A brief background

Humans have always had to contend with uncertainty in the world: in our earliest days, survival depended on rough predictions based on our experience to plan ahead, be it stocking wood for the winter, or storing enough food for dry seasons. Just a small attempt at predicting the weather for the next few weeks can tell you this is not a trivial task.

Before we can attempt to forecast a probable future we must first capture measurements of the past, which is essentially what a time-series is: logged data over time. The earliest attempts at recording data over time come from the Domesday Book (1086 AD), and the Chinese imperial archives, which were used to capture information on assets and crop yields, in order to tax members of a population.

Since these early examples, there has been an explosion of time-series usages, particularly in the last few years as data logging and storage has become cheaper, easier, and more accurate (sometimes). Time series are everywhere in...

The early period

Time series analysis is a statistical method that has been used for centuries to identify patterns in data that change over time. The earliest known use of time series analysis dates back to the 17th century when Sir Isaac Newton used it to predict the movement of planets. However, time series analysis did not start developing as a field for another two centuries. In the early 19th century, Carl Friedrich Gauss developed the concept of least squares regression, which is a statistical technique used to model relationships between variables. This technique was later applied to time series data, leading to the development of early time series models. In the mid-1800s, mathematicians such as Adolphe Quetelet and Francis Galton developed statistical techniques to analyze time series data.

George Airy, the seventh Astronomer Royal, used a statistical approach known as the harmonic method to predict tidal patterns - a rather important topic for a naval power like Britain. The...

The classical era

Important as the lineage discussed in the previous section was, the classical era of time series started with George Yule who introduced the world to autoregression. The Yule-Walker equation demonstrated that autoregression could forecast sunspots, ushering in a new era of time-series forecasting. The next major step was the Box-Jenkins method (named, unsurprisingly, after its authors): it provided a framework for modeling and forecasting time series data based on a combination of autoregressive and moving average components. The Box-Jenkins method became widely used in industry and academia and remains an important tool in time series modeling today; below we list major variants of the approach that are very much used to this day:

• ARIMA Models:
  • Autoregressive integrated moving average (ARIMA): Method that combines autoregression, differencing, and moving averages to model the underlying structure and trends of a time series.
  • Seasonal ARIMA (SARIMA): Extends ARIMA...

The promise of deep learning

In recent years, deep learning techniques have revolutionized the field of time series analysis. The original idea came from the field of natural language processing (NLP), where neural networks like RNN (and later LSTM) have gone supernova from 2015 onward: the ability to model long sequences proved to be a game-changer. Let’s take a closer look at this evolution.

Summary

This concludes our crash-intro-to-time-series-history chapter - quite possibly the one part of this book with no formulas, graphs or tables.

Let's briefly recap our journey; we began by exploring the early origins of time series analysis, from ancient attempts at predicting crop yields to the first recorded instances of data logging in the Domesday Book and Chinese imperial archives. We then moved to the classical era, examining the development of fundamental techniques that still form the backbone of many forecasting today.

We’ve traced the evolution from simple descriptive statistics to more sophisticated modeling techniques like ARIMA and its variants. We discussed the emergence of state space models and the Kalman filter, showcasing the field's adaptability to difficult to model data. We moved on to talk about the development of GARCH models to address volatility clustering in financial time series. Finally, we introduced machine learning and deep learning...