为什么我在ARIMA statsmodel中获得高错误-Python

Question

我有一个时间序列数据。它每周一次。

我想使用ARIMA模型预测接下来几周的数据。

这是我的时间序列数据的图表：

首先，我使用统计模型中的seasonal_decompose方法来检查趋势/会话性/残差外观：

from statsmodels.tsa.seasonal import seasonal_decompose
result = seasonal_decompose(df['comissions'], model='add')
result.plot(); 

我检查我的数据是否稳定：

from statsmodels.tsa.stattools import adfuller

def adf_test(series,title=''):
    """
    Pass in a time series and an optional title, returns an ADF report
    """
    print(f'Augmented Dickey-Fuller Test: {title}')
    result = adfuller(series.dropna(),autolag='AIC') # .dropna() handles differenced data

    labels = ['ADF test statistic','p-value','# lags used','# observations']
    out = pd.Series(result[0:4],index=labels)

    for key,val in result[4].items():
        out[f'critical value ({key})']=val

    print(out.to_string())          # .to_string() removes the line "dtype: float64"

    if result[1] <= 0.05:
        print("Strong evidence against the null hypothesis")
        print("Reject the null hypothesis")
        print("Data has no unit root and is stationary")
    else:
        print("Weak evidence against the null hypothesis")
        print("Fail to reject the null hypothesis")
        print("Data has a unit root and is non-stationary")

adf_test(df['n_transactions'])

Augmented Dickey-Fuller Test: 
ADF test statistic       -3.857922
p-value                   0.002367
# lags used              12.000000
# observations          737.000000
critical value (1%)      -3.439254
critical value (5%)      -2.865470
critical value (10%)     -2.568863
Strong evidence against the null hypothesis
Reject the null hypothesis
Data has no unit root and is stationary

我使用auto_arima来获取模型的最佳参数：

from pmdarima import auto_arima      
auto_arima(df['comissions'],seasonal=True, m = 7).summary()

我用这个参数训练模型：

train = df.loc[:'2020-04-26']
test = df.loc['2020-05-03':]

model = SARIMAX(train['n_transactions'],order=(1, 1, 1))
results = model.fit()
results.plot_diagnostics(figsize=(16, 8))
plt.show()

我计算预测：

start=len(train)
end=len(train)+len(test)-1
predictions = results.predict(start=start, end=end, dynamic=False, typ='levels').rename('SARIMA(0,1,3)(1,0,1,12) Predictions')


ax = test['n_transactions'].plot(legend=True,figsize=(12,6),title=title)
predictions.plot(legend=True)
ax.autoscale(axis='x',tight=True)
ax.set(xlabel=xlabel, ylabel=ylabel);

然后，我想看看我的模型如何预测下周。每周我都会再次训练模型，因为对我而言，只有下个月才更重要。

all_df = pd.DataFrame()
test = df.iloc[-20:]
i = -20
for index, row in test.iterrows():

    train = df.iloc[:i:]
    model = SARIMAX(train['comission'],order=(1, 1, 1))
    results = model.fit()
    start = len(train)
    end = len(train) +1
    predictions = results.predict(start=start, end=end, dynamic=False, typ='levels')
    test_df = pd.DataFrame(columns = {'predictions'})
    test_df['predictions'] = predictions
    all_df = pd.concat([all_df, test_df], axis=0, sort=False)
    i += 1

ax = test['comission'].plot(legend=True,figsize=(12,6),title=title)
all_df['predictions'].plot(legend=True)
ax.autoscale(axis='x',tight=True)
ax.set(xlabel=xlabel, ylabel=ylabel);

我的ARIMA模型无法更精确的可能原因是什么？

我必须如何分析result.plot_diagnostics？