When it comes to time series forecasting, I’m a great believer that the simpler the model, the better.

关于时间序列预测，我坚信模型越简单越好。

However, not all time series are created equal. Some time series have a strongly defined trend — we often see this with economic data, for instance:

但是，并非所有时间序列都是相同的。 某些时间序列具有明确定义的趋势-例如，我们经常在经济数据中看到这一趋势：

Others show a more stationary-like pattern — e.g. monthly air passenger numbers:

其他人则表现出更平稳的模式，例如每月的航空旅客人数：

The choice of time series model will depend highly on the type of time series one is working with. Here are some of the most useful time series models I’ve encountered.

时间序列模型的选择将在很大程度上取决于正在使用的时间序列的类型。 这是我遇到的一些最有用的时间序列模型。

1. ARIMA (1. ARIMA)

In my experience, ARIMA tends to be most useful when modelling time series with a strong trend. The model is also adept at modelling seasonality patterns.

以我的经验，当对具有强烈趋势的时间序列进行建模时，ARIMA往往最有用。 该模型还擅长对季节性模式进行建模。

Let’s take an example.

让我们举个例子。

Suppose we wish to model monthly air passenger numbers over a period of years. The original data is sourced from San Francisco Open Data.

假设我们希望对几年内的每月航空旅客数量进行建模。 原始数据来自San Francisco Open Data 。

Such a time series will have a seasonal component (holiday seasons tend to have higher passenger numbers, for instance) as well as evidence of a trend as indicated when the series is decomposed as below.

这样的时间序列将具有季节性成分(例如，假日季节往往会有更高的乘客人数)，以及当序列分解如下时所指示的趋势的证据。

The purpose of using an ARIMA model is to capture the trend as well as account for the seasonality inherent in the time series.

使用ARIMA模型的目的是捕获趋势并考虑时间序列固有的季节性。

To do this, one can use the auto.arima function in R, which can select the best fit p, d, q coordinates for the model as well as the appropriate seasonal component.

为此，可以使用R中的auto.arima函数，该函数可以为模型选择最佳拟合的p，d，q坐标以及适当的季节分量。

For the above example, the model that performed best in terms of the lowest BIC was as follows:

对于上面的示例，就最低BIC而言表现最佳的模型如下：

Series: passengernumbers 
ARIMA(1,0,0)(0,1,1)[12]Coefficients:
         ar1     sma1
      0.7794  -0.5001
s.e.  0.0609   0.0840sigma^2 estimated as 585834:  log likelihood=-831.27
AIC=1668.54   AICc=1668.78   BIC=1676.44

Here is a visual of the forecasts.

这是预测的视觉效果。

We can see that ARIMA is adequately forecasting the seasonal pattern in the series. In terms of the model performance, the RMSE (root mean squared error) and MFE (mean forecast error) were as follows:

我们可以看到ARIMA可以充分预测该系列的季节性模式。 在模型性能方面，RMSE(均方根误差)和MFE(平均预测误差)如下：

• RMSE: 698

  RMSE： 698

• MFE: -115

  MFE： -115

Given a mean of 8,799 passengers per month across the validation set, the errors recorded were quite small in comparison to the average — indicating that the model is performing well in forecasting air passenger numbers.

假设整个验证集中平均每月有8799名乘客，则记录的误差与平均值相比很小，这表明该模型在预测航空乘客人数方面表现良好。

2.先知 (2. Prophet)

Let’s take a look at the air passenger example once again, but this time using Facebook’s Prophet. Prophet is a time series tool that allows for forecasting bsaed on an additive model, and works especially well with data that has strong seasonal trends.

让我们再来看一次航空乘客示例，但这一次使用Facebook的Prophet 。 Prophet是一个时间序列工具，可用于根据加性模型进行预测，尤其适用于季节性趋势强烈的数据。

The air passenger dataset appears to fit the bill, so let’s see how the model would perform compared to ARIMA.

航空乘客数据集似乎符合要求，因此让我们看看与ARIMA相比该模型的性能如何。

In this example, Prophet can be used to identify the long-term trend for air passenger numbers, as well as seasonal fluctuations throughout the year:

在此示例中，可以使用先知来确定航空客运量的长期趋势以及全年的季节性波动：

prophet_basic = Prophet()
prophet_basic.fit(train_dataset)

A standard Prophet model can be fit to pick up the trend and seasonal components automatically, although these can also be configured manually by the user.

尽管可以由用户手动配置，但标准的Prophet模型可以适合自动获取趋势和季节成分。

One particularly useful component of Prophet is the inclusion of changepoints, or significant structural breaks in a time series.

