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