def test_negloglike():
AR = (np.array([1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5, .3]),
np.array([3, 2, 2]))
MA = (np.array([1, .2, 0, .1, 0, 0, 1, .3]),
np.array([2, 2, 2]))
arma = ARMA(A=AR, B=MA, C=None)
# Noise generated with R for comparison
# ( setRNG(seed=0); noise <- makeTSnoise(10, 2, 2) )
w0_series0 = np.array([1.2629543, -0.3262334])
w0_series1 = np.array([-1.1476570, -0.2894616])
w_series0 = np.array(
[1.329799263, 1.272429321, 0.414641434, -1.539950042, -0.928567035,
-0.294720447, -0.005767173, 2.404653389, 0.763593461, -0.799009249])
w_series1 = np.array(
[-0.2992151, -0.4115108, 0.2522234, -0.8919211, 0.4356833, -1.2375384,
-0.2242679, 0.3773956, 0.1333364, 0.8041895])
noise = (np.vstack([w0_series0, w0_series1]).T,
np.vstack([w_series0, w_series1]).T)
result = arma.simulate(sampleT=10, noise=noise)
pred = arma.forecast(y=result)
negloglike = stats.negloglike(pred, result)
R_negloglike = 25.4247320523
nptest.assert_almost_equal(negloglike, R_negloglike)
def test_negloglike():
AR = (np.array([1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5,
.3]), np.array([3, 2, 2]))
MA = (np.array([1, .2, 0, .1, 0, 0, 1, .3]), np.array([2, 2, 2]))
arma = ARMA(A=AR, B=MA, C=None)
# Noise generated with R for comparison
# ( setRNG(seed=0); noise <- makeTSnoise(10, 2, 2) )
w0_series0 = np.array([1.2629543, -0.3262334])
w0_series1 = np.array([-1.1476570, -0.2894616])
w_series0 = np.array([
1.329799263, 1.272429321, 0.414641434, -1.539950042, -0.928567035,
-0.294720447, -0.005767173, 2.404653389, 0.763593461, -0.799009249
])
w_series1 = np.array([
-0.2992151, -0.4115108, 0.2522234, -0.8919211, 0.4356833, -1.2375384,
-0.2242679, 0.3773956, 0.1333364, 0.8041895
])
noise = (np.vstack([w0_series0,
w0_series1]).T, np.vstack([w_series0, w_series1]).T)
result = arma.simulate(sampleT=10, noise=noise)
pred = arma.forecast(y=result)
negloglike = stats.negloglike(pred, result)
R_negloglike = 25.4247320523
nptest.assert_almost_equal(negloglike, R_negloglike)
def test_forecast():
AR = (np.array([1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5,
.3]), np.array([3, 2, 2]))
MA = (np.array([1, .2, 0, .1, 0, 0, 1, .3]), np.array([2, 2, 2]))
arma = ARMA(A=AR, B=MA, C=None)
series0 = np.array([
1.58239012, 0.85063747, -0.11981462, -1.69017627, -0.19912156,
0.02830831, 0.16284912, 2.42364792, -0.15007052, -1.27531927
])
series1 = np.array([
-0.5172168, -0.4261651, 0.2958942, -0.8559883, 0.7033546, -1.0857290,
-0.2788928, 0.7393030, -0.2999778, 0.6363970
])
R_result = np.vstack([series0, series1]).T
# One ahead forecast generated with R
# ( arma <- l(arma, R_result); R_pred <- arma$estimates$pred )
pred0 = np.array([
0.00000000, -0.37127368, -0.54455969, -0.14820550, 0.72904133,
0.32310958, 0.16860013, 0.01899776, -0.91366463, -0.47630989
])
pred1 = np.array([
0.00000000, -0.05479565, 0.05066136, 0.03484596, 0.26779526,
0.15181266, -0.05463401, 0.36191171, -0.43331575, -0.16779191
])
R_pred = np.vstack([pred0, pred1]).T
pred = arma.forecast(y=R_result)
nptest.assert_almost_equal(R_pred, pred)
# One ahead forecast with trend generated with R
# ( arma_trend <- l(arma_trend, R_result_trend);
# R_pred_trend <- arma_trend$estimates$pred )
TREND = np.array([1., 2.])
