arima(ap, order=(2, 1, 1), seasonal={'order': (0, 1, 0), 'period': 12}, 
      include_mean=False, method='CSS-ML')['coef']

{'ar1': 0.47051736809750594,
 'ar2': 0.22174549894902976,
 'ma1': -1.088591942427617}

`predict_arima`[source]

predict_arima(model, n_ahead, newxreg=None, se_fit=True)

predict_arima(res, 10)

(array([448.08972925, 423.7922724 , 453.50022757, 496.68138142,
        508.6158662 , 572.31747306, 659.85480907, 644.26321316,
        546.57452622, 499.81156619]),
 array([11.52472983, 13.1634063 , 14.67466798, 15.63674637, 16.39162602,
        16.98465381, 17.47757493, 17.89954747, 18.27186588, 18.60809127]))

predict_arima(res_intercept, 10)

(array([470.00979488, 440.51641849, 442.19288043, 430.30732962,
        425.09870714, 417.37227647, 411.26942366, 404.89077868,
        399.07483755, 393.42076235]),
 array([ 30.69910081,  51.71193144,  61.8938269 ,  71.06720305,
         77.98073384,  83.94820591,  88.93458668,  93.25690786,
         96.99562864, 100.27009363]))

newdrift = np.arange(ap.size + 1, ap.size + 10 + 1).reshape(-1, 1)
newxreg = np.concatenate([newdrift, np.sqrt(newdrift)], axis=1)
predict_arima(res_xreg, 10, newxreg=newxreg)

(array([441.89788144, 463.67037804, 489.91183156, 513.32967966,
        528.76742686, 534.25615255, 530.97888695, 522.3581832 ,
        512.68418691, 505.75238209]),
 array([25.04154419, 31.85337573, 33.32711537, 33.3424047 , 34.68174014,
        37.33840844, 39.68800215, 40.77979968, 40.92280668, 40.99296291]))

myarima(ap, order=(2, 1, 1), seasonal={'order': (0, 1, 0), 'period': 12}, 
        constant=False, ic='aicc', method='CSS-ML')['aic']

1020.700659230761

`arima_string`[source]

arima_string(model, padding=False)

arima_string(res_Arima_ex)

'Regression with ARIMA(0,0,0) errors'

arima_string(res_Arima)

'ARIMA(0,0,0) with drift        '

`forecast_arima`[source]

forecast_arima(model, h=None, level=None, fan=False, xreg=None, blambda=None, bootstrap=False, npaths=5000, biasadj=None)

`fitted_arima`[source]

fitted_arima(model, h=1)

Returns h-step forecasts for the data used in fitting the model.

`auto_arima_f`[source]

auto_arima_f(x, d=None, D=None, max_p=5, max_q=5, max_P=2, max_Q=2, max_order=5, max_d=2, max_D=1, start_p=2, start_q=2, start_P=1, start_Q=1, stationary=False, seasonal=True, ic='aicc', stepwise=True, nmodels=94, trace=False, approximation=None, method=None, truncate=None, xreg=None, test='kpss', test_kwargs=None, seasonal_test='seas', seasonal_test_kwargs=None, allowdrift=True, allowmean=True, blambda=None, biasadj=False, parallel=False, num_cores=2, period=1)

mod = auto_arima_f(ap, period=12, method='CSS-ML', trace=True)

ARIMA(2,1,2)(1,1,1)[12]                   :inf

ARIMA(0,1,0)(0,1,0)[12]                   :1031.5393581671838

ARIMA(1,1,0)(1,1,0)[12]                   :1020.5919299313473

ARIMA(0,1,1)(0,1,1)[12]                   :1021.1978414716

ARIMA(1,1,0)(0,1,0)[12]                   :1020.4966626269295

ARIMA(1,1,0)(0,1,1)[12]                   :1021.1141377784866

ARIMA(1,1,0)(1,1,1)[12]                   :1022.6657137275511

ARIMA(2,1,0)(0,1,0)[12]                   :1022.5909032832317

ARIMA(1,1,1)(0,1,0)[12]                   :1022.5906051178998

ARIMA(0,1,1)(0,1,0)[12]                   :1020.7342476851575

ARIMA(2,1,1)(0,1,0)[12]                   :1021.020659230761

ARIMA(2,1,1)(0,1,0)[12]                   :1021.020659230761
Now re-fitting the best model(s) without approximations...


ARIMA(1,1,0)(0,1,0)[12]                   :1020.4966626269295

`print_statsforecast_ARIMA`[source]

print_statsforecast_ARIMA(model, digits=3, se=True)

print_statsforecast_ARIMA(mod)

ARIMA(1,1,0)(0,1,0)[12]                   

Coefficients:
               ar1
coefficient -0.300
s.e.         0.007

sigma^2 = 139.156: log likelihood = -508.20

AIC=1020.4

`class` `ARIMASummary`[source]

ARIMASummary(model)

ARIMA Summary.

