Machine Learning for Time Series Forecasting with Python. Francesca Lazzeri

learning problem

      We can summarize some observations from Figure 1.8 in the following way:

       The value of Sensor_1 at prior time step (for example, 01/01/2020) becomes the input (Value x) in a supervised learning problem.

       The value of Sensor_1 at subsequent time step (for example, 01/02/2020) becomes the output (Value y) in a supervised learning problem.

       It is important to note that the temporal order between the Sensor_1 values needs to be maintained during the training of machine learning algorithms.

       By performing this transformation on our time series data, the resulting supervised learning data set will show an empty value (NaN) in the first row of Value x. This means that no prior Value x can be leveraged to predict the first value in the time series data set. We suggest removing this row because we cannot use it for our time series forecasting solution.

       Finally, the subsequent next value to predict for the last value in the sequence is unknown: this is the value that needs to be predicted by our machine learning model.

      How can we turn any time series data set into a supervised learning problem? Data scientists usually exploit the values of prior time steps to predict the subsequent time step value by using a statistical method, called the sliding window method. Once the sliding window method is applied and a time series data set is converted, data scientists can use can leverage standard linear and nonlinear machine learning methods to model their time series data.

Previously and in Figure 1.8, I used examples of univariate time series: these are data sets where only a single variable is observed at each time, such as energy load at each hour. However, the sliding window method can be applied to a time series data set that includes more than one historical variable observed at each time step and when the goal is to predict more than one variable in the future: this type of time series data set is called multivariate time series (I will discuss this concept in more detail later in this book).

We can reframe this time series data set as a supervised learning problem with a window width of one. This means that we will use the prior time step values of Value 1 and Value 2. We will also have available the next time step value for Value 1. We will then predict the next time step value of Value 2. As illustrated in Figure 1.9, this will give us three input features and one output value to predict for each training pattern.

Figure 1.9: Multivariate time series as supervised learning problem

      In the example of Figure 1.9, we were predicting two different output variables (Value 1 and Value 2), but very often data scientists need to predict multiple time steps ahead for one output variable. This is called multi-step forecasting. In multi-step forecasting, data scientists need to specify the number of time steps ahead to be forecasted, also called forecast horizon in time series. Multi-step forecasting usually presents two different formats:

       One-step forecast: When data scientists need to predict the next time step (t + 1)

       Multi-step forecast: When data scientists need to predict two or more (n) future time steps (t + n)

      For example, demand forecasting models predict the quantity of an item that will be sold the following week and the following two weeks given the sales up until the current week. In the stock market, given the stock prices up until today one can predict the stock prices for the next 24 hours and 48 hours. Using a weather forecasting engine, one can predict the weather for the next day and for the entire week (Brownlee 2017).

The sliding window method can be applied also on a multi-step forecasting solution to transform it into a supervised learning problem. As illustrated in Figure 1.10, we can use the same univariate time series data set from Figure 1.8 as an example, and we can structure it as a two-step forecasting data set for supervised learning with a window width of one (Brownlee 2017).

Figure 1.10: Univariate time series as multi-step supervised learning

      As illustrated in Figure 1.10, data scientists cannot use the first row (time stamp 01/01/2020) and the second to last row (time stamp 01/04/2020) of this sample data set to train their supervised model; hence we suggest removing it. Moreover, this new version of this supervised data set only has one variable Value x that data scientists can exploit to predict the last row (time stamp 01/05/2020) of both Value y and Value y².

      In the next section you will learn about different Python libraries for time series data and how libraries such as pandas, statsmodels, and scikit-learn can help you with data handling, time series modeling, and machine learning, respectively.

      Originally developed for financial time series such as daily stock market prices, the robust and flexible data structures in different Python libraries can be applied to time series data in any domain, including marketing, health care, engineering, and many others. With these tools you can easily organize, transform, analyze, and visualize your data at any level of granularity—examining details during specific time periods of interest and zooming out to explore variations on different time scales, such as monthly or annual aggregations, recurring patterns, and long-term trends.

Python for Time Series Forecasting

In this section, we will look at different Python libraries for time series data and how libraries such as pandas, statsmodels, and scikit-learn can help you with data handling, time series modeling, and machine learning, respectively. The Python ecosystem is the dominant platform for applied machine learning.

      The primary rationale for adopting Python for time series forecasting is that it is a general-purpose programming language that you can use both for experimentation and in production. It is easy to learn and use, primarily because the language focuses on readability. Python is a dynamic language and very suited to interactive development and quick prototyping with the power to support the development of large applications.

      Python is also widely used for machine learning and data science because of the excellent library support, and it has a few libraries for time series, such as NumPy, pandas, SciPy, scikit-learn, statsmodels, Matplotlib, datetime, Keras, and many more. Below we will have a closer look at the time series libraries in Python that we will use in this book:

       SciPy: SciPy is a Python-based ecosystem of open-source software for mathematics, science, and engineering. Some of the core packages are NumPy (a base n-dimensional array package), SciPy library (a fundamental library for scientific computing), Matplotlib (a comprehensive library for 2-D plotting), IPython (an enhanced interactive console), SymPy (a library for symbolic mathematics), and pandas (a library for data structure and analysis). Two SciPy libraries that provide a foundation for most others are NumPy and Matplotlib:NumPy is the fundamental package for scientific