等价于 python 的 auto.arima()

Question

我正在尝试使用 ARMA ARIMA 模型预测每周销售额。我在statsmodels 中找不到用于调整 order(p,d,q) 的函数。目前 R 有一个函数forecast::auto.arima()，它将调整 (p,d,q) 参数。

如何为我的模型选择正确的订单？ python中是否有为此目的可用的库？

Answer 1

您可以实施多种方法：

1. ARIMAResults 包括aic 和bic。根据他们的定义（参见here 和here），这些标准会影响模型中的参数数量。因此，您可以使用这些数字来比较模型。 scipy 还有optimize.brute，它在指定的参数空间上进行网格搜索。所以像这样的工作流程应该可以工作：

   def objfunc(order, exog, endog):
       from statsmodels.tsa.arima_model import ARIMA
       fit = ARIMA(endog, order, exog).fit()
       return fit.aic()
   
   from scipy.optimize import brute
   grid = (slice(1, 3, 1), slice(1, 3, 1), slice(1, 3, 1))
   brute(objfunc, grid, args=(exog, endog), finish=None)
   

   确保您使用finish=None 致电brute。

2. 您可以从ARIMAResults 获得pvalues。因此，一种步进算法很容易实现，其中模型的度数在维度上增加，从而获得添加参数的最低 p 值。

3. 使用ARIMAResults.predict 交叉验证替代模型。最好的方法是将时间序列的尾部（例如最近 5% 的数据）保留在样本之外，并使用这些点来获得拟合模型的测试误差。

Answer 2

其实

def objfunc(order,*params ):    
    from statsmodels.tsa.arima_model import ARIMA   
    p,d,q = order   
    fit = ARIMA(endog, order, exog).fit()  
    return fit.aic()    
from scipy.optimize import brute
grid = (slice(1, 3, 1), slice(1, 3, 1), slice(1, 3, 1))
brute(objfunc, grid, args=params, finish=None)

Answer 3

我编写了这些实用函数来直接计算 pdq 值 get_PDQ_parallel 需要三个以时间戳（日期时间）为索引的系列输入数据。 n_jobs 将提供并行处理器的数量。输出将是具有 aic 和 bic 值的数据帧，索引中的 order=(P,D,Q) p 和 q 范围是 [0,12] 而 d 是 [0,1]

import statsmodels 
from statsmodels import api as sm
from sklearn.metrics import r2_score,mean_squared_error
from sklearn.utils import check_array
from functools import partial
from multiprocessing import Pool
def get_aic_bic(order,series):
    aic=np.nan
    bic=np.nan
    #print(series.shape,order)
    try:
        arima_mod=statsmodels.tsa.arima_model.ARIMA(series,order=order,freq='H').fit(transparams=True,method='css')
        aic=arima_mod.aic
        bic=arima_mod.bic
        print(order,aic,bic)
    except:
        pass
    return aic,bic

def get_PDQ_parallel(data,n_jobs=7):
    p_val=13
    q_val=13
    d_vals=2
    pdq_vals=[ (p,d,q) for p in range(p_val) for d in range(d_vals) for q in range(q_val)]
    get_aic_bic_partial=partial(get_aic_bic,series=data)
    p = Pool(n_jobs)
    res=p.map(get_aic_bic_partial, pdq_vals)  
    p.close()
    return pd.DataFrame(res,index=pdq_vals,columns=['aic','bic']) 

Answer 4

可能的解决方案

df=pd.read_csv("http://vincentarelbundock.github.io/Rdatasets/csv/datasets/AirPassengers.csv")

# Define the p, d and q parameters to take any value between 0 and 2
p = d = q = range(0, 2)
print(p)


import itertools
import warnings

# Generate all different combinations of p, q and q triplets
pdq = list(itertools.product(p, d, q))
print(pdq)

# Generate all different combinations of seasonal p, q and q triplets
seasonal_pdq = [(x[0], x[1], x[2], 12) for x in list(itertools.product(p, d, q))]

print('Examples of parameter combinations for Seasonal ARIMA...')
print('SARIMAX: {} x {}'.format(pdq[1], seasonal_pdq[1]))
print('SARIMAX: {} x {}'.format(pdq[1], seasonal_pdq[2]))
print('SARIMAX: {} x {}'.format(pdq[2], seasonal_pdq[3]))
print('SARIMAX: {} x {}'.format(pdq[2], seasonal_pdq[4]))
Examples of parameter combinations for Seasonal ARIMA...
SARIMAX: (0, 0, 1) x (0, 0, 1, 12)
SARIMAX: (0, 0, 1) x (0, 1, 0, 12)
SARIMAX: (0, 1, 0) x (0, 1, 1, 12)
SARIMAX: (0, 1, 0) x (1, 0, 0, 12)

