return "Moderately Positively Skewed"
elif (s['Skew'] <= 0.5) and (s['Skew'] > -0.5) :
return "Fairly Symmetrical"
elif (s['Skew'] <= -0.5) and (s['Skew'] > -1.0) :
return "Moderately Negatively Skewed"
elif (s['Skew'] <= -1.0) :
return "Highly Negatively Skewed"
# For kurtosis, the general guideline is that if the number is greater than +1, the distribution is too peaked.
# Likewise, a kurtosis of less than –1 indicates a distribution that is too flat
def kurtosisconditions(s):
if (s['Kurtosis'] > 3) :
return "Leptokurtic:Peaked & Fat Tailed"
elif (s['Kurtosis'] <-3):
return "Platykurtic:Flat & Thin Tailed"
else :
return "Mesokurtic"
Kurtosis_Skew['Skew Description'] = Kurtosis_Skew.apply(skewconditions, axis=1)
Kurtosis_Skew['Kurtosis Description'] = Kurtosis_Skew.apply(kurtosisconditions, axis=1)
for i in range(0,len(columnlist)):
data=(dfreturns.iloc[:, i])
res = stats.probplot(data, dist="norm")
xxx=pd.DataFrame(list(zip(res[0][0],res[0][1])),columns =["Theoretical Quantiles","Ordered Values"])
xxx.plot.scatter(x="Theoretical Quantiles",y="Ordered Values",title=columnlist[i],figsize = (7.5, 5))
plt.plot(xxx["Theoretical Quantiles"], res[1][0]*xxx["Theoretical Quantiles"]+res[1][1])
plt.savefig(f'static/{targetfolder}/{imagecounter}_05qqplot{i}.png')
return KSTestResultsDF, ShapiroWilkTestResultsDF, Kurtosis_Skew, ADFTestResultsDF
def bootstrap_w_replc_singleval(dfreturns):
columns=dfreturns.columns
singlesample=pd.DataFrame(dfreturns.values[np.random.randint(len(dfreturns), size=1)], columns=columns)
return singlesample
def bootstrapforecast(dfreturns,T):
columnlist=dfreturns.columns
X=[]
for i in range(0,T):
X.append(bootstrap_w_replc_singleval(dfreturns).values.tolist()[0])
Y=pd.DataFrame(X)
Y.columns=columnlist
Y.loc[-1] = [0]*len(columnlist) # adding a row
Y.index = Y.index + 1 # shifting index
Y = Y.sort_index() # sorting by index
return Y
#Adapted from https://stackoverflow.com/questions/10939213/how-can-i-calculate-the-nearest-positive-semi-definite-matrix
#import numpy as np,numpy.linalg
def _getAplus(A):
eigval, eigvec = np.linalg.eig(A)
Q = np.matrix(eigvec)
xdiag = np.matrix(np.diag(np.maximum(eigval, 0)))
return Q*xdiag*Q.T
def _getPs(A, W=None):
W05 = np.matrix(W**.5)
return W05.I * _getAplus(W05 * A * W05) * W05.I
def _getPu(A, W=None):
Aret = np.array(A.copy())
Aret[W > 0] = np.array(W)[W > 0]
return np.matrix(Aret)
def nearPD(A, nit=10):
n = A.shape[0]
W = np.identity(n)
# W is the matrix used for the norm (assumed to be Identity matrix here)
# the algorithm should work for any diagonal W
deltaS = 0
Yk = A.copy()
for k in range(nit):
Rk = Yk - deltaS
Xk = _getPs(Rk, W=W)
deltaS = Xk - Rk
Yk = _getPu(Xk, W=W)
return Yk
def create_covar(dfreturns):
try:
returns=[]
arrOfReturns=[]
columns = list(dfreturns)
for column in columns:
returns=dfreturns[column].values.tolist()
arrOfReturns.append(returns)
Cov = np.cov(np.array(arrOfReturns))
return Cov
except LinAlgError :
Cov = nearPD(np.array(arrOfReturns), nit=10)
print("WARNING -Original Covariance Matrix is NOT Positive Semi Definite And Has Been Adjusted To Allow For Cholesky Decomposition ")
