Hey,

I'm trying to alter one of the algo's from the strategy library from equities to forex. I've only changed the symbols lines, and I'm getting the error: 

Runtime Error: ValueError : Index contains duplicate entries, cannot reshape
at PairSelection in main.py:line 140
at _get_historical_returns in main.py:line 185
:: history = history.close.unstack(level=0)
ValueError : Index contains duplicate entries, cannot reshape

Any ideas on the error? Here is the code.

import numpy as np
from scipy import stats
from statsmodels.distributions.empirical_distribution import ECDF
from scipy.stats import kendalltau, pearsonr, spearmanr
from scipy.optimize import minimize
from scipy.integrate import quad
import sys
from collections import deque


class CopulaPairsTradingAlgorithm(QCAlgorithm):

def Initialize(self):
'''Initialize algorithm and add universe'''

self.SetStartDate(2010, 1, 1)
self.SetEndDate(2019, 9, 1)
self.SetCash(100000)

self.numdays = 1000 # length of formation period which determine the copula we use
self.lookbackdays = 250 # length of history data in trading period
self.cap_CL = 0.95 # cap confidence level
self.floor_CL = 0.05 # floor confidence level
self.weight_v = 0.5 # desired holding weight of asset v in the portfolio, adjusted to avoid insufficient buying power
self.coef = 0 # to be calculated: requested ratio of quantity_u / quantity_v
self.window = {} # stores historical price used to calculate trading day's stock return

self.day = 0 # keep track of current day for daily rebalance
self.month = 0 # keep track of current month for monthly recalculation of optimal trading pair
self.pair = [] # stores the selected trading pair

# Select optimal trading pair into the universe
self.UniverseSettings.Resolution = Resolution.Daily
self.AddUniverse('PairUniverse', self.PairSelection)


def OnData(self, slice):
'''Main event handler. Implement trading logic.'''

self.SetSignal(slice) # only executed at first day of each month

# Daily rebalance
if self.Time.day == self.day:
return

long, short = self.pair[0], self.pair[1]

# Update current price to trading pair's historical price series
for kvp in self.Securities:
symbol = kvp.Key
if symbol in self.pair:
price = kvp.Value.Price
self.window[symbol].append(price)

if len(self.window[long]) < 2 or len(self.window[short]) < 2:
return

# Compute the mispricing indices for u and v by using estimated copula
MI_u_v, MI_v_u = self._misprice_index()

# Placing orders: if long is relatively underpriced, buy the pair
if MI_u_v < self.floor_CL and MI_v_u > self.cap_CL:

self.SetHoldings(short, -self.weight_v, False, f'Coef: {self.coef}')
self.SetHoldings(long, self.weight_v * self.coef * self.Portfolio[long].Price / self.Portfolio[short].Price)

# Placing orders: if short is relatively underpriced, sell the pair
elif MI_u_v > self.cap_CL and MI_v_u < self.floor_CL:

self.SetHoldings(short, self.weight_v, False, f'Coef: {self.coef}')
self.SetHoldings(long, -self.weight_v * self.coef * self.Portfolio[long].Price / self.Portfolio[short].Price)

self.day = self.Time.day


def SetSignal(self, slice):
'''Computes the mispricing indices to generate the trading signals.
It's called on first day of each month'''

if self.Time.month == self.month:
return

## Compute the best copula

# Pull historical log returns used to determine copula
logreturns = self._get_historical_returns(self.pair, self.numdays)
x, y = logreturns[str(self.pair[0])], logreturns[str(self.pair[1])]

# Convert the two returns series to two uniform values u and v using the empirical distribution functions
ecdf_x, ecdf_y = ECDF(x), ECDF(y)
u, v = [ecdf_x(a) for a in x], [ecdf_y(a) for a in y]

# Compute the Akaike Information Criterion (AIC) for different copulas and choose copula with minimum AIC
tau = kendalltau(x, y)[0] # estimate Kendall'rank correlation
AIC ={} # generate a dict with key being the copula family, value = [theta, AIC]

for i in ['clayton', 'frank', 'gumbel']:
param = self._parameter(i, tau)
lpdf = [self._lpdf_copula(i, param, x, y) for (x, y) in zip(u, v)]
# Replace nan with zero and inf with finite numbers in lpdf list
lpdf = np.nan_to_num(lpdf)
loglikelihood = sum(lpdf)
AIC[i] = [param, -2 * loglikelihood + 2]

# Choose the copula with the minimum AIC
self.copula = min(AIC.items(), key = lambda x: x[1][1])[0]

## Compute the signals

# Generate the log return series of the selected trading pair
logreturns = logreturns.tail(self.lookbackdays)
x, y = logreturns[str(self.pair[0])], logreturns[str(self.pair[1])]

# Estimate Kendall'rank correlation
tau = kendalltau(x, y)[0]

# Estimate the copula parameter: theta
self.theta = self._parameter(self.copula, tau)

# Simulate the empirical distribution function for returns of selected trading pair
self.ecdf_x, self.ecdf_y = ECDF(x), ECDF(y)

# Run linear regression over the two history return series and return the desired trading size ratio
self.coef = stats.linregress(x,y).slope

self.month = self.Time.month


def PairSelection(self, date):
'''Selects the pair of stocks with the maximum Kendall tau value.
It's called on first day of each month'''

if date.month == self.month:
return Universe.Unchanged

symbols = [ Symbol.Create(x, SecurityType.Forex, Market.Oanda)
for x in ["EURUSD","GBPUSD","USDCAD", "AUDUSD", "NZDUSD"] ]

logreturns = self._get_historical_returns(symbols, self.lookbackdays)

tau = 0
for i in range(0, len(symbols), 2):

x = logreturns[str(symbols[i])]
y = logreturns[str(symbols[i+1])]