arma_trend = ARMA(A=AR, B=MA, C=None, TREND=TREND)
series0 = np.array([
2.5823901, 0.9506375, 0.2701854, -1.1311763, 0.1139784, 0.4486183,
0.6048481, 2.8091458, 0.2663152, -0.8590244
])
series1 = np.array([
1.48278321, 0.37383493, 1.17589420, 0.37601165, 1.67255459,
-0.05844899, 0.80133515, 1.76057423, 0.74401876, 1.68619050
])
R_result_trend = np.vstack([series0, series1]).T
pred0 = np.array([
1.00000000, -0.27127368, -0.15455969, 0.41079450, 1.04214133,
0.74341958, 0.61059913, 0.40449566, -0.49727892, -0.06001498
])
pred1 = np.array([
2.00000000, 0.7452043, 0.9306614, 1.2668460, 1.2369953, 1.1790927,
1.0255940, 1.3831829, 0.6106808, 0.8820015
])
R_pred_trend = np.vstack([pred0, pred1]).T
pred_trend = arma_trend.forecast(y=R_result_trend)
nptest.assert_almost_equal(R_pred_trend, pred_trend)
def test_forecast():
AR = (np.array([1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5, .3]),
np.array([3, 2, 2]))
MA = (np.array([1, .2, 0, .1, 0, 0, 1, .3]),
np.array([2, 2, 2]))
arma = ARMA(A=AR, B=MA, C=None)
series0 = np.array(
[1.58239012, 0.85063747, -0.11981462, -1.69017627, -0.19912156,
0.02830831, 0.16284912, 2.42364792, -0.15007052, -1.27531927])
series1 = np.array(
[-0.5172168, -0.4261651, 0.2958942, -0.8559883, 0.7033546, -1.0857290,
-0.2788928, 0.7393030, -0.2999778, 0.6363970])
R_result = np.vstack([series0, series1]).T
# One ahead forecast generated with R
# ( arma <- l(arma, R_result); R_pred <- arma$estimates$pred )
pred0 = np.array(
[0.00000000, -0.37127368, -0.54455969, -0.14820550, 0.72904133,
0.32310958, 0.16860013, 0.01899776, -0.91366463, -0.47630989])
pred1 = np.array(
[0.00000000, -0.05479565, 0.05066136, 0.03484596, 0.26779526,
0.15181266, -0.05463401, 0.36191171, -0.43331575, -0.16779191])
R_pred = np.vstack([pred0, pred1]).T
pred = arma.forecast(y=R_result)
nptest.assert_almost_equal(R_pred, pred)
# One ahead forecast with trend generated with R
# ( arma_trend <- l(arma_trend, R_result_trend);
# R_pred_trend <- arma_trend$estimates$pred )
TREND = np.array([1., 2.])
arma_trend = ARMA(A=AR, B=MA, C=None, TREND=TREND)
series0 = np.array(
[2.5823901, 0.9506375, 0.2701854, -1.1311763, 0.1139784, 0.4486183,
0.6048481, 2.8091458, 0.2663152, -0.8590244])
series1 = np.array(
[1.48278321, 0.37383493, 1.17589420, 0.37601165, 1.67255459,
-0.05844899, 0.80133515, 1.76057423, 0.74401876, 1.68619050])
R_result_trend = np.vstack([series0, series1]).T
pred0 = np.array(
[1.00000000, -0.27127368, -0.15455969, 0.41079450, 1.04214133,
0.74341958, 0.61059913, 0.40449566, -0.49727892, -0.06001498])
pred1 = np.array(
[2.00000000, 0.7452043, 0.9306614, 1.2668460, 1.2369953, 1.1790927,
