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I am maximising the LogLikelihood of an ARMA model, using the scipy.optimize.minimize package and using the BFGS method. However, I get the following error:

The truth value of a Series is ambiguous. Use a.empty, a.bool(), a.item(), a.any() or a.all().

The function I am optimizing returns the correct output, i.e. the log likelihood of a specified ARMA model, hence I am trying to look at the source code of the minimize package, however it's quite complex and I can't figure out what the problem is. I realise it's not a straightforward question, however I hope that someone with experience using the minimize package can give me some guidance on what may be causing the error.

The given traceback is as follows:

    ValueError                                Traceback (most recent call last)



/......../.py in fit_ARMA(data, p, q)

    150     optim_args=(data, p, q)

    151

--> 152     fitted_params = minimize(minus_ll_ARMA, x0=init_params, args=optim_args, method='BFGS')

    153

    154     return fitted_params.x



/anaconda3/lib/python3.6/site-packages/scipy/optimize/_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)

    595         return _minimize_cg(fun, x0, args, jac, callback, **options)

    596     elif meth == 'bfgs':

--> 597         return _minimize_bfgs(fun, x0, args, jac, callback, **options)

    598     elif meth == 'newton-cg':

    599         return _minimize_newtoncg(fun, x0, args, jac, hess, hessp, callback,



/anaconda3/lib/python3.6/site-packages/scipy/optimize/optimize.py in _minimize_bfgs(fun, x0, args, jac, callback, gtol, norm, eps, maxiter, disp, return_all, **unknown_options)

    981             alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = 

    982                      _line_search_wolfe12(f, myfprime, xk, pk, gfk,

--> 983                                           old_fval, old_old_fval, amin=1e-100, amax=1e100)

    984         except _LineSearchError:

    985             # Line search failed to find a better solution.



/anaconda3/lib/python3.6/site-packages/scipy/optimize/optimize.py in _line_search_wolfe12(f, fprime, xk, pk, gfk, old_fval, old_old_fval, **kwargs)

    801     ret = line_search_wolfe1(f, fprime, xk, pk, gfk,

    802                              old_fval, old_old_fval,

--> 803                              **kwargs)

    804

    805     if ret[0] is not None and extra_condition is not None:



/anaconda3/lib/python3.6/site-packages/scipy/optimize/linesearch.py in line_search_wolfe1(f, fprime, xk, pk, gfk, old_fval, old_old_fval, args, c1, c2, amax, amin, xtol)

     99     stp, fval, old_fval = scalar_search_wolfe1(

    100             phi, derphi, old_fval, old_old_fval, derphi0,

--> 101             c1=c1, c2=c2, amax=amax, amin=amin, xtol=xtol)

    102

    103     return stp, fc[0], gc[0], fval, old_fval, gval[0]



/anaconda3/lib/python3.6/site-packages/scipy/optimize/linesearch.py in scalar_search_wolfe1(phi, derphi, phi0, old_phi0, derphi0, c1, c2, amax, amin, xtol)

    153

    154     if old_phi0 is not None and derphi0 != 0:

--> 155         alpha1 = min(1.0, 1.01*2*(phi0 - old_phi0)/derphi0)

    156         if alpha1 < 0:

    157             alpha1 = 1.0



/anaconda3/lib/python3.6/site-packages/pandas/core/generic.py in __nonzero__(self)

   1574         raise ValueError("The truth value of a {0} is ambiguous. "

   1575                          "Use a.empty, a.bool(), a.item(), a.any() or a.all()."

-> 1576                          .format(self.__class__.__name__))

   1577

   1578     __bool__ = __nonzero__



ValueError: The truth value of a Series is ambiguous. Use a.empty, a.bool(), a.item(), a.any() or a.all().

Below are the two functions used:

def ll_ARMA(params, data, p, q):

'''Returns the log-likelihood of the ARMA model.

Data index must be increasing (oldest observations on top)

p= # coeff. AR

q= # coeff MA'''



n = data.shape[0]



if p>0:

    lagged_data = data.shift(1).copy()

    for i in range(1,p):

        lagged_data = pd.concat([lagged_data, data.shift(i+1)], axis=1)



else:

    lagged_data = pd.DataFrame(index = data.index, columns=[i+1 for i in range(p)])



errors_index = pd.Index([i for i in range(q)]).append(data.index)

errors = pd.DataFrame(np.zeros(shape=(n+q,1)),index=errors_index)

for i in range(q, n+q):

    a = data.iloc[i-q,:] - params[0] - np.sum(np.dot(lagged_data, params[1:p+1])) - 

        np.dot(params[p+1:], np.asarray([errors.iloc[i-j,:] for j in range(1, q+1)]))

    errors.iloc[i,:] =  a.item()   



errors = errors[q:] # gets rid of initial q values set at 0

var = np.var(errors)

log_likelihood = np.log(2*np.pi*var)*(-1/2) + (-1/2)*(errors**2)/var



return np.sum(log_likelihood)



def fit_ARMA(data, p, q):

    '''Returns the fitted parameters of an ARMA model (including the constant).

    Order is -constant -p AR coeff -q MA coeff

    Data must be a 1-column DF.

    p is the parameter of the AR, q of the MA'''



init_params = np.random.random(p+q+1)



def minus_ll_ARMA(params, data, p, q):

    return -1*ll_ARMA(params, data, p, q)



optim_args=(data, p, q)



fitted_params = minimize(minus_ll_ARMA, x0=init_params, args=optim_args, method='BFGS')



return fitted_params.x

And this is a workable example that produces the error:

import pandas as pd # version 0.23.4

import numpy as np # version 1.15.4

from scipy.optimize import minimize   # version 1.1.0



data = pd.DataFrame(np.random.random(500)*0.4-0.2, index = [i for i in range(1,501)]) # randomly generates returns in a sensible range

parameters = fit_ARMA(data, 2, 3) # this returns the error

P.S. I already looked into the following question: scipy.optimize.minimize Jacobian function causes 'Value Error: The truth value of an array with more than one element is ambiguous', however I'm not including the gradient, so the error is of different nature.