y=df

#warnings.filterwarnings("ignore") # specify to ignore warning messages

for param in pdq:
    for param_seasonal in seasonal_pdq:
        try:
            mod = sm.tsa.statespace.SARIMAX(y,
                                            order=param,
                                            seasonal_order=param_seasonal,
                                            enforce_stationarity=False,
                                            enforce_invertibility=False)

            results = mod.fit()

            print('ARIMA{}x{}12 - AIC:{}'.format(param, param_seasonal, results.aic))
        except:
            continue
ARIMA(0, 0, 0)x(0, 0, 1, 12)12 - AIC:3618.0303991426763
ARIMA(0, 0, 0)x(0, 1, 1, 12)12 - AIC:2824.7439963684233
ARIMA(0, 0, 0)x(1, 0, 0, 12)12 - AIC:2942.2733127230185
ARIMA(0, 0, 0)x(1, 0, 1, 12)12 - AIC:2922.178151133141
ARIMA(0, 0, 0)x(1, 1, 0, 12)12 - AIC:2767.105066400224
ARIMA(0, 0, 0)x(1, 1, 1, 12)12 - AIC:2691.233398643673
ARIMA(0, 0, 1)x(0, 0, 0, 12)12 - AIC:3890.816777796087
ARIMA(0, 0, 1)x(0, 0, 1, 12)12 - AIC:3541.1171286722
ARIMA(0, 0, 1)x(0, 1, 0, 12)12 - AIC:3028.8377323188824
ARIMA(0, 0, 1)x(0, 1, 1, 12)12 - AIC:2746.77973129136
ARIMA(0, 0, 1)x(1, 0, 0, 12)12 - AIC:3583.523640623017
ARIMA(0, 0, 1)x(1, 0, 1, 12)12 - AIC:3531.2937768990187
ARIMA(0, 0, 1)x(1, 1, 0, 12)12 - AIC:2781.198675746594
ARIMA(0, 0, 1)x(1, 1, 1, 12)12 - AIC:2720.7023088205974
ARIMA(0, 1, 0)x(0, 0, 1, 12)12 - AIC:3029.089945668332
ARIMA(0, 1, 0)x(0, 1, 1, 12)12 - AIC:2568.2832251221016
ARIMA(0, 1, 0)x(1, 0, 0, 12)12 - AIC:2841.315781459511
ARIMA(0, 1, 0)x(1, 0, 1, 12)12 - AIC:2815.4011044132576
ARIMA(0, 1, 0)x(1, 1, 0, 12)12 - AIC:2588.533386513587
ARIMA(0, 1, 0)x(1, 1, 1, 12)12 - AIC:2569.9453272483315
ARIMA(0, 1, 1)x(0, 0, 0, 12)12 - AIC:3327.5177587522303
ARIMA(0, 1, 1)x(0, 0, 1, 12)12 - AIC:2984.716706112334
ARIMA(0, 1, 1)x(0, 1, 0, 12)12 - AIC:2789.128542154043
ARIMA(0, 1, 1)x(0, 1, 1, 12)12 - AIC:2537.0293659293943
ARIMA(0, 1, 1)x(1, 0, 0, 12)12 - AIC:2984.4555708516436
ARIMA(0, 1, 1)x(1, 0, 1, 12)12 - AIC:2939.460958374472
ARIMA(0, 1, 1)x(1, 1, 0, 12)12 - AIC:2578.7862352774437
ARIMA(0, 1, 1)x(1, 1, 1, 12)12 - AIC:2537.771484229265
ARIMA(1, 0, 0)x(0, 0, 0, 12)12 - AIC:3391.5248913820797
ARIMA(1, 0, 0)x(0, 0, 1, 12)12 - AIC:3038.142074281268
C:\Users\Dell\Anaconda3\lib\site-packages\statsmodels\base\model.py:496: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  "Check mle_retvals", ConvergenceWarning)
ARIMA(1, 0, 0)x(0, 1, 0, 12)12 - AIC:2839.809192263449
ARIMA(1, 0, 0)x(0, 1, 1, 12)12 - AIC:2588.50367175184
ARIMA(1, 0, 0)x(1, 0, 0, 12)12 - AIC:2993.4630440139595
ARIMA(1, 0, 0)x(1, 0, 1, 12)12 - AIC:2995.049216326931
ARIMA(1, 0, 0)x(1, 1, 0, 12)12 - AIC:2588.2463284315304
ARIMA(1, 0, 0)x(1, 1, 1, 12)12 - AIC:2592.80110502723
ARIMA(1, 0, 1)x(0, 0, 0, 12)12 - AIC:3352.0350133621478
ARIMA(1, 0, 1)x(0, 0, 1, 12)12 - AIC:3006.5493366627807
ARIMA(1, 0, 1)x(0, 1, 0, 12)12 - AIC:2810.6423724894516
ARIMA(1, 0, 1)x(0, 1, 1, 12)12 - AIC:2559.584031948852
ARIMA(1, 0, 1)x(1, 0, 0, 12)12 - AIC:2981.2250436794675
ARIMA(1, 0, 1)x(1, 0, 1, 12)12 - AIC:2959.3142304724834
ARIMA(1, 0, 1)x(1, 1, 0, 12)12 - AIC:2579.8245645892207
ARIMA(1, 0, 1)x(1, 1, 1, 12)12 - AIC:2563.13922589258
ARIMA(1, 1, 0)x(0, 0, 0, 12)12 - AIC:3354.7462930846423
ARIMA(1, 1, 0)x(0, 0, 1, 12)12 - AIC:3006.702997636003
ARIMA(1, 1, 0)x(0, 1, 0, 12)12 - AIC:2809.3844175191666
ARIMA(1, 1, 0)x(0, 1, 1, 12)12 - AIC:2558.484602766447
ARIMA(1, 1, 0)x(1, 0, 0, 12)12 - AIC:2959.885810636943
ARIMA(1, 1, 0)x(1, 0, 1, 12)12 - AIC:2960.712709764296
ARIMA(1, 1, 0)x(1, 1, 0, 12)12 - AIC:2557.945907092698
ARIMA(1, 1, 0)x(1, 1, 1, 12)12 - AIC:2559.274166458508
ARIMA(1, 1, 1)x(0, 0, 0, 12)12 - AIC:3326.3285511700374
ARIMA(1, 1, 1)x(0, 0, 1, 12)12 - AIC:2985.868532151721
ARIMA(1, 1, 1)x(0, 1, 0, 12)12 - AIC:2790.7677149967103
ARIMA(1, 1, 1)x(0, 1, 1, 12)12 - AIC:2538.820635541546
ARIMA(1, 1, 1)x(1, 0, 0, 12)12 - AIC:2963.2789505804294
ARIMA(1, 1, 1)x(1, 0, 1, 12)12 - AIC:2941.2436984747465
ARIMA(1, 1, 1)x(1, 1, 0, 12)12 - AIC:2559.8258191422606
ARIMA(1, 1, 1)x(1, 1, 1, 12)12 - AIC:2539.712354465328

