ProcessPoolExecutor using a function which is supposed to append to a list not working properly

I'm starting to use Python for forecasting coming from R, and I bumped into this problem while trying to estimate multiple models using multiprocessing. I'm trying to estimate a same model (ARIMA) with multiple combinations of parameters, and had success doing it using a for-loop. However, I was trying to apply multiprocessing to increase efficiency, and I'm having some issues.

This is the function I'm trying to run:

arima_comp = []

def arima_tester(p,q,P,Q):
    mod = ARIMA(training_set, order = (p,1,q), seasonal_order = (P,1,Q,12))
    modfit = mod.fit()
    forecast = modfit.forecast(steps = len(test_set))
    error = forecast - test_set 
    rmse = np.square(error).mean() ** 0.5
    aic = modfit.aic
    model = "ARIMA("+str(p)+",1,"+str(q)+")"+"("+str(P)+",1,"+str(Q)+")[12]: "
    arima_comp.append(
        {
            "Modelo":model,
            "AIC":aic,
            "RMSE":rmse
        }
    )

The idea was to estimate multiple combinations of models and append all of them to this arima_comp list, in order to compare them aftwerwards. It worked fine with the for-loop, but when I run the concurrent.futures.ProcessPoolExecutor.map as follows:

pq_aux = [0,1,2,3]
PQ_aux = [0,1]

with concurrent.futures.ProcessPoolExecutor() as executor:
    executor.map(arima_tester, pq_aux, pq_aux, PQ_aux, PQ_aux)

It seems as if the function was not executed, because if I call the arima_comp list, it returns me an empty list:

arima_comp
#Returns []

Do any of you have any idea what am I doing wrong? It's not as if I'm receiving an error when I run this code, I just don't get the expected result. Thank you in advance.

I expected the same result as if I ran a for-loop over the function for different combinations of p,q,P,Q in the arima_tester function, the it would append to arima_comp list, giving me something like that:

arima_tester(0,0,0,0)
arima_tester(0,0,0,1)
arima_tester(0,0,1,1)
arima_comp


#Returns:[{'Modelo': 'ARIMA(0,1,0)(0,1,0)[12]: ',
  'AIC': 1198.2900239812564,
  'RMSE': 6.653975098794921},
 {'Modelo': 'ARIMA(0,1,0)(0,1,1)[12]: ',
  'AIC': 1127.5935159029652,
  'RMSE': 7.400152967890038},
 {'Modelo': 'ARIMA(0,1,0)(1,1,1)[12]: ',
  'AIC': 1125.0164173629523,
  'RMSE': 7.996184118574912}]

UPDATE

I just followed the answers below, and now I'm getting a "BrokenProcessPool" error. A minimal, reproducible example that leads (at least for me) to the very same error can be found below:

import concurrent.futures

def function(a,b,c,d):
    sum = a+b+c+d
    halfsum = sum/2
    squaredsum = a ** 2 + b ** 2 + c ** 2 + d ** 2
    return {
        "Sum":sum,
        "Sum Divided by 2":halfsum,
        "Squared Sum": squaredsum
    }

ab_values = [0,1,2,3]
cd_values = [0,1]

if __name__ == '__main__':
    with concurrent.futures.ProcessPoolExecutor() as executor:
        final_list = list(executor.map(function, ab_values, ab_values, cd_values, cd_values))

Whenever I run this code I get the following error:

---------------------------------------------------------------------------
BrokenProcessPool                         Traceback (most recent call last)
Cell In[4], line 6
      4 if __name__ == '__main__':
      5     with concurrent.futures.ProcessPoolExecutor() as executor:
----> 6         final_list = list(executor.map(function, ab_values, ab_values, cd_values, cd_values))

File c:\Users\lfval\anaconda3\lib\concurrent\futures\process.py:570, in _chain_from_iterable_of_lists(iterable)
    564 def _chain_from_iterable_of_lists(iterable):
    565     """
    566     Specialized implementation of itertools.chain.from_iterable.
    567     Each item in *iterable* should be a list.  This function is
    568     careful not to keep references to yielded objects.
    569     """
--> 570     for element in iterable:
    571         element.reverse()
    572         while element:

File c:\Users\lfval\anaconda3\lib\concurrent\futures\_base.py:621, in Executor.map..result_iterator()
    618 while fs:
    619     # Careful not to keep a reference to the popped future
    620     if timeout is None:
--> 621         yield _result_or_cancel(fs.pop())
    622     else:
    623         yield _result_or_cancel(fs.pop(), end_time - time.monotonic())

File c:\Users\lfval\anaconda3\lib\concurrent\futures\_base.py:319, in _result_or_cancel(***failed resolving arguments***)
    317 try:
    318     try:
--> 319         return fut.result(timeout)
    320     finally:
    321         fut.cancel()

File c:\Users\lfval\anaconda3\lib\concurrent\futures\_base.py:458, in Future.result(self, timeout)
    456     raise CancelledError()
    457 elif self._state == FINISHED:
--> 458     return self.__get_result()
    459 else:
    460     raise TimeoutError()

File c:\Users\lfval\anaconda3\lib\concurrent\futures\_base.py:403, in Future.__get_result(self)
    401 if self._exception:
    402     try:
--> 403         raise self._exception
    404     finally:
    405         # Break a reference cycle with the exception in self._exception
    406         self = None

I'm trying to run this code on Windows 10 using Python 3.10.9.