`class` `AutoARIMA`[source]

AutoARIMA(d:Optional[int]=None, D:Optional[int]=None, max_p:int=5, max_q:int=5, max_P:int=2, max_Q:int=2, max_order:int=5, max_d:int=2, max_D:int=1, start_p:int=2, start_q:int=2, start_P:int=1, start_Q:int=1, stationary:bool=False, seasonal:bool=True, ic:str='aicc', stepwise:bool=True, nmodels:int=94, trace:bool=False, approximation:Optional[bool]=None, method:Optional[str]=None, truncate:Optional[bool]=None, test:str='kpss', test_kwargs:Optional[str]=None, seasonal_test:str='seas', seasonal_test_kwargs:Optional[Dict[KT, VT]]=None, allowdrift:bool=True, allowmean:bool=True, blambda:Optional[float]=None, biasadj:bool=False, parallel:bool=False, num_cores:int=2, period:int=1)

An AutoARIMA estimator.

Returns best ARIMA model according to either AIC, AICc or BIC value. The function conducts a search over possible model within the order constraints provided.

Parameters

d: int optional (default None) Order of first-differencing. If missing, will choose a value based on test. D: int optional (default None) Order of seasonal-differencing. If missing, will choose a value based on season_test. max_p: int (default 5) Maximum value of p. max_q: int (default 5) Maximum value of q. max_P: int (default 2) Maximum value of P. max_Q: int (default 2) Maximum value of Q. max_order: int (default 5) Maximum value of p+q+P+Q if model selection is not stepwise. max_d: int (default 2) Maximum number of non-seasonal differences max_D: int (default 1) Maximum number of seasonal differences start_p: int (default 2) Starting value of p in stepwise procedure. start_q: int (default 2) Starting value of q in stepwise procedure. start_P: int (default 1) Starting value of P in stepwise procedure. start_Q: int (default 1) Starting value of Q in stepwise procedure. stationary: bool (default False) If True, restricts search to stationary models. seasonal: bool (default True) If False, restricts search to non-seasonal models. ic: str (default 'aicc') Information criterion to be used in model selection. stepwise: bool (default True) If True, will do stepwise selection (faster). Otherwise, it searches over all models. Non-stepwise selection can be very slow, especially for seasonal models. nmodels: int (default 94) Maximum number of models considered in the stepwise search. trace: bool (default False) If True, the list of ARIMA models considered will be reported. approximation: bool optional (default None) If True, estimation is via conditional sums of squares and the information criteria used for model selection are approximated. The final model is still computed using maximum likelihood estimation. Approximation should be used for long time series or a high seasonal period to avoid excessive computation times. method: str optional (default None) fitting method: maximum likelihood or minimize conditional sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood. Can be abbreviated. truncate: bool optional (default None) An integer value indicating how many observations to use in model selection. The last truncate values of the series are used to select a model when truncate is not None and approximation=True. All observations are used if either truncate=None or approximation=False. test: str (default 'kpss') Type of unit root test to use. See ndiffs for details. test_kwargs: str optional (default None) Additional arguments to be passed to the unit root test. seasonal_test: str (default 'seas') This determines which method is used to select the number of seasonal differences. The default method is to use a measure of seasonal strength computed from an STL decomposition. Other possibilities involve seasonal unit root tests. seasonal_test_kwargs: dict optional (default None) Additional arguments to be passed to the seasonal unit root test. See nsdiffs for details. allowdrift: bool (default True) If True, models with drift terms are considered. allowmean: bool (default True) If True, models with a non-zero mean are considered. blambda: float optional (default None) Box-Cox transformation parameter. If lambda="auto", then a transformation is automatically selected using BoxCox.lambda. The transformation is ignored if None. Otherwise, data transformed before model is estimated. biasadj: bool (default False) Use adjusted back-transformed mean for Box-Cox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is True, an adjustment will be made to produce mean forecasts and fitted values. parallel: bool (default False) If True and stepwise = False, then the specification search is done in parallel. This can give a significant speedup on multicore machines. num_cores: int (default 2) Allows the user to specify the amount of parallel processes to be used if parallel = True and stepwise = False. If None, then the number of logical cores is automatically detected and all available cores are used. period: int (default 1) Number of observations per unit of time. For example 24 for Hourly data.

Notes

This implementation is a mirror of Hyndman's forecast::auto.arima.

References

[1] https://github.com/robjhyndman/forecast

model = AutoARIMA()

model = model.fit(ap)

model.predict(h=7)

	mean
0	464.631601
1	483.363283
2	490.196788
3	489.549976
4	485.653256
5	481.407363
6	478.248914

model.predict(h=7, level=80)

	lo_80%	mean	hi_80%
0	426.326488	464.631601	502.936715
1	419.928953	483.363283	546.797613
2	411.105076	490.196788	569.288501
3	401.920876	489.549976	577.179076
4	393.609048	485.653256	577.697464
5	386.910310	481.407363	575.904416
6	382.073456	478.248914	574.424372

model.predict(h=7, level=(80, 90))

	lo_90%	lo_80%	mean	hi_80%	hi_90%
0	415.467520	426.326488	464.631601	502.936715	513.795682
1	401.946202	419.928953	483.363283	546.797613	564.780365
2	388.683674	411.105076	490.196788	569.288501	591.709902
3	377.079244	401.920876	489.549976	577.179076	602.020708
4	367.515794	393.609048	485.653256	577.697464	603.790718
5	360.121709	386.910310	481.407363	575.904416	602.693017
6	354.809050	382.073456	478.248914	574.424372	601.688778

model.predict_in_sample()

	mean
0	111.888000
1	112.688513
2	120.747483
3	136.303743
4	124.909752
...	...
139	630.376069
140	567.956065
141	451.814466
142	443.498419
143	374.088365