return Cov
def GBMsimulatorMultiVar(So, mu, sigma, Cov, T, N):
"""
Parameters
seed: seed of simulation
So: initial stocks' price
mu: expected return
sigma: volatility
Cov: covariance matrix
T: time period
N: number of increments
"""
#np.random.seed(seed) turned off so Monte Carlo can be "randomised"
dim = np.size(So)
t = np.linspace(0., T, int(N))
A = np.linalg.cholesky(Cov)
S = np.zeros([dim, int(N)])
S[:, 0] = So
for i in range(1, int(N)):
drift = (mu - 0.5 * sigma**2) * (t[i] - t[i-1])
Z = np.random.normal(0., 1., dim)
diffusion = np.matmul(A, Z) * (np.sqrt(t[i] - t[i-1]))
S[:, i] = S[:, i-1]*np.exp(drift + diffusion)
return S, t
def GBMsimulatorUniVar(So, mu, sigma, T, N):
"""
Parameters
seed: seed of simulation
So: initial stocks' price
mu: expected return
sigma: volatility
Cov: covariance matrix
T: time period
N: number of increments
"""
#np.random.seed(seed) turned off so Monte Carlo can be "randomised"
dim = np.size(So)
t = np.linspace(0., T, int(N))
S = np.zeros([dim, int(N)])
S[:, 0] = So
for i in range(1, int(N)):
drift = (mu - 0.5 * sigma**2) * (t[i] - t[i-1])
Z = np.random.normal(0., 1., dim)
diffusion = sigma* Z * (np.sqrt(t[i] - t[i-1]))
S[:, i] = S[:, i-1]*np.exp(drift + diffusion)
return S, t
def calculateRMSE(final,T,backtest_duration,dfprices):
xyz=final.tail(T)
xyz=xyz.head(backtest_duration)
xyz
qrs=pd.DataFrame(index=xyz.index)
for i in range(0,len(dfprices.columns)):
x=1+(len(dfprices.columns)-i)*-3
qrs["Actual "+dfprices.columns[i]]=xyz.iloc[:,i]
qrs["P50 "+dfprices.columns[i]]=xyz.iloc[:,x]
for i in range(0,len(dfprices.columns)):
x=i*2
qrs["RMSE "+dfprices.columns[i]]=(qrs.iloc[:,x]-qrs.iloc[:,x+1])**2
qrs
RMSE=[]
for i in range(0,len(dfprices.columns)):
z=-(len(dfprices.columns)-i)
RMSE.append((qrs.iloc[:,z].mean())**0.5)
RMSE_DF=pd.DataFrame(RMSE,index=[dfprices.columns],columns=["RMSE For Backtest From "+qrs.index[0].strftime("%Y-%m-%d")+" To "+qrs.index[-1].strftime("%Y-%m-%d")\
+" ("+str(len(qrs))+" Days)"])
return RMSE_DF
def MonteCarlo_GBM(start_date,end_date,backtest_duration,percentile_range,symbols,\
portfolioWeights,portfolioValue,T,N,NoOfIterationsMC,imagecounter,targetfolder):
forecastresults=pd.DataFrame()
percentiles=pd.DataFrame()
extended_dates_future=[]
lowerpercentile=int(percentile_range[1:3])
upperpercentile=int(percentile_range[5:7])
plotpiechart(symbols,portfolioWeights,imagecounter,targetfolder)
if len(symbols)==1:
dfpricesFULL, noOfSharesFULL, share_split_tableFULL = extract_prices(start_date,end_date,symbols,portfolioWeights,portfolioValue)
backtest_end_date=dfpricesFULL.index[-(backtest_duration+1)].strftime("%Y-%m-%d")
dfprices, noOfShares, share_split_table = extract_prices(start_date,backtest_end_date,symbols,portfolioWeights,portfolioValue)
dfprices["Adj Close Portfolio"]=dfprices[list(dfprices.iloc[:,:-1].columns)].mul(noOfSharesFULL).sum(1)
else:
dfpricesFULL, noOfSharesFULL, share_split_tableFULL = extract_prices(start_date,end_date,symbols,portfolioWeights,portfolioValue)
backtest_end_date=dfpricesFULL.index[-(backtest_duration+1)].strftime("%Y-%m-%d")