1.0255940, 1.3831829, 0.6106808, 0.8820015])
R_pred_trend = np.vstack([pred0, pred1]).T
pred_trend = arma_trend.forecast(y=R_result_trend)
nptest.assert_almost_equal(R_pred_trend, pred_trend)
def test_print():
AR = (np.array([1, .5, .31, 0, .2, .1, 0, .2, .01, 1, .49,
.3]), np.array([3, 2, 2]))
MA = (np.array([1, .21, 0, .1, 0, -0.01, 1, .3]), np.array([2, 2, 2]))
X = (np.array([1, .3, 0, .05, 0, 0.1, 1, .3]), np.array([2, 2, 2]))
TREND = [[1, 21], [2, 22], [3, 23], [4, 24]]
arma = ARMA(A=AR, B=MA, C=X, TREND=TREND)
print(arma)
arma = ARMA(A=AR, B=MA, C=X, TREND=[1, 2])
print(arma)
AR = (np.array([1, .5, .31, 0, .2, .1, 0, .2, .01, 1, .49,
.3]), np.array([3, 2, 2]))
MA = (np.array([1., 2., 3., 0, 0, 0, 0, 0, 0, 1., 2.,
3.]), np.array([3, 2, 2]))
arma = ARMA(A=AR, B=MA)
print(arma)
def test_non_consts():
AR = (np.array([1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5, .3]),
np.array([3, 2, 2]))
MA = (np.array([1, .2, 0, .1, 0, 0, 1, .3]),
np.array([2, 2, 2]))
arma = ARMA(A=AR, B=MA, C=None)
arma.Aconst[:, 0, 0] = True
arma.Bconst[0, :, 0] = True
new_values = np.repeat(-999., 9 + 6)
arma.non_consts = new_values
result_A = np.array([1, .5, .3, -999., -999., -999., -999., -999., -999.,
-999., -999., -999.]).reshape((3, 2, 2), order='F')
nptest.assert_array_equal(arma.A, result_A)
result_B = np.array([1, -999., 0, -999., -999., -999., -999.,
-999.]).reshape((2, 2, 2), order='F')
nptest.assert_array_equal(arma.B, result_B)
set_values = arma.non_consts
nptest.assert_array_equal(set_values, new_values)
def test_est_params():
rand_state = np.random.RandomState()
rand_state.seed(42)
# Generate a target series
AR = (np.array([1, 0.3, 0.5]), np.array([3, 1, 1]))
MA = (np.array([1, .1]), np.array([2, 1, 1]))
arma = ARMA(A=AR, B=MA, C=None, rand_state=rand_state)
series = arma.simulate(sampleT=1000)
# Estimate parameters by simulated series
AR_est = (np.array([1, .01, .01]), np.array([3, 1, 1]))
MA_est = (np.array([1, .01]), np.array([2, 1, 1]))
arma_est = ARMA(A=AR_est, B=MA_est, C=None)
arma_est.fix_constants()
arma_est.est_params(y=series)
nptest.assert_almost_equal(arma_est.A, arma.A, decimal=1)
nptest.assert_almost_equal(arma_est.B, arma.B, decimal=1)
def test_non_consts():
AR = (np.array([1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5,
.3]), np.array([3, 2, 2]))
MA = (np.array([1, .2, 0, .1, 0, 0, 1, .3]), np.array([2, 2, 2]))
arma = ARMA(A=AR, B=MA, C=None)
arma.Aconst[:, 0, 0] = True
arma.Bconst[0, :, 0] = True
new_values = np.repeat(-999., 9 + 6)
arma.non_consts = new_values
result_A = np.array([
1, .5, .3, -999., -999., -999., -999., -999., -999., -999., -999.,
-999.
