def test_fi():
#test identity of ma and ar representation of fi lag polynomial
n = 100
mafromar = arma_impulse_response(lpol_fiar(0.4, n=n), [1], n)
assert_array_almost_equal(mafromar, lpol_fima(0.4, n=n), 13)
riinv = signal.lfilter([1], ri, [1]+[0]*(n-1))#[[5,10,20,25]]
'''
array([-0.029952 , -0.01100641, -0.00410998, -0.00299859])
>>> d=0.4; j=np.arange(1000);ri=gamma(d+j)/(gamma(j+1)*gamma(d))
>>> # (1-L)^d, d<1 is
>>> lfilter([1], ri, [1]+[0]*30)
array([ 1. , -0.4 , -0.12 , -0.064 , -0.0416 ,
-0.029952 , -0.0229632 , -0.01837056, -0.01515571, -0.01279816,
-0.01100641, -0.0096056 , -0.00848495, -0.00757118, -0.00681406,
-0.00617808, -0.0056375 , -0.00517324, -0.00477087, -0.00441934,
-0.00410998, -0.00383598, -0.00359188, -0.00337324, -0.00317647,
-0.00299859, -0.00283712, -0.00269001, -0.00255551, -0.00243214,
-0.00231864])
>>> # verified for points [[5,10,20,25]] at 4 decimals with Bhardwaj, Swanson, Journal of Eonometrics 2006
'''
print lpol_fiar(0.4, n=20)
print lpol_fima(-0.4, n=20)
print np.sum((lpol_fima(-0.4, n=n)[1:] + riinv[1:])**2) #different signs
print np.sum((lpol_fiar(0.4, n=n)[1:] - riinv[1:])**2) #corrected signs
#test is now in gwstatsmodels.tsa.tests.test_arima_process
from gwstatsmodels.tsa.tests.test_arima_process import test_fi
test_fi()
ar_true = [1, -0.4]
ma_true = [1, 0.5]
ar_desired = arma_impulse_response(ma_true, ar_true)
ar_app, ma_app, res = ar2arma(ar_desired, 2,1, n=100, mse='ar', start=[0.1])
print ar_app, ma_app