144 rows × 1 columns

model.predict_in_sample(level=50)

	lo_50%	mean	hi_50%
0	91.727745	111.888000	132.048255
1	92.528257	112.688513	132.848768
2	100.587228	120.747483	140.907738
3	116.143488	136.303743	156.463999
4	104.749497	124.909752	145.070007
...	...	...	...
139	610.215814	630.376069	650.536324
140	547.795810	567.956065	588.116320
141	431.654211	451.814466	471.974721
142	423.338164	443.498419	463.658674
143	353.928110	374.088365	394.248620

144 rows × 3 columns

model.predict_in_sample(level=(80, 90))

	lo_90%	lo_80%	mean	hi_80%	hi_90%
0	62.723919	73.582886	111.888000	150.193114	161.052081
1	63.524432	74.383399	112.688513	150.993626	161.852594
2	71.583402	82.442370	120.747483	159.052597	169.911564
3	87.139662	97.998630	136.303743	174.608857	185.467824
4	75.745671	86.604639	124.909752	163.214866	174.073833
...	...	...	...	...	...
139	581.211988	592.070955	630.376069	668.681182	679.540150
140	518.791984	529.650951	567.956065	606.261178	617.120146
141	402.650385	413.509352	451.814466	490.119580	500.978547
142	394.334338	405.193306	443.498419	481.803533	492.662500
143	324.924284	335.783252	374.088365	412.393479	423.252446

144 rows × 5 columns

model.model_.summary()

ARIMA(2,1,1)                   

Coefficients:
               ar1    ar2    ma1
coefficient  1.166 -0.460 -0.846
s.e.         0.004  0.006  0.007

sigma^2 = 893.391: log likelihood = -687.03

AIC=1382.05

model.summary()

ARIMA(2,1,1)                   

Coefficients:
               ar1    ar2    ma1
coefficient  1.166 -0.460 -0.846
s.e.         0.004  0.006  0.007

sigma^2 = 893.391: log likelihood = -687.03

AIC=1382.05

model_x = AutoARIMA(approximation=False)

model_x = model_x.fit(ap, np.hstack([np.sqrt(drift), np.log(drift)]))

model_x.predict(h=12, X=np.hstack([np.sqrt(newdrift), np.log(newdrift)]), level=(80, 90))

	lo_90%	lo_80%	mean	hi_80%	hi_90%
0	434.808281	444.848076	480.263550	515.679025	525.718820
1	398.250812	414.132285	470.154335	526.176385	542.057858
2	403.968806	422.259587	486.780495	551.301404	569.592185
3	379.813843	398.925989	466.344269	533.762548	552.874694
4	381.849918	400.962063	468.380343	535.798623	554.910769
5	383.880201	402.992346	470.410626	537.828906	556.941052
6	385.904743	405.016888	472.435168	539.853448	558.965594
7	387.923594	407.035740	474.454019	541.872299	560.984445
8	389.936804	409.048950	476.467230	543.885510	562.997655
9	391.944422	411.056568	478.474848	545.893128	565.005273

model_x.predict_in_sample()

	mean
0	73.205301
1	116.318916
2	100.318857
3	107.862716
4	108.927618
...	...
139	608.317510
140	564.682721
141	429.362373
142	442.344731
143	391.284051

144 rows × 1 columns

model_x.predict_in_sample(level=(80, 90))

	lo_90%	lo_80%	mean	hi_80%	hi_90%
0	27.750032	37.789827	73.205301	108.620776	118.660570
1	70.863647	80.903442	116.318916	151.734390	161.774185
2	54.863588	64.903383	100.318857	135.734332	145.774127
3	62.407447	72.447242	107.862716	143.278191	153.317985
4	63.472349	73.512144	108.927618	144.343093	154.382887
...	...	...	...	...	...
139	562.862241	572.902036	608.317510	643.732985	653.772780
140	519.227452	529.267247	564.682721	600.098196	610.137991
141	383.907103	393.946898	429.362373	464.777847	474.817642
142	396.889462	406.929257	442.344731	477.760206	487.800001
143	345.828782	355.868577	391.284051	426.699526	436.739321

144 rows × 5 columns

model_x.summary()

Regression with ARIMA(0,0,3) errors

Coefficients:
               ma1    ma2    ma3    ex_1    ex_2
coefficient  1.226  0.904  0.552  57.136 -45.775
s.e.         0.023  0.038  0.021  15.549  44.130

sigma^2 = 763.684: log likelihood = -679.81

AIC=1371.61

predict_arima[source]

arima_string[source]

forecast_arima[source]

fitted_arima[source]

auto_arima_f[source]

print_statsforecast_ARIMA[source]

class ARIMASummary[source]

class AutoARIMA[source]