dfprices, noOfShares, share_split_table = extract_prices(start_date,backtest_end_date,symbols,portfolioWeights,portfolioValue)
dfprices["Adj Close Portfolio"]=dfprices[list(dfprices.iloc[:,:-1].columns)].mul(noOfSharesFULL).sum(1)
symbolsWPortfolio=symbols+["Portfolio"]
dfreturns ,df_mean_stdev = calc_returns(dfprices,symbolsWPortfolio)
S0=np.array(dfprices.tail(1).values.tolist()[0])
mu=np.array(df_mean_stdev["Mean Log Daily Return"].values.tolist())
sigma=np.array(df_mean_stdev["StdDev Log Daily Return"].values.tolist())
backtestdateslist=(list((dfpricesFULL.tail(backtest_duration+1).index)))
backtestdates=[]
for i in backtestdateslist:
backtestdates.append(np.datetime64(datetime.strptime(str(i), '%Y-%m-%d %H:%M:%S').strftime("%Y-%m-%d")))
for i in range(0,N-backtest_duration):
extended_dates_future.append(np.busday_offset(end_date, i, roll='forward'))
extended_dates=backtestdates[0:len(backtestdates)-1]+extended_dates_future
if len(symbols)==1:
for x in range(1,NoOfIterationsMC+1):
stocks, time = GBMsimulatorUniVar(S0, mu, sigma, T, N)
prediction=pd.DataFrame(stocks)
prediction=prediction.T
prediction.index=extended_dates
prediction.columns=dfprices.columns
prediction=prediction.add_prefix('Iter_'+str(x)+'_')
forecastresults=pd.concat([forecastresults, prediction], axis=1)
for x in range(1,NoOfIterationsMC+1):
forecastresults["Iter_"+str(x)+"_Adj Close Portfolio"]=forecastresults["Iter_"+str(x)+"_Adj Close "+symbols[0]]*noOfSharesFULL
else:
Cov=create_covar(dfreturns)
for x in range(1,NoOfIterationsMC+1):
stocks, time = GBMsimulatorMultiVar(S0, mu, sigma, Cov, T, N)
prediction=pd.DataFrame(stocks)
prediction=prediction.T
prediction.index=extended_dates
prediction.columns=dfprices.columns
prediction=prediction.add_prefix('Iter_'+str(x)+'_')
forecastresults=pd.concat([forecastresults, prediction], axis=1)
for y in range(0,len(symbolsWPortfolio)):
percentiles["P"+str(lowerpercentile)+"_"+symbolsWPortfolio[y]]=forecastresults.filter(regex=symbolsWPortfolio[y]).quantile(float(lowerpercentile)/100,1)
percentiles["P50_"+symbolsWPortfolio[y]]=forecastresults.filter(regex=symbolsWPortfolio[y]).quantile(0.5,1)
percentiles["P"+str(upperpercentile)+"_"+symbolsWPortfolio[y]]=forecastresults.filter(regex=symbolsWPortfolio[y]).quantile(float(upperpercentile)/100,1)
forecastresults=pd.concat([forecastresults,percentiles[["P"+str(lowerpercentile)+"_"+symbolsWPortfolio[y],"P50_"+symbolsWPortfolio[y],"P"+str(upperpercentile)+"_"+symbolsWPortfolio[y]]]], axis=1, sort=False)
final=pd.concat([dfpricesFULL,forecastresults], axis=1, sort=False)
for z in range(0,len(symbolsWPortfolio)):
final.filter(regex="Adj Close "+symbolsWPortfolio[z]).tail(60).plot(legend=False,figsize = (20, 5),title=symbolsWPortfolio[z]+": Monte Carlo Simulations For "+str(NoOfIterationsMC)+" Iter-s")
plt.axvline(x=end_date,linestyle='dashed')
plt.savefig(f'static/{targetfolder}/{imagecounter}_totaliterations{z}.png')
percentileplot=pd.DataFrame()
percentileplot=pd.concat([final["Adj Close "+symbolsWPortfolio[z]],final.filter(regex="P??_"+symbolsWPortfolio[z])], axis=1, sort=False)