来自https://www.digitalocean.com/community/tutorials/a-guide-to-time-series-forecasting-with-arima-in-python-3

另见https://github.com/decisionstats/pythonfordatascience/blob/master/time%2Bseries%20(1).ipynb

Answer 5

现在有一个合适的 python 包来做 auto-arima。 https://github.com/tgsmith61591/pmdarima

文档： http://alkaline-ml.com/pmdarima

用法示例：https://github.com/tgsmith61591/pmdarima/blob/master/examples/quick_start_example.ipynb

Answer 6

def evaluate_arima_model(X, arima_order):
    # prepare training dataset
    train_size = int(len(X) * 0.90)
    train, test = X[0:train_size], X[train_size:]
    history = [x for x in train]
    # make predictions
    predictions = list()
    for t in range(len(test)):
        model = ARIMA(history, order=arima_order)
        model_fit = model.fit(disp=0)
        yhat = model_fit.forecast()[0]
        predictions.append(yhat)
        history.append(test[t])
    # calculate out of sample error
    error = mean_squared_error(test, predictions)
    return error

# evaluate combinations of p, d and q values for an ARIMA model
def evaluate_models(dataset, p_values, d_values, q_values):
    dataset = dataset.astype('float32')
    best_score, best_cfg = float("inf"), None
    for p in p_values:
        for d in d_values:
            for q in q_values:
                order = (p,d,q)
                try:
                    mse = evaluate_arima_model(dataset, order)
                    if mse < best_score:
                        best_score, best_cfg = mse, order
                    print('ARIMA%s MSE=%.3f' % (order,mse))
                except:
                    continue
    print('Best ARIMA%s MSE=%.3f' % (best_cfg, best_score))

# load dataset
def parser(x):
    return datetime.strptime('190'+x, '%Y-%m')



import datetime
p_values = [4,5,6,7,8]
d_values = [0,1,2]
q_values = [2,3,4,5,6]
warnings.filterwarnings("ignore")
evaluate_models(train, p_values, d_values, q_values)

这将为您提供 p、d、q 值，然后将这些值用于您的 ARIMA 模型

Answer 7

目前，我们可以直接使用 PyPI 中的pyramid-arima 包。

Answer 8

在 conda 中，使用conda install -c saravji pmdarima 进行安装。

用户saravji已将其放入anaconda云中。

然后使用，

from pmdarima.arima import auto_arima

（注意名称pyramid-arima改为pmdarima）。