]).reshape((3, 2, 2), order='F')
nptest.assert_array_equal(arma.A, result_A)
result_B = np.array([1, -999., 0, -999., -999., -999., -999.,
-999.]).reshape((2, 2, 2), order='F')
nptest.assert_array_equal(arma.B, result_B)
set_values = arma.non_consts
nptest.assert_array_equal(set_values, new_values)
def test_fix_constants():
AR = (np.array([1, .5, .31, 0, .2, .1, 0, .2, .01, 1, .49,
.3]), np.array([3, 2, 2]))
MA = (np.array([1, .21, 0, .1, 0, -0.01, 1, .3]), np.array([2, 2, 2]))
arma = ARMA(A=AR, B=MA, C=None)
arma.fix_constants()
Aconst = np.array(
[[[True, True], [True, True]], [[True, True], [True, False]],
[[False, False], [True, True]]],
dtype=bool)
nptest.assert_array_equal(arma.Aconst, Aconst)
Bconst = np.array(
[[[True, True], [True, True]], [[False, False], [True, True]]],
dtype=bool)
nptest.assert_array_equal(arma.Bconst, Bconst)
def test_forecast_with_horizon():
rand_state = np.random.RandomState()
rand_state.seed(0)
AR = (np.array([1, 0.3, 0.5]), np.array([3, 1, 1]))
MA = (np.array([1, .1]), np.array([2, 1, 1]))
TREND = np.arange(1, 21)[:, np.newaxis]
arma = ARMA(A=AR, B=MA, C=None, TREND=TREND, rand_state=rand_state)
truth = np.array([
2.4560947, 2.6685808, 1.5132628, 0.7132449, 2.9468331, 4.3717505,
4.1798191, 6.9642557, 5.8248726, 4.0477605, 5.6456776, 7.8781892,
7.4855431, 7.3738101, 9.2561578
])
result = np.array([
1., 1.408781, 1.097358, 2.253321, 3.875388, 4.666472, 4.185586,
4.559602, 5.061279, 4.846770, 6.793335, 8.167651, 7.784758, 7.785321,
9.003934, 9.561470, 9.503480, 10.368221, 11.137794, 11.474551
])
pred = arma.forecast(truth, horizon=5)
nptest.assert_almost_equal(pred, result[:, np.newaxis], decimal=5)
def test_est_params():
rand_state = np.random.RandomState()
rand_state.seed(42)
# Generate a target series
AR = (np.array([1, 0.3, 0.5]), np.array([3, 1, 1]))
MA = (np.array([1, .1]), np.array([2, 1, 1]))
arma = ARMA(A=AR, B=MA, C=None, rand_state=rand_state)
series = arma.simulate(sampleT=1000)
# Estimate parameters by simulated series
AR_est = (np.array([1, .01, .01]), np.array([3, 1, 1]))
MA_est = (np.array([1, .01]), np.array([2, 1, 1]))
arma_est = ARMA(A=AR_est, B=MA_est, C=None)
arma_est.fix_constants()
arma_est.est_params(y=series)
nptest.assert_almost_equal(arma_est.A, arma.A, decimal=1)
nptest.assert_almost_equal(arma_est.B, arma.B, decimal=1)
def test_simulate_arma():
AR = (np.array([1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5,
.3]), np.array([3, 2, 2]))
MA = (np.array([1, .2, 0, .1, 0, 0, 1, .3]), np.array([2, 2, 2]))
arma = ARMA(A=AR, B=MA, C=None)
# noise generated with R for comparison
# ( setRNG(seed=0); noise <- makeTSnoise(10, 2, 2) )
w0_series0 = np.array([1.2629543, -0.3262334])
w0_series1 = np.array([-1.1476570, -0.2894616])
w_series0 = np.array([
1.329799263, 1.272429321, 0.414641434, -1.539950042, -0.928567035,
-0.294720447, -0.005767173, 2.404653389, 0.763593461, -0.799009249
])
w_series1 = np.array([
-0.2992151, -0.4115108, 0.2522234, -0.8919211, 0.4356833, -1.2375384,
-0.2242679, 0.3773956, 0.1333364, 0.8041895
])
noise = (np.vstack([w0_series0,
w0_series1]).T, np.vstack([w_series0, w_series1]).T)
# R simulation results ( arma <- ARMA(A=AR, B=MA, C=NULL);
# R_result <- simulate(arma, noise=noise, sampleT=10) )
series0 = np.array([
1.58239012, 0.85063747, -0.11981462, -1.69017627, -0.19912156,
0.02830831, 0.16284912, 2.42364792, -0.15007052, -1.27531927
])
series1 = np.array([
-0.5172168, -0.4261651, 0.2958942, -0.8559883, 0.7033546, -1.0857290,
-0.2788928, 0.7393030, -0.2999778, 0.6363970
])
R_result = np.vstack([series0, series1]).T
result = arma.simulate(sampleT=10, noise=noise)
nptest.assert_almost_equal(result, R_result)
# R simulations results with trend ( TREND <- c(1,2);
# arma_trend <- ARMA(A=AR, B=MA, C=NULL, TREND=TREND);
# R_result_trend <- simulate(arma_trend, noise=noise, sampleT=sampleT) )
TREND = np.array([1., 2.])