percentileplot.tail(60).plot(legend=True,figsize = (20, 5),title=symbolsWPortfolio[z]+": Monte Carlo Simulations For "+percentile_range+" Range")
plt.axvline(x=end_date,linestyle='dashed')
if NoOfIterationsMC>0:
plt.savefig(f'static/{targetfolder}/{imagecounter}_percentile{z}.png')
ReturnsAtForecastEndDate=final.tail(1).iloc[:,-(len(symbolsWPortfolio))*3:].T
HelperTable=pd.concat([dfpricesFULL.tail(1).round(3).T]*(3))
HelperTable["Sym"]=HelperTable.index
HelperTable['Sym'] =pd.Categorical(HelperTable["Sym"], list(dfprices.columns))
HelperTable=HelperTable.sort_values(['Sym'])
ReturnsAtForecastEndDate.insert(0, end_date, HelperTable.iloc[:,:-1].values)
ReturnsAtForecastEndDate["Returns Based On GBM"]=round((ReturnsAtForecastEndDate.iloc[:, 1]/ReturnsAtForecastEndDate.iloc[:, 0]-1)*100,2)
return final, share_split_tableFULL , dfreturns , df_mean_stdev , ReturnsAtForecastEndDate, dfprices
def MonteCarlo_Bootstrap(start_date,end_date,backtest_duration,percentile_range,symbols,\
portfolioWeights,portfolioValue,T,N,NoOfIterationsMC,imagecounter,targetfolder):
forecastresults=pd.DataFrame()
percentiles=pd.DataFrame()
extended_dates_future=[]
lowerpercentile=int(percentile_range[1:3])
upperpercentile=int(percentile_range[5:7])
plotpiechart(symbols,portfolioWeights,imagecounter,targetfolder)
if len(symbols)==1:
dfpricesFULL, noOfSharesFULL, share_split_tableFULL = extract_prices(start_date,end_date,symbols,portfolioWeights,portfolioValue)
backtest_end_date=dfpricesFULL.index[-(backtest_duration+1)].strftime("%Y-%m-%d")
dfprices, noOfShares, share_split_table = extract_prices(start_date,backtest_end_date,symbols,portfolioWeights,portfolioValue)
dfprices["Adj Close Portfolio"]=dfprices[list(dfprices.iloc[:,:-1].columns)].mul(noOfSharesFULL).sum(1)
else:
dfpricesFULL, noOfSharesFULL, share_split_tableFULL = extract_prices(start_date,end_date,symbols,portfolioWeights,portfolioValue)
backtest_end_date=dfpricesFULL.index[-(backtest_duration+1)].strftime("%Y-%m-%d")
dfprices, noOfShares, share_split_table = extract_prices(start_date,backtest_end_date,symbols,portfolioWeights,portfolioValue)
dfprices["Adj Close Portfolio"]=dfprices[list(dfprices.iloc[:,:-1].columns)].mul(noOfSharesFULL).sum(1)
symbolsWPortfolio=symbols+["Portfolio"]
dfreturns ,df_mean_stdev = calc_returns(dfprices,symbolsWPortfolio)
backtestdateslist=(list((dfpricesFULL.tail(backtest_duration+1).index)))
backtestdates=[]
for i in backtestdateslist:
backtestdates.append(np.datetime64(datetime.strptime(str(i), '%Y-%m-%d %H:%M:%S').strftime("%Y-%m-%d")))
for i in range(0,N-backtest_duration):
extended_dates_future.append(np.busday_offset(end_date, i, roll='forward'))
extended_dates=backtestdates[0:len(backtestdates)-1]+extended_dates_future
for x in range(1,NoOfIterationsMC+1):
futurereturns=bootstrapforecast(dfreturns,T)
futurereturns=np.exp(futurereturns)
futurereturns=futurereturns.cumprod()
stocks=pd.DataFrame()
for i in range(0,len(symbolsWPortfolio)):
futurereturns[str(i)+"Price"]=(futurereturns.iloc[:, i])*dfprices.tail(1).iloc[:, i][0]
stocks=futurereturns[futurereturns.columns[-len(symbolsWPortfolio):]]
stocks.columns=list(dfreturns.columns)
prediction=stocks