# Estimate Kendall rank correlation for each pair
tau_ = kendalltau(x, y)[0]

if tau > tau_:
continue

tau = tau_
self.pair = symbols[i:i+2]

return [x.Value for x in self.pair]


def OnSecuritiesChanged(self, changes):
'''Warms up the historical price for the newly selected pair.
It's called when current security universe changes'''

for security in changes.RemovedSecurities:
symbol = security.Symbol
self.window.pop(symbol)
if security.Invested:
self.Liquidate(symbol, "Removed from Universe")

for security in changes.AddedSecurities:
self.window[security.Symbol] = deque(maxlen = 2)

# Get historical prices
history = self.History(list(self.window.keys()), 2, Resolution.Daily)
history = history.close.unstack(level=0)
for symbol in self.window:
self.window[symbol].append(history[str(symbol)][0])


def _get_historical_returns(self, symbols, period):
'''Get historical returns for a given set of symbols and a given period
'''

history = self.History(symbols, period, Resolution.Daily)
history = history.close.unstack(level=0)
return (np.log(history) - np.log(history.shift(1))).dropna()


def _parameter(self, family, tau):
''' Estimate the parameters for three kinds of Archimedean copulas
according to association between Archimedean copulas and the Kendall rank correlation measure
'''

if family == 'clayton':
return 2 * tau / (1 - tau)

elif family == 'frank':

'''
debye = quad(integrand, sys.float_info.epsilon, theta)[0]/theta is first order Debye function
frank_fun is the squared difference
Minimize the frank_fun would give the parameter theta for the frank copula
'''

integrand = lambda t: t / (np.exp(t) - 1) # generate the integrand
frank_fun = lambda theta: ((tau - 1) / 4.0 - (quad(integrand, sys.float_info.epsilon, theta)[0] / theta - 1) / theta) ** 2

return minimize(frank_fun, 4, method='BFGS', tol=1e-5).x

elif family == 'gumbel':
return 1 / (1 - tau)


def _lpdf_copula(self, family, theta, u, v):
'''Estimate the log probability density function of three kinds of Archimedean copulas
'''

if family == 'clayton':
pdf = (theta + 1) * ((u ** (-theta) + v ** (-theta) - 1) ** (-2 - 1 / theta)) * (u ** (-theta - 1) * v ** (-theta - 1))

elif family == 'frank':
num = -theta * (np.exp(-theta) - 1) * (np.exp(-theta * (u + v)))
denom = ((np.exp(-theta * u) - 1) * (np.exp(-theta * v) - 1) + (np.exp(-theta) - 1)) ** 2
pdf = num / denom

elif family == 'gumbel':
A = (-np.log(u)) ** theta + (-np.log(v)) ** theta
c = np.exp(-A ** (1 / theta))
pdf = c * (u * v) ** (-1) * (A ** (-2 + 2 / theta)) * ((np.log(u) * np.log(v)) ** (theta - 1)) * (1 + (theta - 1) * A ** (-1 / theta))

return np.log(pdf)


def _misprice_index(self):
'''Calculate mispricing index for every day in the trading period by using estimated copula
Mispricing indices are the conditional probability P(U < u | V = v) and P(V < v | U = u)'''

return_x = np.log(self.window[self.pair[0]][-1] / self.window[self.pair[0]][-2])
return_y = np.log(self.window[self.pair[1]][-1] / self.window[self.pair[1]][-2])

# Convert the two returns to uniform values u and v using the empirical distribution functions
u = self.ecdf_x(return_x)
v = self.ecdf_y(return_y)

if self.copula == 'clayton':
MI_u_v = v ** (-self.theta - 1) * (u ** (-self.theta) + v ** (-self.theta) - 1) ** (-1 / self.theta - 1) # P(U<u|V=v)
MI_v_u = u ** (-self.theta - 1) * (u ** (-self.theta) + v ** (-self.theta) - 1) ** (-1 / self.theta - 1) # P(V<v|U=u)

elif self.copula == 'frank':
A = (np.exp(-self.theta * u) - 1) * (np.exp(-self.theta * v) - 1) + (np.exp(-self.theta * v) - 1)
B = (np.exp(-self.theta * u) - 1) * (np.exp(-self.theta * v) - 1) + (np.exp(-self.theta * u) - 1)
C = (np.exp(-self.theta * u) - 1) * (np.exp(-self.theta * v) - 1) + (np.exp(-self.theta) - 1)
MI_u_v = B / C
MI_v_u = A / C

elif self.copula == 'gumbel':
A = (-np.log(u)) ** self.theta + (-np.log(v)) ** self.theta
C_uv = np.exp(-A ** (1 / self.theta)) # C_uv is gumbel copula function C(u,v)
MI_u_v = C_uv * (A ** ((1 - self.theta) / self.theta)) * (-np.log(v)) ** (self.theta - 1) * (1.0 / v)
MI_v_u = C_uv * (A ** ((1 - self.theta) / self.theta)) * (-np.log(u)) ** (self.theta - 1) * (1.0 / u)

return MI_u_v, MI_v_u