arma = ARMA(A=AR, B=MA, C=None, TREND=TREND)
series0 = np.array([
2.5823901, 0.9506375, 0.2701854, -1.1311763, 0.1139784, 0.4486183,
0.6048481, 2.8091458, 0.2663152, -0.8590244
])
series1 = np.array([
1.48278321, 0.37383493, 1.17589420, 0.37601165, 1.67255459,
-0.05844899, 0.80133515, 1.76057423, 0.74401876, 1.68619050
])
R_result = np.vstack([series0, series1]).T
result = arma.simulate(sampleT=10, noise=noise)
nptest.assert_almost_equal(result, R_result)
# R simulations results with trend and external series
# arma_trend_ext <- ARMA(A=AR, B=MA, C=X, TREND=TREND)
# input0 <- array(c(0.1, 0.2, 0.15, 0.05), dim=c(2,2))
# input <- array(c(0.1*c(1:10), 0.05*c(1:10)), dim=c(10,2))
# R_result_trend_ext <- simulate(arma_trend_ext, noise=noise,
# sampleT=sampleT, input0=input0, input=input)
X = (np.array([1, .3, 0, .05, 0, 0.1, 1, .3]), np.array([2, 2, 2]))
arma = ARMA(A=AR, B=MA, C=X, TREND=TREND)
input0 = np.array([0.1, 0.2, 0.15, 0.05]).reshape((2, 2), order='F')
input = np.hstack([0.1 * np.arange(1, 11), 0.05 * np.arange(1, 11)])
input = input.reshape((10, 2), order='F')
series0 = np.array([
2.7273901, 1.0931375, 0.5122354, -0.8113013, 0.4892429, 0.9042891,
1.1312726, 3.4036172, 0.9345114, -0.1201090
])
series1 = np.array([
1.5827832, 0.4148349, 1.2723942, 0.5128017, 1.8170296, 0.1212361,
1.0094895, 1.9917395, 1.0044531, 1.9735374
])
R_result = np.vstack([series0, series1]).T
result = arma.simulate(sampleT=10, noise=noise, u0=input0, u=input)
nptest.assert_almost_equal(result, R_result)
def test_arma_construction():
AR = ([1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5, .3], [3, 2, 2])
MA = ([1, .2, 0, .1, 0, 0, 1, .3], [2, 2, 2])
X = ([1, 2, 3, 4, 5, 6], [1, 2, 3])
# Check construction
ARMA(A=AR, B=MA)
ARMA(A=AR)
ARMA(A=AR, B=MA, C=X)
MA = ([1, 0.2, 0, .1], [2, 2, 1])
X = ([1, 2, 3, 4, 5, 6], [2, 1, 3])
with pytest.raises(ARMAError):
ARMA(A=AR, B=MA)
ARMA(A=AR, C=X)
AR = ([1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5, .3], [3, 2, 2])
MA = ([1, 2, 0, .1, 0, 0, 1, .3], [2, 2, 2])
TREND = [1, 2]
ARMA(A=AR, B=MA, TREND=TREND)
TREND = [[1, 2], [3, 4]]
ARMA(A=AR, B=MA, TREND=TREND)
TREND = [[1, 2], [3, 4], [4, 5]]
ARMA(A=AR, B=MA, TREND=TREND)
TREND = [1, 2, 3]
# give a (3,) array while expecting a (2,) array as p = 2
with pytest.raises(ARMAError):
ARMA(A=AR, B=MA, TREND=TREND)
TREND = [[1, 2, 3], [1, 2, 3], [1, 2, 3]]
# give a (3, 3) array while expect a (X, 2) array as p = 2
with pytest.raises(ARMAError):
ARMA(A=AR, B=MA, TREND=TREND)
TREND = [[[1, 2, 3], [1, 2, 3], [1, 2, 3]],
[[1, 2, 3], [1, 2, 3], [1, 2, 3]],
[[1, 2, 3], [1, 2, 3], [1, 2, 3]]]
# give a (3, 3, 3) array while expect a 2-d matrix
with pytest.raises(ARMAError):
ARMA(A=AR, B=MA, TREND=TREND)