All multivariate time series are not born equal
By: Michaël Hoarau
Tags: Getting Started, Time Series Analysis, Editors Pick, Machine Learning, Artificial Intelligence

If you’re looking for good strategies to explore, analyze and model univariate time series, you will probably find hundreds of them (including some great pieces on Medium): checking stationarity, building autoregressive models, uncovering seasonality, detecting and cleaning outliers, etc. Check out this series of articles from Mehul Gupta, starting with some basic terminologies:

Now… Let’s say you want to learn more about multivariate timeseries? In this case, if you’re like me, most of the articles and books you can find might not be of great help either from a theoretical or a practical standpoint… Even worse, if you’re interested into dealing with industrial time series, most of the examples you find are about weather data, financial trading stocks, e-commerce or retail data… Most of them are data small enough that you can actually have a sneak peak in Excel…

You may have hundreds if not thousand of sensors data coming from industrial pieces of equipment at a high frequency (imagine 5 years of data coming from 5,000 sensors at a 10ms frequency)… This is where a sound framework for multivariate time series is desperately needed: in this article, we are going to look into what makes multivariate industrial data so different from most univariate time series we can find in usual data science challenges. In the conclusion, we will set the stage for future articles that will specifically deal with industrial time series.

N.B.: in this article, you will see me use indifferently time series, signal or tag: these are quite common terminology when dealing with such type data.

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I intend to continue exploring industrial time series in future articles and even build Python packages and example Jupyter notebooks. If anyone has some industrial time series data they are ready to make publicly available so that we can blog about them (and even build benchmarks), leave me note! Happy to work together on ways to anonymize them and find a suitable way to host them!

Univariate? Multivariate?

Let’s dive in the different flavors of time series signals one can find:

Univariate time series data: a single series of a time-dependent variable (e.g. the energy output in kWh of a power plant).

time series data: a single series of a time-dependent variable (e.g. the energy output in kWh of a power plant). Multiple time series: multiple univariate time series about different phenomena, entities or events (e.g. the electricity consumption of all the arc furnaces a steel producer operates in Europe)

time series: multiple univariate time series about different phenomena, entities or events (e.g. the electricity consumption of all the arc furnaces a steel producer operates in Europe) Continuous multivariate time series: multiple time series applied to the same phenomenon, entity or event which is operating or happening continuously (e.g. the measurements taken by all the temperature, pressure and vibration sensors installed on a compressor)

time series: multiple time series applied to the same phenomenon, entity or event which is operating or happening continuously (e.g. the measurements taken by all the temperature, pressure and vibration sensors installed on a compressor) Discrete multivariate time series: multiple time series applied to a sequence of successive events (e.g. the measurements taken by all the sensors on a shampoo production lines that produces several batches of different products every days)

Univariate time series

A univariate time series is a series of a single time-dependent variable. For instance, this is what the maximum temperature around London looked like in early November 2011: