使用Python训练arima模型时如何解决LinAlgError和ValueError

Question

我正在尝试实现一个时间序列模型，但得到了一些奇怪的异常，但这些异常对我来说没有任何意义。我想知道我是否犯了一个错误，或者这是否完全是预料之中的。详细信息来了...

训练模型时，我尝试进行网格搜索以找到最佳（p、d、q）设置。这是完整的代码（我将在下面解释这里发生的事情）：

下面的可重现代码本质上是来自https://machinelearningmastery.com/grid-search-arima-hyperparameters-with-python/的副本，有一些细微的变化......：

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)

这是输出（不是全部，但它提供了足够的信息）：

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.

该代码只是尝试所有不同的给定设置，训练模型，计算每个给定设置的 MSE（均方误差），然后选择最佳设置（基于最小 MSE）。

但在训练过程中，代码不断抛出LinAlgError异常ValueError，这对我来说没有任何意义。

据我所知，当抛出这些异常时，代码并没有真正训练某些设置，然后只是跳转到将要尝试的下一个设置。

为什么我会看到这些异常？他们可以被忽视吗？我需要做什么才能解决它？

Answer 1

首先，回答你的具体问题：我认为“SVD 没有收敛”是 Statsmodels 的 ARIMA 模型中的一个错误。如今 SARIMAX 模型得到了更好的支持（并且可以完成 ARIMA 模型所做的所有事情以及更多），因此我建议使用它。为此，请将模型创建替换为：

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

话虽如此，我认为考虑到您的时间序列和您正在尝试的规范，您仍然不太可能获得良好的结果。

特别是，您的时间序列非常短，并且您只考虑极长的自回归滞后长度 (p > 6)。使用如此少的数据点来估计许多参数将是困难的，特别是当您还进行积分（d = 1 或 d = 2）并且还添加了移动平均分量时。我建议您重新评估您正在考虑的模型。