prediction.index=extended_dates
prediction.columns=dfprices.columns
prediction=prediction.add_prefix('Iter_'+str(x)+'_')
forecastresults=pd.concat([forecastresults,prediction], axis=1, sort=False)
for y in range(0,len(symbolsWPortfolio)):
percentiles["P"+str(lowerpercentile)+"_"+symbolsWPortfolio[y]]=forecastresults.filter(regex=symbolsWPortfolio[y]).quantile(float(lowerpercentile)/100,1)
percentiles["P50_"+symbolsWPortfolio[y]]=forecastresults.filter(regex=symbolsWPortfolio[y]).quantile(0.5,1)
percentiles["P"+str(upperpercentile)+"_"+symbolsWPortfolio[y]]=forecastresults.filter(regex=symbolsWPortfolio[y]).quantile(float(upperpercentile)/100,1)
forecastresults=pd.concat([forecastresults,percentiles[["P"+str(lowerpercentile)+"_"+symbolsWPortfolio[y],"P50_"+symbolsWPortfolio[y],"P"+str(upperpercentile)+"_"+symbolsWPortfolio[y]]]], axis=1, sort=False)
final=pd.concat([dfpricesFULL,forecastresults], axis=1, sort=False)
for z in range(0,len(symbolsWPortfolio)):
final.filter(regex="Adj Close "+symbolsWPortfolio[z]).tail(60).plot(legend=False,figsize = (20, 5),title=symbolsWPortfolio[z]+": Monte Carlo Simulations For "+str(NoOfIterationsMC)+" Iter-s")
plt.axvline(x=end_date,linestyle='dashed')
plt.savefig(f'static/{targetfolder}/{imagecounter}_totaliterations{z}.png')
percentileplot=pd.DataFrame()
percentileplot=pd.concat([final["Adj Close "+symbolsWPortfolio[z]],final.filter(regex="P??_"+symbolsWPortfolio[z])], axis=1, sort=False)
percentileplot.tail(60).plot(legend=True,figsize = (20, 5),title=symbolsWPortfolio[z]+": Monte Carlo Simulations For "+percentile_range+" Range")
plt.axvline(x=end_date,linestyle='dashed')
if NoOfIterationsMC>1:
plt.savefig(f'static/{targetfolder}/{imagecounter}_percentile{z}.png')
if len(symbols)==1:
ReturnsAtForecastEndDate=final.tail(1).iloc[:,-(len(symbolsWPortfolio))*3:].T
HelperTable=pd.concat([dfpricesFULL.tail(1).round(3).T]*(3))
HelperTable["Sym"]=HelperTable.index
HelperTable['Sym'] =pd.Categorical(HelperTable["Sym"], list(dfprices.columns))
HelperTable=HelperTable.sort_values(['Sym'])
ReturnsAtForecastEndDate.insert(0, end_date, HelperTable.iloc[:,:-1].values)
else:
ReturnsAtForecastEndDate=final.tail(1).iloc[:,-(len(symbolsWPortfolio))*3:].T
HelperTable=pd.concat([dfpricesFULL.tail(1).round(3).T]*(3))
HelperTable["Sym"]=HelperTable.index
HelperTable['Sym'] =pd.Categorical(HelperTable["Sym"], list(dfprices.columns))
HelperTable=HelperTable.sort_values(['Sym'])
ReturnsAtForecastEndDate.insert(0, end_date, HelperTable.iloc[:,:-1].values)
ReturnsAtForecastEndDate["Returns Based On BStrp"]=round((ReturnsAtForecastEndDate.iloc[:, 1]/ReturnsAtForecastEndDate.iloc[:, 0]-1)*100,2)
return final, share_split_tableFULL , dfreturns , df_mean_stdev, ReturnsAtForecastEndDate, dfprices
def clear_cache(subfolder):
fileDir = os.path.dirname(os.path.realpath('__file__'))
mydir = os.path.join(fileDir, f'static/{subfolder}')
filelist = [ f for f in os.listdir(mydir) if f.endswith(".csv") or f.endswith(".png") ]
for f in filelist:
os.remove(os.path.join(mydir, f))
#Adapted from https://intellipaat.com/community/34075/numpy-version-of-exponential-weighted-moving-average-equivalent-to-pandas-ewm-mean
