使用Python訓練Arima模型時如何解決LinAlgError和ValueError

Question

我正在嘗試實現時間序列模型，並得到一些奇怪的異常，這些異常對我沒有任何幫助。 我想知道我是在犯錯誤還是完全可以預期。 這是細節...

在訓練模型時，我嘗試進行網格搜索以找到最佳的（p，d，q）設置。 這是完整的代碼（下面我將解釋發生的事情）：

下面的可復制代碼本質上是https://machinelearningmastery.com/grid-search-arima-hyperparameters-with-python/的副本，但有一些細微變化...：

import warnings
from pandas import Series
from statsmodels.tsa.arima_model import ARIMA
from sklearn.metrics import mean_squared_error

# evaluate an ARIMA model for a given order (p,d,q)
def evaluate_arima_model(X, arima_order):
    # prepare training dataset
    train_size = int(len(X) * 0.66)
    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('float64')
    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:
                    print("Evaluating the settings: ", p, d, q)
                    mse = evaluate_arima_model(dataset, order)
                    if mse < best_score:
                        best_score, best_cfg = mse, order
                    print('ARIMA%s MSE=%.3f' % (order,mse))
                except Exception as exception:
                    print("Exception occured...", type(exception).__name__, "\n", exception)

    print('Best ARIMA%s MSE=%.3f' % (best_cfg, best_score))

# dataset
values = np.array([-1.45, -9.04, -3.64, -10.37, -1.36, -6.83, -6.01, -3.84, -9.92, -5.21,
                   -8.97, -6.19, -4.12, -11.03, -2.27, -4.07, -5.08, -4.57, -7.87, -2.80,
                   -4.29, -4.19, -3.76, -22.54, -5.87, -6.39, -4.19, -2.63, -8.70, -3.52, 
                   -5.76, -1.41, -6.94, -12.95, -8.64, -7.21, -4.05, -3.01])

# evaluate parameters
p_values = [7, 8, 9, 10]
d_values = range(0, 3)
q_values = range(0, 3)
warnings.filterwarnings("ignore")
evaluate_models(values, p_values, d_values, q_values)

這是輸出（不是所有內容，但它提供了足夠的信息）：

Evaluating the settings:  7 0 0
Exception occured... LinAlgError 
 SVD did not converge
Evaluating the settings:  7 0 1
Exception occured... LinAlgError 
 SVD did not converge
Evaluating the settings:  7 0 2
Exception occured... ValueError 
 The computed initial AR coefficients are not stationary
You should induce stationarity, choose a different model order, or you can
pass your own start_params.
Evaluating the settings:  7 1 0
Exception occured... LinAlgError 
 SVD did not converge
Evaluating the settings:  7 1 1
Exception occured... ValueError 
 The computed initial AR coefficients are not stationary
You should induce stationarity, choose a different model order, or you can
pass your own start_params.
Evaluating the settings:  7 1 2
Exception occured... ValueError 
 The computed initial AR coefficients are not stationary
You should induce stationarity, choose a different model order, or you can
pass your own start_params.
Evaluating the settings:  7 2 0
Exception occured... LinAlgError 
 SVD did not converge
Evaluating the settings:  7 2 1
Exception occured... ValueError 
 The computed initial AR coefficients are not stationary
You should induce stationarity, choose a different model order, or you can
pass your own start_params.
Evaluating the settings:  7 2 2
Exception occured... ValueError 
 The computed initial AR coefficients are not stationary
You should induce stationarity, choose a different model order, or you can
pass your own start_params.

代碼只是簡單地嘗試所有不同的給定設置，訓練模型，為每個給定設置計算MSE（均方誤差），然后選擇最佳設置（基於最小MSE）。

但是在培訓過程中，代碼不斷拋出LinAlgError和ValueError異常，這對我沒有任何幫助。

據我所知，當拋出這些異常時，代碼並不是真正地在真正訓練某些設置，然后只是跳到將要嘗試的下一個設置。

為什么我看到這些例外？ 他們可以被忽略嗎？ 我需要怎么做才能解決？

Answer 1

首先，回答您的特定問題：我認為“ SVD未收斂”是Statsmodels的ARIMA模型中的錯誤。 如今，SARIMAX模型得到了更好的支持（並且ARIMA模型所做的一切以及更多功能都得到了支持），所以我建議改用它。 為此，將模型創建替換為：

model = sm.tsa.SARIMAX(history, trend='c', order=arima_order, enforce_stationarity=False, enforce_invertibility=False)

話雖如此，我認為鑒於時間序列和所嘗試的規范，您仍然不太可能獲得良好的結果。

特別是，您的時間序列非常短，並且您僅考慮極長的自回歸滯后長度（p> 6）。 很難估計許多參數具有很少的數據點，尤其是當您還具有積分（d = 1或d = 2）並且還添加移動平均成分時。 我建議您重新評估您正在考慮的模型。