ARIMA预测通过新的python statsmodels提供不同的结果 [英] ARIMA forecast gives different results with new python statsmodels

问题描述

我正在使用ARIMA(0,1,0)进行预测(样本外).

I'm (out-of-sample) forecasting with ARIMA(0,1,0).

在python的statsmodels中，最新的稳定版本是0.12.我计算:

In python's statsmodels latest stable version 0.12. I calculate:

import statsmodels.tsa.arima_model as stats

time_series = [2, 3.0, 5, 7, 9, 11, 13, 17, 19]
steps = 4
alpha = 0.05

model = stats.ARIMA(time_series, order=(0, 1, 0))
model_fit = model.fit(disp=0)

forecast, _, intervals = model_fit.forecast(steps=steps, exog=None, alpha=alpha)

结果

forecast = [21.125, 23.25, 25.375, 27.5]
intervals = [[19.5950036, 22.6549964 ], [21.08625835, 25.41374165], [22.72496851, 28.02503149], [24.44000721, 30.55999279]]

和未来警告，提示:

FutureWarning: 
statsmodels.tsa.arima_model.ARMA and statsmodels.tsa.arima_model.ARIMA have
been deprecated in favor of statsmodels.tsa.arima.model.ARIMA (note the .
between arima and model) and
statsmodels.tsa.SARIMAX. These will be removed after the 0.12 release.

在新版本中，如未来警告中所述，我计算:

In the new version, as hinted to in the Future Warning, I calculate:

import statsmodels.tsa.arima.model as stats

time_series = [2, 3.0, 5, 7, 9, 11, 13, 17, 19]
steps = 4
alpha = 0.05

model = stats.ARIMA(time_series, order=(0, 1, 0))
model_fit = model.fit()

forecast = model_fit.get_forecast(steps=steps)
forecasts_and_intervals = forecast.summary_frame(alpha=alpha)

给出不同的结果:

forecasts_and_intervals =
y  mean   mean_se  mean_ci_lower  mean_ci_upper
0  19.0  2.263842      14.562951      23.437049
1  19.0  3.201556      12.725066      25.274934
2  19.0  3.921089      11.314806      26.685194
3  19.0  4.527684      10.125903      27.874097

我希望获得与以前相同的结果.我是否正确使用新界面?

I would like to obtain the same results as before. Am I using the new interface correctly?

我既需要预测，又需要间隔.我已经尝试过使用新界面提供的 forecast 等不同功能.

I need both the forecast and the intervals. I tried already to use different functions as just forecast the new interface offers.

我特别想知道为什么整个列表的预测结果都是19.

In particular I'm wondering why the forecast result is 19 for the entire list.

非常感谢您的帮助.

这是statsmodels 0.12.2的文档:

Here is the documentation for statsmodels 0.12.2: https://www.statsmodels.org/stable/generated/statsmodels.tsa.arima_model.ARIMA.html?highlight=arima#statsmodels.tsa.arima_model.ARIMA

以下是Arima较新版本的文档:

Here is the documentation for newer version of Arima: https://www.statsmodels.org/stable/generated/statsmodels.tsa.arima.model.ARIMA.html?highlight=arima#statsmodels.tsa.arima.model.ARIMA

推荐答案

差异是由于模型是否包含常量"变量而导致的.期限与否.对于第一种情况，即较旧的 statsmodels.tsa.arima_model.ARIMA ，它会自动包含一个常数项(并且没有打开/关闭的选项).如果您有差异，它也会包含差异，但在差异域中会包含差异(否则将被消除).这是它的ARIMA(0，1，0)模型:

The difference is due to whether the models include a "constant" term or not. For the first case i.e. older statsmodels.tsa.arima_model.ARIMA, it automatically includes a constant term (and no option to turn on/off). If you have a differencing, it also includes it but does so in the differenced domain (otherwise it would be eliminated anyway). So here is its ARIMA(0, 1, 0) model:

y_t - y_{t-1} = c + e_t

这是随波逐流的随机漫步".

which is "random walk with drift".

对于新的 statsmodels.tsa.arima.model.ARIMA ，正如您所链接的文档所述，不是任何趋势项(包括常数，即 c )当涉及到差异时，将包括在内，这就是您的情况.这是它的ARIMA(0，1，0)模型:

For the new statsmodels.tsa.arima.model.ARIMA, as the documentation you linked says, not any kind of trend term (including constant, i.e. c) is included when differencing is involved, which is the case for you. So here is its ARIMA(0, 1, 0) model:

y_t - y_{t-1} = e_t

是随机游走"而且我们知道，从中得出的预测就相当于天真的预测，即重复最后一个值(在您的情况下为19).

which is "random walk" and as we know, forecasts from it corresponds to naive forecasts i.e. repeating the last value (19 in your case).

然后，该怎么做才能使新的工作正常?

Then, what to do to make the new one work?

它包含一个名为 trend 的参数，您可以指定该参数以获取相同的行为.由于您使用的是差分(d = 1)，因此传递 trend ="t" 的模型应与旧模型相同.("t" 表示线性趋势，但是由于 d = 1 ，它将在差分域中减小为常数):

It includes a parameter called trend which you can specify to get the same behaviour. Since you are using a differencing (d=1), passing trend="t" should give the same model as the old one. ("t" means linear trend but since d = 1, it will reduce to a constant in the differenced domain):

import statsmodels.tsa.arima.model as stats

time_series = [2, 3.0, 5, 7, 9, 11, 13, 17, 19]
steps = 4
alpha = 0.05

model = stats.ARIMA(time_series, order=(0, 1, 0), trend="t")   # only change is here!
model_fit = model.fit()

forecast = model_fit.get_forecast(steps=steps)
forecasts_and_intervals = forecast.summary_frame(alpha=alpha)

这是我得到的 forecasts_and_intervals :

y       mean   mean_se  mean_ci_lower  mean_ci_upper
0  21.124995  0.780622      19.595004      22.654986
1  23.249990  1.103966      21.086256      25.413724
2  25.374985  1.352077      22.724962      28.025008
3  27.499980  1.561244      24.439997      30.559963

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