def numpy_ewma_vectorized_v2(data, window):
alpha = 2 /(window + 1.0)
alpha_rev = 1-alpha
n = data.shape[0]
pows = alpha_rev**(np.arange(n+1))
scale_arr = 1/pows[:-1]
offset = data[0]*pows[1:]
pw0 = alpha*alpha_rev**(n-1)
mult = data*pw0*scale_arr
cumsums = mult.cumsum()
out = offset + cumsums*scale_arr[::-1]
return out
def movingaverageforecast(start_date,end_date,backtest_duration,symbols,portfolioWeights,portfolioValue,T,N,averagetype,windowsize,imagecounter,targetfolder):
dfprices, noOfShares, share_split_table = extract_prices(start_date,end_date,symbols,portfolioWeights,portfolioValue)
dfreturns ,df_mean_stdev=calc_returns(dfprices,symbols)
symbolsWPortfolio=symbols+["Portfolio"]
resultantDF=[]
if backtest_duration>0:
backtestdateslist=(list((dfprices.tail(backtest_duration).index)))
elif backtest_duration<=0:
backtestdateslist=(list((dfprices.tail(backtest_duration+1).index)))
backtestdates=[]
for i in backtestdateslist:
backtestdates.append(np.datetime64(datetime.strptime(str(i), '%Y-%m-%d %H:%M:%S').strftime("%Y-%m-%d")))
extended_dates_future=[]
if backtest_duration>0:
for i in range(0,N-backtest_duration):
extended_dates_future.append(np.busday_offset(end_date, i, roll='forward'))
elif backtest_duration<=0:
for i in range(1,N-backtest_duration):
extended_dates_future.append(np.busday_offset(end_date, i, roll='forward'))
extended_dates=backtestdates[0:len(backtestdates)-1]+extended_dates_future
for i in range (0,len(dfreturns.columns)):
train=dfreturns.iloc[:,i][:len(dfreturns)-backtest_duration].values
dfpricestrain=dfprices.iloc[:,i][:len(dfreturns)-backtest_duration+1]
predictions = list()
history=train.tolist()
for j in range(0,T):
# make prediction
if averagetype=="SMA" :
yhat = mean(history[-windowsize:])
elif averagetype=="EWMA":
yhat=numpy_ewma_vectorized_v2(np.array(history), windowsize)[-1]
history.append(yhat)
predictions.append(yhat)
predictions=np.exp(predictions)
predictions=predictions.cumprod()*dfpricestrain.tail(1).values[0]
stocks=pd.DataFrame(predictions,index=extended_dates,columns=[f"{averagetype} Forecast"])
QQQ=pd.DataFrame(dfpricestrain.tail(1))
QQQ.columns=[f"{averagetype} Forecast"]
stocks=pd.concat([QQQ,stocks])
stocks=pd.concat([dfprices.iloc[:,i],stocks],axis=1)
stocks.tail(60).plot(figsize=(15,5))
plt.title(f"{dfprices.columns[i]}: Forecast Via {averagetype} of {str(windowsize)} Days")
plt.axvline(x=end_date,linestyle='dashed')
plt.savefig(f'static/{targetfolder}/{imagecounter}_movingaverage_{i}.png')
resultantDF.append(stocks)
if backtest_duration>0:
RMSE=[]
anothertable=[]
for i in range(0,len(dfprices.columns)):
temptable=resultantDF[i].tail(T).head(backtest_duration)
temptable["RMSE"]=(temptable.iloc[:,0]-temptable.iloc[:,1])**2
RMSE.append((temptable.iloc[:,2].mean())**0.5)
RMSE_DF=pd.DataFrame(RMSE,index=dfprices.columns,columns=["RMSE For Backtest From "+temptable.index[0].strftime("%Y-%m-%d")+" To "+temptable.index[-1].strftime("%Y-%m-%d")\
+" ("+str(len(temptable))+" Days)"])
elif backtest_duration<=0:
RMSE_DF=pd.DataFrame()
return resultantDF, RMSE_DF, share_split_table
