Python statsmodels ARIMA LinAlgError：SVD 沒有收斂

Question

背景：我正在使用 statsmodels 開發一個程序，該程序將 27 個 arima 模型 (p,d,q=0,1,2) 擬合到 100 多個變量，並為 AR/選擇具有最低 aic 和統計顯着 t 統計量的模型dickey fuller 檢驗的 MA 系數和統計顯着 p 值...

對於一個特定的變量和一組特定的參數，我得到

LinAlgError: SVD did not converge    

對於復制，變量和失敗的代碼如下

rollrate =[0.3469842191781748,
 0.9550689157572028,
 0.48170862494888256,
 0.15277985674197356,
 0.46102487817508747,
 0.32777706854320243,
 0.5163787896482797,
 0.01707716528127215,
 0.015036662424309755,
 0.2299825242910243,
 0.03719773802216722,
 0.24392098372995807,
 0.1783587055969874,
 0.6759904243574179,
 0.1197617555878022,
 0.04274682226635633,
 0.27369984820298465,
 0.18999355015483932,
 0.2985208240580264,
 0.2872064881442138,
 1.0522764728046277,
 0.3694114556631419,
 0.09613536093441034,
 0.6648215681632191,
 0.3223120091564835,
 0.9274048223872483,
 0.2763221143255601,
 0.4501460109958479,
 0.2220472247972312,
 0.3644512582291407,
 0.7790042237519584,
 0.3749145302678043,
 1.2771681290160286,
 0.6760112486224217,
 0.5214358465170098,
 0.84041997296269,
 0.12054593136059581,
 0.18900376737686622,
 0.042561102427304424,
 0.17189805124670604,
 0.11383752243305952,
 0.2687780002387387,
 0.717538770963329,
 0.26636160206108384,
 0.04221743047344771,
 0.3259506533106764,
 0.20146525340606328,
 0.4059344185647537,
 0.07503287726465639,
 0.3011594076817088,
 0.1433563136989911,
 0.14803562944375281,
 0.23096999679467808,
 0.31133672787599703,
 0.2313639154827471,
 0.30343086620083537,
 0.4608439884577555,
 0.19149827372467804,
 0.2506814947310181,
 1.008458195025946,
 0.3776434264127751,
 0.344728062930179,
 0.2110402015365776,
 0.26582041849423843,
 1.1019000121595244,
 0.0,
 0.023068095385979804,
 0.014256779894199491,
 0.3209225608633755,
 0.00294468492742426,
 0.0,
 0.3346732726544143,
 0.38256681208088283,
 0.4916019617068597,
 0.06922156984602362,
 0.34458053250016984,
 0.0,
 0.09615667784109984,
 1.8271531669931351,
 0,
 0,
 0.0,
 0,
 0.0,
 0.03205594450156685,
 0.0,
 0.0,
 0.0,
 0,
 0.0,
 0,
 0.0,
 0,
 0,
 1.0,
 0]


p=2
q=2
d=0
fit = statsmodels.api.tsa.ARIMA(rollRate, (p,d,q)).fit(transparams=False)   

我知道特定參數 p=2,d=2,q=0 對於這個特定變量可能是一個糟糕的 ARIMA 模型，並且由於許多零或不穩定的特性，變量本身可能不是 ARIMA 模型的合適候選者，但我需要一種可能繞過此錯誤或修復問題的方法，以保持程序迭代參數。 謝謝

Answer 1

也許可以考慮嘗試這種方式，因為這是我從機器學習精通 Jason Brownlee（博士）那里學到的方法的組合

https://machinelearningmastery.com/arima-for-time-series-forecasting-with-python/

和法哈德·馬利克，數學家

https://towardsdatascience.com/forecasting-exchange-rates-using-arima-in-python-f032f313fc56