先知的一个特别有用的组成部分是包含变更点 ，即时间序列中的重大结构中断。

Through trial and error, 4 changepoints were shown to minimise the MFE and RMSE:

通过反复试验，显示了4个更改点以最大程度地减少MFE和RMSE：

pro_change= Prophet(n_changepoints=4)
forecast = pro_change.fit(train_dataset).predict(future)
fig= pro_change.plot(forecast);
a = add_changepoints_to_plot(fig.gca(), pro_change, forecast)

The RMSE and MAE can now be calculated as follows:

现在可以按以下方式计算RMSE和MAE：

>>> from sklearn.metrics import mean_squared_error
>>> from math import sqrt
>>> mse = mean_squared_error(passenger_test, yhat14)
>>> rmse = sqrt(mse)
>>> print('RMSE: %f' % rmse)RMSE: 524.263928>>> forecast_error = (passenger_test-yhat14)
>>> forecast_error
>>> mean_forecast_error = np.mean(forecast_error)
>>> mean_forecast_error71.58326743881493

The RMSE and MFE for Prophet are both lower than that obtained using ARIMA, suggesting that the model has performed better in forecasting monthly air passenger numbers.

先知的RMSE和MFE均低于使用ARIMA获得的值，这表明该模型在预测每月航空乘客人数方面表现更好。

3. TensorFlow概率 (3. TensorFlow Probability)

In the aftermath of COVID-19, many time series forecasts have proven to be erroneous as they have been made with the wrong set of assumptions.

在COVID-19之后，许多时间序列的预测被证明是错误的，因为它们是用错误的假设集做出的。

Increasingly, it is coming to be recognised that time series models which can produce a range of forecasts can be more practically applied, as they allow for a “scenario analysis” of what might happen in the future.

人们越来越认识到，可以产生一系列预测的时间序列模型可以更实际地应用，因为它们可以对未来可能发生的情况进行“情景分析”。

As an example, an ARIMA model built using the air passenger data as above could not have possibly forecasted the sharp drop in passenger numbers that came about as a result of COVID-19.

例如，使用上述航空旅客数据构建的ARIMA模型可能无法预测由于COVID-19而导致的旅客人数急剧下降。

However, using more recent air passenger data, let’s see how a model built using TensorFlow Probability would have performed:

但是，使用最近的航空乘客数据，让我们看看使用TensorFlow Probability构建的模型将如何执行：

While the model would not have forecasted the sharp drop that ultimately came to pass, we do see that the model is forecasting a drop in passenger numbers to below 150,000. Use of this model can allow for more of a “what-if” series of forecasts — e.g. an airline could forecast monthly passenger numbers for a particular airport and note that passenger numbers could be significantly lower than usual — which could inform the company in terms of managing resources such as fleet utilisation, for instance.

尽管该模型无法预测最终会发生的急剧下降，但我们确实看到该模型预测的乘客人数将下降到150,000以下。 使用此模型可以进行更多的“假设分析”系列预测-例如，航空公司可以预测特定机场的每月乘客人数，并请注意，乘客人数可能大大低于平时-这可以向公司传达例如，管理资源，例如车队利用。

Specifically, TensorFlow Probability makes forecasts using the assumption of a posterior distribution — which is comprised of a prior distribution (prior data) and the likelihood function.

具体来说，TensorFlow概率使用后验分布的假设进行预测，该后验分布由先验分布(先验数据)和似然函数组成。

For reference, the example illustrated here uses the template from the Structural Time Series modeling in TensorFlow Probability tutorial, of which the original authors (Copyright 2019 The TensorFlow Authors) have made available under the Apache 2.0 license.

作为参考，此处显示的示例使用TensorFlow概率教程中的结构时间序列建模中的模板，该原始模板的作者(Copyright 2019 The TensorFlow Authors)已获得Apache 2.0许可。

结论 (Conclusion)

Time series analysis is about making reliable forecasts using models suited to the data in question. For data with defined trend and seasonal components, it has been my experience that these models work quite well.

时间序列分析是关于使用适用于相关数据的模型进行可靠的预测。 对于具有定义的趋势和季节性成分的数据，根据我的经验，这些模型非常有效。

Hope you found the above article of use, and feel free to leave any questions or feedback in the comments section.

希望您找到了上面的使用文章，并随时在评论部分中留下任何问题或反馈。

Disclaimer: This article is written on an “as is” basis and without warranty. It was written with the intention of providing an overview of data science concepts, and should not be interpreted as professional advice in any way.

免责声明：本文按“原样”撰写，不作任何担保。 它旨在提供数据科学概念的概述，并且不应以任何方式解释为专业建议。