auto.arima() 相當於 python

Question

我正在嘗試使用 ARMA ARIMA 模型預測每周銷售額。 我找不到 function 來調整statsmodels中的順序（p，d，q）。 當前 R 有一個 function forecast::auto.arima()它將調整 (p,d,q) 參數。

go 如何為我的 model 選擇正確的順序？ python 中是否有用於此目的的庫？

Answer 1

您可以實施多種方法：

1. ARIMAResults包括aic和bic 。 根據它們的定義（參見此處和此處），這些標准會懲罰模型中的參數數量。 因此，您可以使用這些數字來比較模型。 scipy 也有optimize.brute ，它在指定的參數空間上進行網格搜索。 所以像這樣的工作流程應該可以工作：

    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)

   確保您使用finish=None調用brute 。

2. 您可以從ARIMAResults獲得pvalues 。 因此，一種漸進算法很容易實現，其中模型的度數在維度上增加，從而獲得添加參數的最低 p 值。

3. 使用ARIMAResults.predict交叉驗證替代模型。 最好的方法是將時間序列的尾部（比如最近 5% 的數據）保留在樣本之外，並使用這些點來獲得擬合模型的測試誤差。

Answer 2

現在有一個合適的 python 包來做 auto-arima。 https://github.com/tgsmith61591/pmdarima

文檔： http : //alkaline-ml.com/pmdarima

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

Answer 3

最簡單的方法是通過statsforecast package ( https://github.com/Nixtla/statsforecast ) 使用 Nixtla 的auto_arima model。 它是forecast::auto.arima function 的鏡像實現，使用numba進行了優化。 它具有更好的性能並且比 R 和pmdarima實現更快。

只需pip使用pip install statsforecast庫。 然后，

from statsforecast.core import StatsForecast
from statsforecast.models import auto_arima

fcst = StatsForecast(
     df, #your data 
     models=[auto_arima], 
     freq='W', # frequency of your data
     n_jobs=7, # you can also define the number of cores used for parallelizing

)
forecasts = fcst.forecast(12) #your horizon

這是一個帶有示例的筆記本。

Answer 4

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)

這將為您提供 p、d、q 值，然后將這些值用於您的 ARIMA 模型

Answer 5

我編寫了這些實用程序函數來直接計算 pdq 值get_PDQ_parallel需要三個輸入數據，這些數據以時間戳（日期時間）為索引。 n_jobs 將提供並行處理器的數量。 輸出將是具有 aic 和 bic 值的數據幀，索引 p 中的 order=(P,D,Q) 和 q 范圍是 [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 6

可能的解決方案

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

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

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

Answer 7

截至目前，我們可以直接使用 PyPI 中的pyramid-arima包。

Answer 8

在 conda 中，使用conda install -c saravji pmdarima進行安裝。

用戶saravji已將其放入 anaconda cloud。

然后使用，

from pmdarima.arima import auto_arima

（請注意，名稱pyramid-arima已更改為pmdarima ）。

Answer 9

實際上

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)