#Adapted from https://medium.com/analytics-vidhya/arima-garch-forecasting-with-python-7a3f797de3ff
# Use this code snippet to customize the auto-arima
# arima_model = pmdarima.auto_arima(train,start_p=0, d=1, start_q=0,
# max_p=5, max_d=5, max_q=5, seasonal=False,
# error_action='warn',trace = True,
# supress_warnings=True,stepwise = True,
# random_state=20,n_fits = 50 )
# Use for seasonal effects
# seasonal=True,start_P=0,D=1, start_Q=0, max_P=0, max_D=0, max_Q=0, m=0,
def UnivarArimaGarchPredict(start_date,end_date,backtest_duration,symbols,portfolioWeights,portfolioValue,T,N,imagecounter,targetfolder):
dfprices, noOfShares, share_split_table = extract_prices(start_date,end_date,symbols,portfolioWeights,portfolioValue)
dfreturns ,df_mean_stdev=calc_returns(dfprices,symbols)
symbolsWPortfolio=symbols+["Portfolio"]
backtest_end_date=str(np.busday_offset(end_date, -backtest_duration, roll='backward'))
extended_dates=[]
resultantDF=[]
backtestdateslist=(list((dfprices.tail(backtest_duration).index)))
backtestdates=[]
for i in backtestdateslist:
backtestdates.append(np.datetime64(datetime.strptime(str(i), '%Y-%m-%d %H:%M:%S').strftime("%Y-%m-%d")))
extended_dates_future=[]
for i in range(0,N-backtest_duration):
extended_dates_future.append(np.busday_offset(end_date, i, roll='forward'))
extended_dates=backtestdates[0:len(backtestdates)-1]+extended_dates_future
for i in range (0,len(dfreturns.columns)):
returns=dfreturns.iloc[:,i][:len(dfreturns)-backtest_duration]*100 #*100 is for scaling purposes
dfpricestrain=dfprices.iloc[:,i][:len(dfprices)-backtest_duration] #Used later to extract last row prices
# fit ARIMA on returns
arima_model = pmdarima.auto_arima(returns,trace = True)
p, d, q = arima_model.order
arimaaicvalue=round(arima_model.aic())
arima_residuals = arima_model.arima_res_.resid
# fit a GARCH(1,1) model on the residuals of the ARIMA model
garch = arch.arch_model(arima_residuals, p=1, q=1)
garch_fitted = garch.fit()
garchaicvalue=round(garch_fitted.aic)
print(garch_fitted.summary())
# Use ARIMA to predict mu mean term
# Use GARCH to predict the residual error term
predicted_mu = pd.DataFrame(arima_model.predict(n_periods=int(T)))
garch_forecast = garch_fitted.forecast(horizon=int(T))
predicted_et = garch_forecast.mean.iloc[-1:]
predicted_et=predicted_et.T
predictions=pd.DataFrame()
predictions["ARIMA predicted mu"]=predicted_mu.iloc[:,0].values
predictions["GARCH 1,1, predicted et"]=list(predicted_et.iloc[:,0])
predictions["ARIMA+GARCH"]=predictions["ARIMA predicted mu"]+predictions["GARCH 1,1, predicted et"]
predictions=predictions/100
futurereturns=np.exp(predictions.iloc[:,2])
futurereturns=futurereturns.cumprod()
stocks=pd.DataFrame()
stocks["ARIMAGarch Forecast "+symbolsWPortfolio[i]]=futurereturns*dfpricestrain.tail(1)[0]
if backtest_duration>0:
stocks.index= extended_dates
elif backtest_duration<=0:
stocks.index= extended_dates[1:]
QQQ=pd.DataFrame(dfpricestrain.tail(1))
QQQ.columns=["ARIMAGarch Forecast "+symbolsWPortfolio[i]]
stocks=pd.concat([QQQ,stocks])
XYZ=pd.concat([dfprices.iloc[:,i],stocks], axis=1, sort=False)
resultantDF.append(XYZ)