statsmodels ARIMA 模型中的 LU 分解错误

Question

我知道 stackoverflow 上有一个非常相似的问题和答案（ here ），但这似乎明显不同。 我正在使用 statsmodels v 0.13.2，并且我使用的是 ARIMA 模型而不是 SARIMAX 模型。

我正在尝试使用 ARIMA 模型拟合时间序列数据集列表。 我的代码中有问题的部分在这里：

import numpy as np
from statsmodels.tsa.arima.model import ARIMA

items = np.log(og_items)
items['count'] = items['count'].apply(lambda x: 0 if math.isnan(x) or math.isinf(x) else x)
model = ARIMA(items, order=(14, 0, 7))
trained = model.fit()

items是一个包含日期索引和单列count的数据框。

我在第二行应用了 lambda，因为一些计数可能为 0，导致应用 log 后的负无穷大。 进入 ARIMA 的最终产品不包含任何 NaN 或无限数。 但是，当我在不使用日志功能的情况下尝试此操作时，我没有收到错误消息。 这仅发生在某些系列上，但似乎没有韵律或原因受到影响。 一个系列在应用 lambda 后大约有一半的值为零，而另一个系列没有一个零。 这是错误：

Traceback (most recent call last):
  File "item_pipeline.py", line 267, in <module>
    main()
  File "item_pipeline.py", line 234, in main
    restaurant_predictions = make_predictions(restaurant_data=restaurant_data, models=models,
  File "item_pipeline.py", line 138, in make_predictions
    predictions = model(*data_tuple[:2], min_date=min_date, max_date=max_date,
  File "/Users/rob/Projects/5out-ml/models/item_level/items/predict_arima.py", line 127, in predict_daily_arima
    predict_date_arima(prediction_dict, item_dict, prediction_date, x_days_out=x_days_out, log_vals=log_vals,
  File "/Users/rob/Projects/5out-ml/models/item_level/items/predict_arima.py", line 51, in predict_date_arima
    raise e
  File "/Users/rob/Projects/5out-ml/models/item_level/items/predict_arima.py", line 47, in predict_date_arima
    fitted = model.fit()
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/tsa/arima/model.py", line 390, in fit
    res = super().fit(
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/tsa/statespace/mlemodel.py", line 704, in fit
    mlefit = super(MLEModel, self).fit(start_params, method=method,
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/base/model.py", line 563, in fit
    xopt, retvals, optim_settings = optimizer._fit(f, score, start_params,
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/base/optimizer.py", line 241, in _fit
    xopt, retvals = func(objective, gradient, start_params, fargs, kwargs,
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/base/optimizer.py", line 651, in _fit_lbfgs
    retvals = optimize.fmin_l_bfgs_b(func, start_params, maxiter=maxiter,
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/scipy/optimize/_lbfgsb_py.py", line 199, in fmin_l_bfgs_b
    res = _minimize_lbfgsb(fun, x0, args=args, jac=jac, bounds=bounds,
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/scipy/optimize/_lbfgsb_py.py", line 362, in _minimize_lbfgsb
    f, g = func_and_grad(x)
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/scipy/optimize/_differentiable_functions.py", line 286, in fun_and_grad
    self._update_grad()
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/scipy/optimize/_differentiable_functions.py", line 256, in _update_grad
    self._update_grad_impl()
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/scipy/optimize/_differentiable_functions.py", line 173, in update_grad
    self.g = approx_derivative(fun_wrapped, self.x, f0=self.f,
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/scipy/optimize/_numdiff.py", line 505, in approx_derivative
    return _dense_difference(fun_wrapped, x0, f0, h,
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/scipy/optimize/_numdiff.py", line 576, in _dense_difference
    df = fun(x) - f0
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/scipy/optimize/_numdiff.py", line 456, in fun_wrapped
    f = np.atleast_1d(fun(x, *args, **kwargs))
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/scipy/optimize/_differentiable_functions.py", line 137, in fun_wrapped
    fx = fun(np.copy(x), *args)
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/base/model.py", line 531, in f
    return -self.loglike(params, *args) / nobs
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/tsa/statespace/mlemodel.py", line 939, in loglike
    loglike = self.ssm.loglike(complex_step=complex_step, **kwargs)
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/tsa/statespace/kalman_filter.py", line 983, in loglike
    kfilter = self._filter(**kwargs)
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/tsa/statespace/kalman_filter.py", line 903, in _filter
    self._initialize_state(prefix=prefix, complex_step=complex_step)
  File "/Users/rob/Projects/5out-ml/venv/lib/python3.8/site-packages/statsmodels/tsa/statespace/representation.py", line 983, in _initialize_state
    self._statespaces[prefix].initialize(self.initialization,
  File "statsmodels/tsa/statespace/_representation.pyx", line 1362, in statsmodels.tsa.statespace._representation.dStatespace.initialize
  File "statsmodels/tsa/statespace/_initialization.pyx", line 288, in statsmodels.tsa.statespace._initialization.dInitialization.initialize
  File "statsmodels/tsa/statespace/_initialization.pyx", line 406, in statsmodels.tsa.statespace._initialization.dInitialization.initialize_stationary_stationary_cov
  File "statsmodels/tsa/statespace/_tools.pyx", line 1206, in statsmodels.tsa.statespace._tools._dsolve_discrete_lyapunov
numpy.linalg.LinAlgError: LU decomposition error.

另一个stackoverflow帖子中的解决方案是以不同的方式初始化状态空间。 如果您查看错误的最后几行，则看起来涉及状态空间。 但是，该工作流程似乎并未在较新版本的 statsmodels 中公开。 是吗？ 如果没有，我还能尝试什么来规避这个错误？

到目前为止，我已经尝试手动将模型初始化为approximate diffuse ，并手动将initialize属性设置为approximate diffuse 。 在新的 statsmodels 代码中似乎都不是有效的。

Answer 1

原来有一种新的初始化方法。 下面的第二行是手术行。

model = ARIMA(items, order=(14, 0, 7))
model.initialize_approximate_diffuse() # this line
trained = model.fit()