通過結合他們的方法和技術，我能夠提出我認為接近可行且可靠的模型。

這是我花了幾個小時痛苦地拼湊起來的代碼：

import warnings
import pandas as pd
from statsmodels.tsa.arima_model import ARIMA
from sklearn.metrics import mean_squared_error
from math import sqrt
from matplotlib import pyplot

rollRate=[0.3469842191781748,0.9550689157572028,0.48170862494888256,0.15277985674197356,0.46102487817508747,0.32777706854320243,
0.5163787896482797,0.01707716528127215,0.015036662424309755,0.2299825242910243,0.03719773802216722,0.24392098372995807,
0.1783587055969874,0.6759904243574179,0.1197617555878022,
0.04274682226635633,0.27369984820298465,0.18999355015483932,0.2985208240580264,0.2872064881442138,1.0522764728046277,
0.3694114556631419,0.09613536093441034,0.6648215681632191,0.3223120091564835,0.9274048223872483,0.2763221143255601,
0.4501460109958479,0.2220472247972312,0.3644512582291407,0.7790042237519584,0.3749145302678043,
1.2771681290160286,0.6760112486224217,0.5214358465170098,0.84041997296269,0.12054593136059581,
0.18900376737686622,0.042561102427304424,0.17189805124670604,0.11383752243305952,0.2687780002387387,
0.717538770963329,0.26636160206108384,0.04221743047344771,0.3259506533106764,0.20146525340606328,0.4059344185647537,
0.07503287726465639,0.3011594076817088,0.1433563136989911,0.14803562944375281,0.23096999679467808,
0.31133672787599703,0.2313639154827471,0.30343086620083537,0.4608439884577555,0.19149827372467804,
0.2506814947310181,1.008458195025946,0.3776434264127751,0.344728062930179,0.2110402015365776,0.26582041849423843,
1.1019000121595244,0.0,0.023068095385979804,0.014256779894199491,0.3209225608633755,0.00294468492742426,0.0,
0.3346732726544143,0.38256681208088283,0.4916019617068597,0.06922156984602362,0.34458053250016984,0.0,
0.09615667784109984,1.8271531669931351,0,0,0.0,0,0.0,0.03205594450156685,0.0,0.0,0.0,0,0.0,0,0.0,0,0,1.0,0]

# Evaluate an ARIMA model for a given order (p,d,q) and return RMSE
def evaluate_arima_model(X, arima_order):
    # prepare training dataset
    X = X.astype('float32')
    train_size = int(len(X) * 0.50)
    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)
        model_fit = model.fit(trend='nc', disp=0)
        yhat = model_fit.forecast()[0]
        predictions.append(yhat)
        history.append(test[t])
    # calculate out of sample error
    rmse = sqrt(mean_squared_error(test, predictions))
    return rmse

# 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:
                    rmse = evaluate_arima_model(dataset, order)
                    print(rmse)
                    if rmse < best_score:
                        best_score, best_cfg = rmse, order
                    print('ARIMA%s RMSE=%.3f' % (order, rmse))
                except:
                    continue
    print('Best ARIMA%s RMSE=%.3f' % (best_cfg, best_score))

p_values = range(0, 2)
d_values = range(0, 1)
q_values = range(0, 2)
warnings.filterwarnings("ignore")

dataset = pd.Series([356,386,397,397,413,458,485,344,390,360,420,435,439,454,462,454,469,500,492,473,458,469,481,
          488,466,462,473,530,662,651,587,515,526,503,503,503,515,522,492,503,503,450,432,432,458,462,
          503,488,466,492,503,515,500,522,575,583,587,628,640,609,606,632,617,613,598,575,564,549,538,
          568,575,579,587,602,594,587,587,625,613])

dataset = dataset.values
print('\n==============================\n')
evaluate_models(dataset, p_values, d_values, q_values)

pp = 2
dd = 1
qq = 2

def StartProducingARIMAForecastValues(dataVals, p, d, q):
    model = ARIMA(dataVals, order=(p, d, q))
    model_fit = model.fit(disp=0)
    pred = model_fit.forecast()[0]
    return pred

print('\n==============================\n')

predictions = StartProducingARIMAForecastValues(rollRate, 1, 1, 0)
print('First Prediction=%f' % (predictions))

Actual = [x for x in rollRate]
Predictions = list()

for timestamp in range(len(rollRate)):
    ActualValue = rollRate[timestamp]
    Prediction = StartProducingARIMAForecastValues(Actual, 3, 1, 0)
    print('Actual=%f, Predicted=%f' % (ActualValue, Prediction))

    Predictions.append(Prediction)
    Actual.append(ActualValue)

Error = mean_squared_error(rollRate, Predictions)

print('Test Mean Squared Error : %.3f' % Error)
# plot
pyplot.plot(rollRate)
pyplot.plot(Predictions, color='red')
pyplot.show()

和輸出圖：

和輸出本身：